Signal processing apparatus

[0002] This is a divisional of U.S. patent application Ser. No. 08/859,837, filed May 16, 1997 entitled Signal Processing Apparatus, which is a continuation of U.S. patent application Ser. No. 08/320,154, (now U.S. Pat. No. 5,632,272), filed Oct. 7, 1994, entitled Signal Processing Apparatus, which is a continuation-in-part of U.S. patent application Ser. No. 08/132,812 (now U.S. Pat. No. 5,490,505) filed Oct. 6, 1993, entitled Signal Processing Apparatus, which is a continuation-in-part of U.S. application Ser. No. 07/666,060, filed Mar. 7, 1991, entitled Signal Processing Apparatus, now abandoned.

[0003] 1. Field of the Invention

[0004] The present invention relates to the field of signal processing. More specifically, the present invention relates to the processing of measured signals, containing a primary signal portion and a secondary signal portion, for the removal or derivation of either the primary or secondary signal portion when little is known about either of these components. More particularly, the present invention relates to modeling the measured signals in a novel way which facilitates minimizing the correlation between the primary signal portion and the secondary signal portion in order to produce a primary and/or secondary signal. The present invention is especially useful for physiological monitoring systems including blood oxygen saturation systems.

[0005] 2. Description of the Related Art

[0006] Signal processors are typically employed to remove or derive either the primary or secondary signal portion from a composite measured signal including a primary signal portion and a secondary signal portion. For example, a composite signal may contain noise and desirable portions. If the secondary signal portion occupies a different frequency spectrum than the primary signal portion, then conventional filtering techniques such as low pass, band pass, and high pass filtering are available to remove or derive either the primary or the secondary signal portion from the total signal. Fixed single or multiple notch filters could also be employed if the primary and/or secondary signal portion(s) exist at a fixed frequency(s).

[0007] It is often the case that an overlap in frequency spectrum between the primary and secondary signal portions exists. Complicating matters further, the statistical properties of one or both of the primary and secondary signal portions change with time. In such cases, conventional filtering techniques are ineffective in extracting either the primary or secondary signal. If, however, a description of either the primary or secondary signal portion can be derived, correlation canceling, such as adaptive noise canceling, can be employed to remove either the primary or secondary signal portion of the signal isolating the other portion. In other words, given sufficient information about one of the signal portions, that signal portion can be extracted.

[0008] Conventional correlation cancelers, such as adaptive noise cancelers, dynamically change their transfer function to adapt to and remove portions of a composite signal. However, correlation cancelers require either a secondary reference or a primary reference which correlates to either the secondary signal portion only or the primary signal portion only. For instance, for a measured signal containing noise and desirable signal, the noise can be removed with a correlation canceler if a noise reference is available. This is often the case. Although the amplitude of the reference signals are not necessarily the same as the amplitude of the corresponding primary or secondary signal portions, they have a frequency spectrum which is similar to that of the primary or secondary signal portions.

[0009] In many cases, nothing or very little is known about the secondary and/or primary signal portions. One area where measured signals comprising a primary signal portion and a secondary signal portion about which no information can easily be determined is physiological monitoring. Physiological monitoring generally involves measured signals derived from a physiological system, such as the human body. Measurements which are typically taken with physiological monitoring systems include electrocardiographs, blood pressure, blood gas saturation (such as oxygen saturation), capnographs, other blood constituent monitoring, heart rate, respiration rate, electro-encephalograph (EEG) and depth of anesthesia, for example. Other types of measurements include those which measure the pressure and quantity of a substance within the body such as cardiac output, venous oxygen saturation, arterial oxygen saturation, bilirubin, total hemoglobin, breathalyzer testing, drug testing, cholesterol testing, glucose testing, extra vasation, and carbon dioxide testing, protein testing, carbon monoxide testing, and other in-vivo measurements, for example. Complications arising in these measurements are often due to motion of the patient, both external and internal (muscle movement, vessel movement, and probe movement, for example), during the measurement process.

[0010] Many types of physiological measurements can be made by using the known properties of energy attenuation as a selected form of energy passes through a medium.

[0011] A blood gas monitor is one example of a physiological monitoring system which is based upon the measurement of energy attenuated by biological tissues or substances. Blood gas monitors transmit light into the test medium and measure the attenuation of the light as a function of time. The output signal of a blood gas monitor which is sensitive to the arterial blood flow contains a component which is a waveform representative of the patient's arterial pulse. This type of signal, which contains a component related to the patient's pulse, is called a plethysmographic wave, and is shown in FIG. 1 as curve s. Plethysmographic waveforms are used in blood gas saturation measurements. As the heart beats, the amount of blood in the arteries increases and decreases, causing increases and decreases in energy attenuation, illustrated by the cyclic wave s in FIG. 1.

[0012] Typically, a digit such as a finger, an ear lobe, or other portion of the body where blood flows close to the skin, is employed as the medium through which light energy is transmitted for blood gas attenuation measurements. The finger comprises skin, fat, bone, muscle, etc., shown schematically in FIG. 2, each of which attenuates energy incident on the finger in a generally predictable and constant manner. However, when fleshy portions of the finger are compressed erratically, for example by motion of the finger, energy attenuation becomes erratic.

[0013] An example of a more realistic measured waveform S is shown in FIG. 3, illustrating the effect of motion. The primary plethysmographic waveform portion of the signal s is the waveform representative of the pulse, corresponding to the sawtooth-like pattern wave in FIG. 1. The large, secondary motion-induced excursions in signal amplitude obscure the primary plethysmographic signal s. Even small variations in amplitude make it difficult to distinguish the primary signal component s in the presence of a secondary signal component n.

[0014] A pulse oximeter is a type of blood gas monitor which non-invasively measures the arterial saturation of oxygen in the blood. The pumping of the heart forces freshly oxygenated blood into the arteries causing greater energy attenuation. As well understood in the art, the arterial saturation of oxygenated blood may be determined from the depth of the valleys relative to the peaks of two plethysmographic waveforms measured at separate wavelengths. Patient movement introduces motion artifacts to the composite signal as illustrated in the plethysmographic waveform illustrated in FIG. 3. These motion artifacts distort the measured signal.

[0015] This invention provides improvements upon the methods and apparatus disclosed in U.S. patent application Ser. No. 08/132,812, filed Oct. 6, 1993, entitled Signal Processing Apparatus, which earlier application has been assigned to the assignee of the instant application. The present invention involves several different embodiments using the novel signal model in accordance with the present invention to isolate either a primary signal portion or a secondary signal portion of a composite measured signal. In one embodiment, a signal processor acquires a first measured signal and a second measured signal that is correlated to the first measured signal. The first signal comprises a first primary signal portion and a first secondary signal portion. The second signal comprises a second primary signal portion and a second secondary signal portion. The signals may be acquired by propagating energy through a medium and measuring an attenuated signal after transmission or reflection. Alternatively, the signals may be acquired by measuring energy generated by the medium.

[0016] In one embodiment, the first and second measured signals are processed to generate a secondary reference which does not contain the primary signal portions from either of the first or second measured signals. This secondary reference is correlated to the secondary signal portion of each of the first and second measured signals. The secondary reference is used to remove the secondary portion of each of the first and second measured signals via a correlation canceler, such as an adaptive noise canceler. The correlation canceler is a device which takes a first and second input and removes from the first input all signal components which are correlated to the second input. Any unit which performs or nearly performs this function is herein considered to be a correlation canceler.

[0017] An adaptive correlation canceler can be described by analogy to a dynamic multiple notch filter which dynamically changes its transfer function in response to a reference signal and the measured signals to remove frequencies from the measured signals that are also present in the reference signal. Thus, a typical adaptive correlation canceler receives the signal from which it is desired to remove a component and receives a reference signal of the undesired portion. The output of the correlation canceler is a good approximation to the desired signal with the undesired component removed.

[0018] Alternatively, the first and second measured signals may be processed to generate a primary reference which does not contain the secondary signal portions from either of the first or second measured signals. The primary reference may then be used to remove the primary portion of each of the first and second measured signals via a correlation canceler. The output of the correlation canceler is a good approximation to the secondary signal with the primary signal removed and may be used for subsequent processing in the same instrument or an auxiliary instrument. In this capacity, the approximation to the secondary signal may be used as a reference signal for input to a second correlation canceler together with either the first or second measured signals for computation of, respectively, either the first or second primary signal portions.

[0019] Physiological monitors can benefit from signal processors of the present invention. Often in physiological measurements a first signal comprising a first primary portion and a first secondary portion and a second signal comprising a second primary portion and a second secondary portion are acquired. The signals may be acquired by propagating energy through a patient's body (or a material which is derived from the body, such as breath, blood, or tissue, for example) or inside a vessel and measuring an attenuated signal after transmission or reflection. Alternatively, the signal may be acquired by measuring energy generated by a patient's body, such as in electrocardiography. The signals are processed via the signal processor of the present invention to acquire either a secondary reference or a primary reference which is input to a correlation canceler, such as an adaptive noise canceler.

[0020] One physiological monitoring apparatus which benefits from the present invention is a monitoring system which determines a signal which is representative of the arterial pulse, called a plethysmographic wave. This signal can be used in blood pressure calculations, blood constituent measurements, etc. A specific example of such a use is in pulse oximetry. Pulse oximetry involves determining the saturation of oxygen in the blood. In this configuration, the primary portion of the signal is the arterial blood contribution to attenuation of energy as it passes through a portion of the body where blood flows close to the skin. The pumping of the heart causes blood flow to increase and decrease in the arteries in a periodic fashion, causing periodic attenuation wherein the periodic waveform is the plethysmographic waveform representative of the arterial pulse. The secondary portion is noise. In accordance with the present invention, the measured signals are modeled such that this secondary portion of the signal is related to the venous blood contribution to attenuation of energy as it passes through the body. The secondary portion also includes artifacts due to patient movement which causes the venous blood to flow in an unpredictable manner, causing unpredictable attenuation and corrupting the otherwise periodic plethysmographic waveform. Respiration also causes the secondary or noise portion to vary, although typically at a lower frequency than the patients pulse rate. Accordingly, the measured signal which forms a plethysmographic waveform is modeled in accordance with the present invention such that the primary portion of the signal is representative of arterial blood contribution to attenuation and the secondary portion is due to several other parameters,

[0021] A physiological monitor particularly adapted to pulse oximetry oxygen saturation measurement comprises two light emitting diodes (LED's) which emit light at different wavelengths to produce first and second signals. A detector registers the attenuation of the two different energy signals after each passes through an absorptive media, for example a digit such as a finger, or an earlobe. The attenuated signals generally comprise both primary (arterial attenuator) and secondary (noise) signal portions. A static filtering system, such as a bandpass filter, removes a portion of the secondary signal which is outside of a known bandwidth of interest, leaving an erratic or random secondary signal portion, often caused by motion and often difficult to remove, along with the primary signal portion.

[0022] A processor in accordance with one embodiment of the present invention removes the primary signal portions from the measured signals yielding a secondary reference which is a combination of the remaining secondary signal portions. The secondary reference is correlated to both of the secondary signal portions. The secondary reference and at least one of the measured signals are input to a correlation canceler, such as an adaptive noise canceler, which removes the random or erratic portion of the secondary signal. This yields a good approximation to a primary plethysmographic signal as measured at one of the measured signal wavelengths. As is known in the art, quantitative measurements of the amount of oxygenated arterial blood in the body can be determined from the plethysmographic signal in a variety of ways.

[0023] The processor of the present invention may also remove the secondary signal portions from the measured signals yielding a primary reference which is a combination of the remaining primary signal portions. The primary reference is correlated to both of the primary signal portions. The primary reference and at least one of the measured signals are input to a correlation canceler which removes the primary portions of the measured signals. This yields a good approximation to the secondary signal at one of the measured signal wavelengths. This signal may be useful for removing secondary signals from an auxiliary instrument as well as determining venous blood oxygen saturation.

[0024] In accordance with the signal model of the present invention, the two measured signals each having primary and secondary signal portions can be related by coefficients. By relating the two equations with respect to coefficients defined in accordance with the present invention, the coefficients provide information about the arterial oxygen saturation and about the noise (the venous oxygen saturation and other parameters). In accordance with this aspect of the present invention, the coefficients can be determined by minimizing the correlation between the primary and secondary signal portions as defined in the model. Accordingly, the signal model of the present invention can be utilized in many ways in order to obtain information about the measured signals as will be further apparent in the detailed description of the preferred embodiments.

[0025] One aspect of the present invention is a method for use in a signal processor in a signal processor for processing at least two measured signals S₁and S₂each containing a primary signal portion s and a secondary signal portion n, the signals S₁and S₂being in accordance with the following relationship:

[0026] S₁=s₁+n₁

[0027] S₂=s₂+n₂

[0028] where s₁and s₂, and n₁and n₂are related by:

[0029] s₁=r_as₂and n₁=r_vn₂

[0030] and where r_aand r_vare coefficients.

[0031] The method comprises a number of steps. A value of coefficient r_ais determined which minimize correlation between s₁and n₁. Then, at least one of the first and second signals is processed using the determined value for r_ato significantly reduce n from at least one of the first or second measured signal to form a clean signal.

[0032] In one embodiment, the clean signal is displayed on a display. In another embodiment, wherein the first and second signals are physiological signals, the method further comprises the step of processing the clean signal to determine a physiological parameter from the first or second measured signals. In one embodiment, the parameter is arterial oxygen saturation. In another embodiment, the parameter is an ECG signal. In yet another embodiment, wherein the first portion of the measured signals is indicative of a heart plethysmograph, the method further comprises the step of calculating the pulse rate.

[0033] Another aspect of the present invention involves a physiological monitor. The monitor has a first input configured to receive a first measured signal S₁having a primary portion, s₁, and a secondary portion n₁. The monitor also has a second input configured to received a second measured signal S₂having a primary portion s₂and a secondary portion n₂. Advantageously, the first and the second measured signals S₁and S₂are in accordance with the following relationship:

[0034] S₁=s₁+n₁

[0035] S₂=s₂+n₂

[0036] where s₁and s₂, and n₁and n₂are related by:

[0037] s₁=r_as₂and n₁=r_vn₂

[0038] and where r_aand r_vare coefficients.

[0039] The monitor further has a scan reference processor, the scan reference processor responds to a plurality of possible values for r_ato multiply the second measured signal by each of the possible values for r_aand for each of the resulting values, to subtract the resulting values from the first measured signal to provide a plurality of output signals. A correlation canceler having a first input configured to receive the first measured signal, and having a second input configured to receive the plurality of output signals from the saturation scan reference processor, provides a plurality of output vectors corresponding to the correlation cancellation between the plurality of output signals and the first measured signal. An integrator having an input configured to receive the plurality of output vectors from the correlation canceler is responsive to the plurality of output vectors to determine a corresponding power for each output vector. An extremum detector is coupled at its input to the output of the integrator. The extremum detector is responsive to the corresponding power for each output vector to detect a selected power.

[0040] In one embodiment, the plurality of possible values correspond to a plurality of possible values for a selected blood constituent. In one embodiment the, the selected blood constituent is arterial blood oxygen saturation. In another embodiment, the selected blood constituent is venous blood oxygen saturation. In yet another embodiment, the selected blood constituent is carbon monoxide.

[0041] Another aspect of the present invention involves a physiological monitor. The monitor has a first input configured to receive a first measured signal S₁having a primary portion, s₁, and a secondary portion, n₁. The monitor also has a second input configured to received a second measured signal S₂having a primary portion s₂and a secondary portion n₂. The first and the second measured signals S₁and S₂are in accordance with the following relationship:

[0042] S₁=s₁+n₁

[0043] S₂=s₂+n₂

[0044] where s₁and s₂, and n₁and n₂are related by:

[0045] s₁=r_as₂and n₁=r_vn₂

[0046] and where r_aand r_vare coefficients.

[0047] A transform module is responsive to the first and the second measured signals and responsive to a plurality of possible values for r_ato provide at least one power curve as an output. An extremum calculation module is responsive to the at least one power curve to select a value for r_awhich minimizes the correlation between s and n, and to calculate from the value for r_aa corresponding saturation value as an output. A display module is responsive to the output of saturation calculation to display the saturation value.

[0048] FIG. 1 illustrates an ideal plethysmographic waveform.

[0049] FIG. 2 schematically illustrates a typical finger.

[0050] FIG. 3 illustrates a plethysmographic waveform which includes a motion-induced erratic signal portion.

[0051] FIG. 4aillustrates a schematic diagram of a physiological monitor to compute primary physiological signals.

[0052] FIG. 4billustrates a schematic diagram of a physiological monitor to compute secondary signals.

[0053] FIG. 5aillustrates an example of an adaptive noise canceler which could be employed in a physiological monitor, to compute primary physiological signals.

[0054] FIG. 5billustrates an example of an adaptive noise canceler which could be employed in a physiological monitor, to compute secondary motion artifact signals.

[0055] FIG. 5cillustrates the transfer function of a multiple notch filter.

[0056] FIG. 6aillustrates a schematic of absorbing material comprising N constituents within the absorbing material.

[0057] FIG. 6billustrates another schematic of absorbing material comprising N constituents, including one mixed layer, within the absorbing material.

[0058] FIG. 6cillustrates another schematic of absorbing material comprising N constituents, including two mixed layers, within the absorbing material.

[0059] FIG. 7aillustrates a schematic diagram of a monitor, to compute primary and secondary signals in accordance with one aspect of the present invention.

[0060] FIG. 7billustrates the ideal correlation canceler energy or power output as a function of the signal coefficients r₁, r₂, . . . r_n. In this particular example, r₃=r_aand r₇=r_v.

[0061] FIG. 7cillustrates the non-ideal correlation canceler energy or power output as a function of the signal coefficients r₁, r₂, . . . r_n. In this particular example, r₃=r_aand r₇=r_a.

[0062] FIG. 8 is a schematic model of a joint process estimator comprising a least-squares lattice predictor and a regression filter.

[0063] FIG. 8ais a schematic model of a joint process estimator comprising a QRD least-squares lattice (LSL) predictor and a regression filter.

[0064] FIG. 9 is a flowchart representing a subroutine for implementing in software a joint process estimator as modeled in FIG. 8.

[0065] FIG. 9ais a flowchart representing a subroutine for implementing in software a joint process estimator as modeled in FIG. 8a.

[0066] FIG. 10 is a schematic model of a joint process estimator with a least-squares lattice predictor and two regression filters.

[0067] FIG. 10ais a schematic model of a joint process estimator with a QRD least-squares lattice predictor and two regression filters.

[0068] FIG. 11 is an example of a physiological monitor in accordance with the teachings of one aspect of the present invention.

[0069] FIG. 11aillustrates an example of a low noise emitter current driver with accompanying digital to analog converter.

[0070] FIG. 12 illustrates the front end analog signal conditioning circuitry and the analog to digital conversion circuitry of the physiological monitor of FIG. 11.

[0071] FIG. 13 illustrates further detail of the digital signal processing circuitry of FIG. 11.

[0072] FIG. 14 illustrates additional detail of the operations performed by the digital signal processing circuitry of FIG. 11.

[0073] FIG. 15 illustrates additional detail regarding the demodulation module of FIG. 14.

[0074] FIG. 16 illustrates additional detail regarding the decimation module of FIG. 14.

[0075] FIG. 17 represents a more detailed block diagram of the operations of the statistics module of FIG. 14.

[0076] FIG. 18 illustrates a block diagram of the operations of one embodiment of the saturation transform module of FIG. 14.

[0077] FIG. 19 illustrates a block diagram of the operation of the saturation calculation module of FIG. 14.

[0078] FIG. 20 illustrates a block diagram of the operations of the pulse rate calculation module of FIG. 14.

[0079] FIG. 21 illustrates a block diagram of the operations of the motion artifact suppression module of FIG. 20.

[0080] FIG. 21aillustrates an alternative block diagram for the operations of the motion artifact suppression module of FIG. 20.

[0081] FIG. 22 illustrates a saturation transform curve in accordance with the principles of the present invention.

[0082] FIG. 23 illustrates a block diagram of an alternative embodiment to the saturation transform in order to obtain a saturation value.

[0083] FIG. 24 illustrates a histogram saturation transform in accordance with the alternative embodiment of FIG. 23.

[0084] FIGS. 25A-25C illustrate yet another alternative embodiment in order to obtain the saturation.

[0085] FIG. 26 illustrates a signal measured at a red wavelength λa=λred=660 nm for use in a processor of the present invention for determining the secondary reference n′(t) or the primary reference s′(t) and for use in a correlation canceler. The measured signal comprises a primary portion s_λa(t) and a secondary portion n_λa(t).

[0086] FIG. 27 illustrates a signal measured at an infrared wavelength λb=λ_IR=910 nm for use in a processor of the present invention for determining the secondary reference n′(t) or the primary reference s′(t) and for use in a correlation canceler. The measured signal comprises a primary portion s_λb(t) and a secondary portion n_λb(t).

[0087] FIG. 28 illustrates the secondary reference n′(t) determined by a processor of the present invention.

[0088] FIG. 29 illustrates a good approximation s″_λa(t) to the primary portion s_λa(t) of the signal S_λa(t) measured at λa=λred=660 nm estimated by correlation cancellation with a secondary reference n′(t).

[0089] FIG. 30 illustrates a good approximation s″_λb(t) to the primary portion s_λb(t) of the signal S_λb(t) measured at λb=λIR=910 nm estimated by correlation cancellation with a secondary reference n′(t).

[0090] FIG. 31 depicts a set of 3 concentric electrodes, i.e., a tripolar electrode sensor, to derive electrocardiography (ECG) signals, denoted as S₁, S₂and S₃, for use with the present invention. Each of the ECG signals contains a primary portion and a secondary portion.

[0091] The present invention involves a system which utilizes first and second measured signals that each contain a primary signal portion and a secondary signal portion. In other words, given a first and second composite signals S₁(t)=s₁(t)+n₁(t) and S₂(t)=s₂(t)+n₂(t), the system of the present invention can be used to isolate either the primary signal portion s(t) or the secondary signal portion n(t). Following processing, the output of the system provides a good approximation n″(t) to the secondary signal portion n(t) or a good approximation s″(t) to the primary signal portion s(t).

[0092] The system of the present invention is particularly useful where the primary and/or secondary signal portion n(t) may contain one or more of a constant portion, a predictable portion, an erratic portion, a random portion, etc. The primary signal approximation s″(t) or secondary signal approximation n″(t) is derived by removing as many of the secondary signal portions n(t) or primary signal portions s(t) from the composite signal S(t) as possible. The remaining signal forms either the primary signal approximation s″(t) or secondary signal approximation n″(t), respectively. The constant portion and predictable portion of the secondary signal n(t) are easily removed with traditional filtering techniques, such as simple subtraction, low pass, band pass, and high pass filtering. The erratic portion is more difficult to remove due to its unpredictable nature. If something is known about the erratic signal, even statistically, it could be removed, at least partially, from the measured signal via traditional filtering techniques. However, often no information is known about the erratic portion of the secondary signal n(t). In this case, traditional filtering techniques are usually insufficient.

[0093] In order to remove the secondary signal n(t), a signal model in accordance with the present invention is defined as follows for the first and second measured signals S₁and S₂:

[0094] S₁=s₁+n₁

[0095] S₂=s₂+n₂

[0096] with

[0097] s₁=r_as₂and n₁=r_vn₂

[0098] $\mathrm{or}{r}_a=\frac{s_1}{s_2}\mathrm{and}{n}_1=\frac{n_1}{n_2}$

[0099] where s₁and n₁are at least somewhat (preferably substantially) uncorrelated and s₂and n₂are at least somewhat (preferably substantially) uncorrelated. The first and second measured signals S₁and S₂are related by correlation coefficients r_aand r_vas defined above. The use and selection of these coefficients is described in further detail below.

[0100] In accordance with one aspect of the present invention, this signal model is used in combination with a correlation canceler, such as an adaptive noise canceler, to remove or derive the erratic portion of the measured signals.

[0101] Generally, a correlation canceler has two signal inputs and one output. One of the inputs is either the secondary reference n′(t) or the primary reference s′(t) which are correlated, respectively, to the secondary signal portions n(t) and the primary signal portions s(t) present in the composite signal S(t). The other input is for the composite signal S(t). Ideally, the output of the correlation canceler s″(t) or n″(t) corresponds, respectively, to the primary signal s(t) or the secondary signal n(t) portions only. Often, the most difficult task in the application of correlation cancelers is determining the reference signals n′(t) and s′(t) which are correlated to the secondary n(t) and primary s(t) portions, respectively, of the measured signal S(t) since, as discussed above, these portions are quite difficult to isolate from the measured signal S(t). In the signal processor of the present invention, either a secondary reference n′(t) or a primary reference s′(t) is determined from two composite signals measured simultaneously, or nearly simultaneously, at two different wavelengths, λa and λb.

[0102] A block diagram of a generic monitor incorporating a signal processor according to the present invention, and a correlation canceler is shown in FIGS. 4aand 4b.Two measured signals, S_λa(t) and S_λb(t), are acquired by a detector 20. One skilled in the art will realize that for some physiological measurements, more than one detector may be advantageous. Each signal is conditioned by a signal conditioner 22aand 22b.Conditioning includes, but is not limited to, such procedures as filtering the signals to remove constant portions and amplifying the signals for ease of manipulation. The signals are then converted to digital data by an analog-to-digital converter 24aand 24b.The first measured signal S_λa(t) comprises a first primary signal portion, labeled herein s_λa(t), and a first secondary signal portion, labeled herein n_λa(t). The second measured signal S_λb(t) is at least partially correlated to the first measured signal S_λa(t) and comprises a second primary signal portion, labeled herein s_λb(t), and a second secondary signal portion, labeled herein n_λb(t). Typically the first and second secondary signal portions, n_λa(t) and n_λb(t), are uncorrelated and/or erratic with respect to the primary signal portions s_λa(t) and s_λb(t). The secondary signal portions n_λa(t) and n_λb(t) are often caused by motion of a patient in physiological measurements.

[0103] The signals S_λa(t) and S_λb(t) are input to a reference processor 26. The reference processor 26 multiplies the second measured signal S_λb(t) by either a factor r_a=s_λa(t)/s_λb(t) or a factor r_v=n_λa(t)/n_λb(t) and then subtracts the second measured signal S_λb(t) from the first measured signal S_λa(t). The signal coefficient factors r_aand r_vare determined to cause either the primary signal portions s_λa(t) and s_λb(t) or the secondary signal portions nxa(t) and n_λb(t) to cancel, respectively, when the two signals S_λa(t) and S_λb(t) are subtracted. Thus, the output of the reference processor 26 is either a secondary reference signal n′(t)=n_λa(t)−r_an_λb(t), in FIG. 4a,which is correlated to both of the secondary signal portions n_λa(t) and n_λb(t) or a primary reference signal s′(t)=s_λa(t)−r_vs_λb(t), in FIG. 4b,which is correlated to both of the primary signal portions s_λa(t) and s_λb(t). A reference signal n′(t) or s′(t) is input, along with one of the measured signals S_λa(t) or S_λb(t), to a correlation canceler 27 which uses the reference signal n′(t) or s′(t) to remove either the secondary signal portions n_λa(t) or n_λb(t) or the primary signal portions s_λa(t) or s_λb(t) from the measured signal S_λa(t) or S_λb(t). The output of the correlation canceler 27 is a good primary signal approximation s″(t) or secondary signal approximation n″(t). In one embodiment, the approximation s″(t) or n″(t) is displayed on a display 28.

[0104] In one embodiment, an adaptive noise canceler 30, an example of which is shown in block diagram form in FIG. 5a,is employed as the correlation canceler 27, to remove either one of the erratic, secondary signal portions n_λa(t) and n_λb(t) from the first and second signals S_λa(t) and S_λb(t). The adaptive noise canceler 30 in FIG. 5ahas as one input a sample of the secondary reference n′(t) which is correlated to the secondary signal portions n_λa(t) and n_λb(t). The secondary reference n′(t) is determined from the two measured signals S_λa(t) and S_λb(t) by the processor 26 of the present invention as described herein. A second input to the adaptive noise canceler, is a sample of either the first or second composite measured signals S_λa(t)=s_λa(t)+n_λa(t) or S_λb(t)=s_λb(t)+n_λb(t).

[0105] The adaptive noise canceler 30, in FIG. 5b,may also be employed to remove either one of primary signal portions s_λa(t) and s_λb(t) from the first and second measured signals S_λa(t) and S_λb(t). The adaptive noise canceler 30 has as one input a sample of the primary reference s′(t) which is correlated to the primary signal portions s_λa(t) and s_λb(t). The primary reference s′(t) is determined from the two measured signals S_λa(t) and S_λb(t) by the processor 26 of the present invention as described herein. A second input to the adaptive noise canceler 30 is a sample of either the first or second measured signals S_λa(t)=s_λa(t)+n_λa(t) or S_λb(t)=s_λb(t)+n_λb(t).

[0106] The adaptive noise canceler 30 functions to remove frequencies common to both the reference n′(t) or s′(t) and the measured signal S_λa(t) or S_λb(t). Since the reference signals are correlated to either the secondary signal portions n_λa(t) and n_λb(t) or the primary signal portions s_λa(t) and s_λb(t), the reference signals will be correspondingly erratic or well behaved. The adaptive noise canceler 30 acts in a manner which may be analogized to a dynamic multiple notch filter based on the spectral distribution of the reference signal n′(t) or s′(t).

[0107] FIG. 5cillustrates an exemplary transfer function of a multiple notch filter. The notches, or dips in the amplitude of the transfer function, indicate frequencies which are attenuated or removed when a signal passes through the notch filter. The output of the notch filter is the composite signal having frequencies at which a notch is present removed. In the analogy to an adaptive noise canceler 30, the frequencies at which notches are present change continuously based upon the inputs to the adaptive noise canceler 30.

[0108] The adaptive noise canceler 30 (FIGS. 5aand 5b) produces an output signal, labeled herein as s″_λa(t), s″_λb(t), n″_λa(t) or n″_λb(t) which is fed back to an internal processor 32 within the adaptive noise canceler 30. The internal processor 32 automatically adjusts its own transfer function according to a predetermined algorithm such that the output of the internal processor 32 labeled b_λ(t) in FIG. 5aand c_λ(t) in FIG. 5b,closely resembles either the secondary signal portion n_λa(t) or n_λb(t) or the primary signal portion s_λa(t) or s_λb(t). The output b_λ(t) of the internal processor 32 in FIG. 5ais subtracted from the measured signal, S_λa(t) or S_λb(t), yielding a signal output s″_λa(t)=S_λa(t)+n_λa(t)−b_λa(t) or a signal output s″_λb(t)=s_λb(t)+n_λb(t)−b_λb(t). The internal processor optimizes s″_λa(t) or s″_λb(t) such that s″_λa(t) or s″_λb(t) is approximately equal to the primary signal s_λa(t) or s_λb(t), respectively. The output c_λ(t) of the internal processor 32 in FIG. 5bis subtracted from the measured signal, S_λa(t) or S_λb(t), yielding a signal output given by n″_λa(t)=s_λa(t)+n_λa(t)−c_λa(t) or a signal output given by n″_λb(t)=s_λb(t)+n_λb(t)−c_λb(t). The internal processor optimizes n″_λa(t) or n″_λb(t) such that n″_λa(t) or n″_λb(t) is approximately equal to the secondary signal portion n_λa(t) or n_λb(t), respectively.

[0109] One algorithm which may be used for the adjustment of the transfer function of the internal processor 32 is a least-squares algorithm, as described in Chapter 6 and Chapter 12 of the book Adaptive Signal Processingby Bernard Widrow and Samuel Stearns, published by Prentice Hall, copyright 1985. This entire book, including Chapters 6 and 12, is hereby incorporated herein by reference.

[0110] Adaptive processors 30 in FIGS. 5aand 5bhave been successfully applied to a number of problems including antenna sidelobe canceling, pattern recognition, the elimination of periodic interference in general, and the elimination of echoes on long distance telephone transmission lines. However, considerable ingenuity is often required to find a suitable reference signal n′(t) or s′(t) since the portions n_λa(t), n_λb(t), s_λa(t) and s_λb(t) cannot easily be separated from the measured composite signals S_λa(t) and S_λb(t). If either the actual secondary portion n_λa(t) or n_λb(t) or the primary signal portion s_λa(t) or s_λb(t) were a priori available, techniques such as correlation cancellation would not be necessary.

[0111] An explanation which describes how the reference signals n′(t) and s′(t) may be determined follows. A first signal is measured at, for example, a wavelength λa, by a detector yielding a signal S_λa(t):

[0112] S_λa(t)=s_λa(t)+n_λa(t)  (1)

[0113] where s_λa(t) is the primary signal portion and n_λa(t) is the secondary signal portion.

[0114] A similar measurement is taken simultaneously, or nearly simultaneously, at a different wavelength, λb, yielding:

[0115] S_λb(t)=s_λb(t)+n_λb(t).  (2)

[0116] Note that as long as the measurements, S_λa(t) and S_λb(t), are taken substantially simultaneously, the secondary signal components, n_λa(t) and n_λb(t), are correlated because any random or erratic functions affect each measurement in nearly the same fashion. The substantially predictable primary signal components, s_λa(t) and s_λb(t), are also correlated to one another.

[0117] To obtain the reference signals n′(t) and s′(t), the measured signals S_λa(t) and S_λb(t) are transformed to eliminate, respectively, the primary or secondary signal components. In accordance with the present invention one way of doing this is to find proportionality constants, r_aand r_v, between the primary signal portions s_λa(t) and s_λb(t) and the secondary signal portions n_λa(t) and n_λb(t) such that the signals can be modeled as follows:

[0118] s_λa(t)=r_as_λb(t) n_λa(t)=r_vn_λb(t).  (3)

[0119] In accordance with the inventive signal model of the present invention, these proportionality relationships can be satisfied in many measurements, including but not limited to absorption measurements and physiological measurements. Additionally, in accordance with the signal model of the present invention, in most measurements, the proportionality constants r_aand r_vcan be determined such that:

[0120] n_λa(t)≠r_an_λb(t) s_λa(t)≠r_vs_λb(t).  (4)

[0121] Multiplying equation (2) by r_aand then subtracting equation (2) from equation (1) results in a single equation wherein the primary signal terms s_λa(t) and s_λb(t) cancel:

[0122] n′(t)=S_λa(t)−r_aS_λb(t)=n_λa(t)−r_an_λb(t);  (5a)

[0123] a non-zero signal which is correlated to each secondary signal portion n_λa(t) and n_λb(t) and can be used as the secondary reference n′(t) in a correlation canceler such as an adaptive noise canceler.

[0124] Multiplying equation (2) by r_vand then subtracting equation (2) from equation (1) results in a single equation wherein the secondary signal terms n_λa(t) and n_λb(t) cancel, leaving:

[0125] s′(t)=S_λa(t)−r_vS_λb(t)=s_λa(t)−r_vs_λb(t);  (5b)

[0126] a non-zero signal which is correlated to each of the primary signal portions s_λa(t) and s_λb(t) and can be used as the signal reference s′(t) in a correlation canceler such as an adaptive noise canceler.

[0127] Correlation canceling is particularly useful in a large number of measurements generally described as absorption measurements. An example of an absorption type monitor which can advantageously employ correlation canceling, such as adaptive noise canceling, based upon a reference n′(t) or s′(t) determined by a processor of the present invention is one which determines the concentration of an energy absorbing constituent within an absorbing material when the material is subject to change. Such changes can be caused by forces about which information is desired or primary, or alternatively, by random or erratic secondary forces such as a mechanical force on the material. Random or erratic interference, such as motion, generates secondary components in the measured signal. These secondary components can be removed or derived by the correlation canceler if a suitable secondary reference n′(t) or primary reference s′(t) is known.

[0128] A schematic N constituent absorbing material comprising a container 42 having N different absorbing constituents, labeled A₁, A₂, A₃, . . . A_N, is shown in FIG. 6a.The constituents A₁through A_Nin FIG. 6aare arranged in a generally orderly, layered fashion within the container 42. An example of a particular type of absorptive system is one in which light energy passes through the container 42 and is absorbed according to the generalized Beer-Lambert Law of light absorption. For light of wavelength λa, this attenuation may be approximated by: $\begin{array}{cc}I=I_o\exp \left(-\sum _{i=1}^N{\epsilon }_{i,\lambda a}{c}_i{x}_i\right)& \left(6\right)\end{array}$

[0129] Initially transforming the signal by taking the natural logarithm of both sides and manipulating terms, the signal is transformed such that the signal components are combined by addition rather than multiplication, i.e.: $\begin{array}{cc}{S}_{\lambda a}=\ln \left(I_0/I\right)=\sum _{i=1}^N{\epsilon }_{i,\lambda a}{c}_i{x}_i& \left(7\right)\end{array}$

[0130] where I₀is the incident light energy intensity; I is the transmitted light energy intensity; ε_i,λais the absorption coefficient of the i^thconstituent at the wavelength λa; x_i(t) is the optical path length of i^thlayer, i.e., the thickness of material of the i^thlayer through which optical energy passes; and c_i(t) is the concentration of the i^thconstituent in the volume associated with the thickness x_i(t). The absorption coefficients ε₁through ε_Nare known values which are constant at each wavelength. Most concentrations c₁(t) through c_N(t) are typically unknown, as are most of the optical path lengths x_i(t) of each layer. The total optical path length is the sum of each of the individual optical path lengths x_i(t) of each layer.

[0131] When the material is not subject to any forces which cause change in the thicknesses of the layers, the optical path length of each layer, x_i(t), is generally constant. This results in generally constant attenuation of the optical energy and thus, a generally constant offset in the measured signal. Typically, this offset portion of the signal is of little interest since knowledge about a force which perturbs the material is usually desired. Any signal portion outside of a known bandwidth of interest, including the constant undesired signal portion resulting from the generally constant absorption of the constituents when not subject to change, is removed. This is easily accomplished by traditional band pass filtering techniques. However, when the material is subject to forces, each layer of constituents may be affected by the perturbation differently than other layers. Some perturbations of the optical path lengths of each layer x_i(t) may result in excursions in the measured signal which represent desired or primary information. Other perturbations of the optical path length of each layer x_i(t) cause undesired or secondary excursions which mask primary information in the measured signal. Secondary signal components associated with secondary excursions must also be removed to obtain primary information from the measured signal. Similarly, the ability to compute secondary signal components caused by secondary excursions directly allows one to obtain primary signal components from the measured signal via simple subtraction, or correlation cancellation techniques.

[0132] The correlation canceler may selectively remove from the composite signal, measured after being transmitted through or reflected from the absorbing material, either the secondary or the primary signal components caused by forces which perturb or change the material differently from the forces which perturbed or changed the material to cause respectively, either the primary or secondary signal component. For the purposes of illustration, it will be assumed that the portion of the measured signal which is deemed to be the primary signal s_λa(t) is the attenuation term ε₅c₅x₅(t) associated with a constituent of interest, namely A₅, and that the layer of constituent A₅is affected by perturbations different than each of the layers of other constituents A₁through A₄and A₆through A_N. An example of such a situation is when layer A₅is subject to forces about which information is deemed to be primary and, additionally, the entire material is subject to forces which affect each of the layers. In this case, since the total force affecting the layer of constituent A₅is different than the total forces affecting each of the other layers and information is deemed to be primary about the forces and resultant perturbation of the layer of constituent A₅, attenuation terms due to constituents A₁through A₄and A₆through A_Nmake up the secondary signal portion n_λa(t). Even if the additional forces which affect the entire material cause the same perturbation in each layer, including the layer of A₅, the total forces on the layer of constituent A₅cause it to have different total perturbation than each of the other layers of constituents A₁through A₄and A₆through A_N.

[0133] It is often the case that the total perturbation affecting the layers associated with the secondary signal components is caused by random or erratic forces. This causes the thickness of layers to change erratically and the optical path length of each layer, x_i(t), to change erratically, thereby producing a random or erratic secondary signal component n_λa(t). However, regardless of whether or not the secondary signal portion n_λa(t) is erratic, the secondary signal component n_λa(t) can be either removed or derived via a correlation canceler, such as an adaptive noise canceler, having as one input, respectively, a secondary reference n′(t) or a primary reference s′(t) determined by a processor of the present invention as long as the perturbation on layers other than the layer of constituent A₅is different than the perturbation on the layer of constituent A₅. The correlation canceler yields a good approximation to either the primary signal s_λa(t) or the secondary signal n_λa(t). In the event that an approximation to the primary signal is obtained, the concentration of the constituent of interest, c₅(t), can often be determined since in some physiological measurements, the thickness of the primary signal component, x₅(t) in this example, is known or can be determined.

[0134] The correlation canceler utilizes either the secondary reference n′(t) or the primary reference s′(t) determined from two substantially simultaneously measured signals S_λa(t) and S_λb(t). S_λa(t) is determined as above in equation (7). S_λb(t) is determined similarly at a different wavelength λb. To find either the secondary reference n′(t) or the primary reference s′(t), attenuated transmitted energy is measured at the two different wavelengths λa and λb and transformed via logarithmic conversion. The signals S_λa(t) and S_λb(t) can then be written (logarithm converted) as: $\begin{array}{cc}{S}_{\lambda a}\left(t\right)={\epsilon }_{5,\lambda a}{c}_5{x}_5\left(t\right)+\sum _{i=1}^4{\epsilon }_{i,\lambda a}{c}_i{x}_i+\sum _{i=6}^N{\epsilon }_{i,\lambda a}{c}_i{x}_i& \left(8\right)\end{array}$  S_λa(t)=ε_5,λac₅x₅(t)+n_λa(t)  (9)

[0135] $\begin{array}{cc}{S}_{\lambda b}\left(t\right)={\epsilon }_{5,\lambda b}{c}_5{x}_5\left(t\right)+\sum _{i=1}^4{\epsilon }_{i,\lambda b}{c}_i{x}_i+\sum _{i=6}^N{\epsilon }_{i,\lambda b}{c}_i{x}_i& \left(10\right)\end{array}$  S_λb(t)=ε_5,λbc₅x₅(t)+n_λb(t)  (11)

[0136] Further transformations of the signals are the proportionality relationships in accordance with the signal model of the present invention defining r_aand r_v,similar to equation (3), which allows determination of a noise reference n′(t) and a primary reference s′(t). These are:

[0137] ε_5,λa=r_aε_5,λb  (12a)

[0138] n_λa=r_vn_λb  (12b)

[0139] where

[0140] n_λa≠r_an_λb  (13a)

[0141] ε_5,λa≠r_vε_5,λb.  (13b)

[0142] It is often the case that both equations (12) and (13) can be simultaneously satisfied. Multiplying equation (11) by r_aand subtracting the result from equation (9) yields a non-zero secondary reference which is a linear sum of secondary signal components: $\begin{array}{cc}\begin{array}{c}{n}^{\prime }\left(t\right)=S_{\lambda a}\left(t\right)-r_a{S}_{\lambda b}\left(t\right)\\ =n_{\lambda a}\left(t\right)-r_a{n}_{\lambda b}\left(t\right)\\ =\sum _{i=1}^4{\epsilon }_{i,\mathrm{\lambda a}}{c}_i{x}_i\left(t\right)+\sum _{i=6}^N{\epsilon }_{i,\lambda a}{c}_i{x}_i\left(t\right)-\end{array}& \text{(14a)}\\ \begin{array}{c}\sum _{i=1}^4{r}_a{\epsilon }_{i,\lambda b}{c}_i{x}_i\left(t\right)+\sum _{i=6}^N{r}_a{\epsilon }_{i,\lambda b}{c}_i{x}_i\left(t\right)\\ =\sum _{i=1}^4{c}_i{x}_i\left(t\right)\left[{\epsilon }_{i,\lambda a}-r_a{\epsilon }_{i,\lambda b}\right]+\end{array}& \text{(15a)}\\ \sum _{i=6}^N{c}_i{x}_i\left(t\right)\left[{\epsilon }_{i,\lambda a}-r_a{\epsilon }_{i,\lambda b}\right]& \text{(16a)}\end{array}$

[0143] Multiplying equation (11) by r_vand subtracting the result from equation (9) yields a primary reference which is a linear sum of primary signal components: $\begin{array}{cc}{s}^{\prime }\left(t\right)=S_{\lambda a}\left(t\right)-r_v{S}_{\lambda b}\left(t\right)=s_{\lambda a}\left(t\right)-r_v{s}_{\lambda b}\left(t\right)& \text{(14b)}\\ =c_5{x}_5\left(t\right){\epsilon }_{5,\lambda a}-r_v{c}_5{x}_5\left(t\right){\epsilon }_{5,\lambda b}& \text{(15b)}\\ =c_5{x}_5\left(t\right)\left[{\epsilon }_{5,\lambda a}-r_v{\epsilon }_{5,\lambda b}\right].& \text{(16b)}\end{array}$

[0144] A sample of either the secondary reference n′(t) or the primary reference s′(t), and a sample of either measured signal S_λa(t) or S_λb(t), are input to a correlation canceler 27, such as an adaptive noise canceler 30, an example of which is shown in FIGS. 5aand 5band a preferred example of which is discussed herein under the heading PREFERRED CORRELATION CANCELER USING A JOINT PROCESS ESTIMATOR IMPLEMENTATION. The correlation canceler 27 removes either the secondary portion n_λa(t) or n_λb(t), or the primary portions, s_λa(t) or s_λb(t), of the measured signal yielding a good approximation to either the primary signals s″_λa(t)≈ε_5,λac₅x₅(t) or s″_λb(t)≈ε_5,λbc₅x₅(t) or the secondary signals n″_λa(t)≈n_λa(t) or n″_λb(t)≈n_λb(t). In the event that the primary signals are obtained, the concentration c₅(t) may then be determined from the approximation to the primary signal s″_λa(t) or s″_λb(t) according to:

[0145] c₅(t)≈s″_λa(t)/ε_5,λax₅(t)  (17a)

[0146] or

[0147] c₅(t)≈s″_λb(t)/ε_5,λbx₅(t)  (17b)

[0148] As discussed previously, the absorption coefficients are constant at each wavelength λa and λb and the thickness of the primary signal component, x₅(t) in this example, is often known or can be determined as a function of time, thereby allowing calculation of the concentration c₅(t) of constituent A₅.

[0149] Referring to FIG. 6b,another material having N different constituents arranged in layers is shown. In this material, two constituents A₅and A₆are found within one layer having thickness x_5,6(t)=x₅(t)+x₆(t), located generally randomly within the layer. This is analogous to combining the layers of constituents A₅and A₆in FIG. 6a.A combination of layers, such as the combination of layers of constituents A₅and A₆, is feasible when the two layers are under the same total forces which result in the same change of the optical path lengths x₅(t) and x₆(t) of the layers.

[0150] Often it is desirable to find the concentration or the saturation, i.e., a percent concentration, of one constituent within a given thickness which contains more than one constituent and is subject to unique forces. A determination of the concentration or the saturation of a constituent within a given volume may be made with any number of constituents in the volume subject to the same total forces and therefore under the same perturbation or change. To determine the saturation of one constituent in a volume comprising many constituents, as many measured signals as there are constituents which absorb incident light energy are necessary. It will be understood that constituents which do not absorb light energy are not consequential in the determination of saturation. To determine the concentration, as many signals as there are constituents which absorb incident light energy are necessary as well as information about the sum of concentrations.

[0151] It is often the case that a thickness under unique motion contains only two constituents. For example, it may be desirable to know the concentration or saturation of A₅within a given volume which contains A₅and A₆. In this case, the primary signals s_λa(t) and s_λb(t) comprise terms related to both A₅and A₆so that a determination of the concentration or saturation of A₅or A₆in the volume may be made. A determination of saturation is discussed herein. It will be understood that the concentration of A₅in a volume containing both A₅and A₆could also be determined if it is known that A₅+A₆=1, i.e., that there are no constituents in the volume which do not absorb incident light energy at the particular measurement wavelengths chosen. The measured signals S_λa(t) and S_λb(t) can be written (logarithm converted) as:

[0152] S_λa(t)=ε_5,λac₅x_5,6(t)+ε_6,λac₆x_5,6(t)+n_λa(t)  (18a)

[0153] =s_λa(t)+n_λa(t)  (18b)

[0154] S_λb(t)=ε_5,λbc₅x_5,6(t)+ε_6,λbc₆x_5,6(t)+n_λb(t)  (19a)

[0155] =s_λb(t)+n_λb(t).  (19b)

[0156] It is also often the case that there may be two or more thicknesses within a medium each containing the same two constituents but each experiencing a separate motion as in FIG. 6c.For example, it may be desirable to know the concentration or saturation of A₅within a given volume which contains A₅and A₆as well as the concentration or saturation of A₃within a given volume which contains A₃and A₄, A₃and A₄having the same constituency as A₅and A₆respectively. In this case, the primary signals s_λa(t) and s_λb(t) again comprise terms related to both A₅and A₆and portions of the secondary signals n_λa(t) and n_λb(t) comprise terms related to both A₃and A₄. The layers, A₃and A₄, do not enter into the primary equation because they are assumed to be perturbed by a different frequency, or random or erratic secondary forces which are uncorrelated with the primary force. Since constituents 3 and 5 as well as constituents 4 and 6 are taken to be the same, they have the same absorption coefficients (i.e., ε_3,λa=ε_5,λa; ε_3,λb=ε_5,λb; ε_4,λa=ε_6,λaand ε_4,λb=ε_6,b. Generally speaking, however, A_εand A₄will have different concentrations than A₅and A₆and will therefore have a different saturation. Consequently a single constituent within a medium may have one or more saturations associated with it. The primary and secondary signals according to this model may be written as:

[0157] s_λa(t)=[ε_5,λac₅+ε_6,λac₆]x_5,6(t)  (20a)

[0158] n_λa(t)=[ε_5,λac₃+ε_6,λac₄]x_3,4(t) +ε_i,λac_ix_i(t)+ε_i,λac_ix_i(t)  (20b)

[0159] n_λa(t)=[ε_5,λac₃+ε_6,λac₄]x_3,4(t)+n_λa(t)  (20c)

[0160] s_λb(t)=[ε_5,λbc₅+ε_6,λbc₆]x_5,6(t)  (21a)

[0161] n_λb(t)=[ε_5,λbc₃+ε_6,λbc₄]x_3,4(t) +ε_i,λbc_ix_i(t)+ε_i,λbc_ix_i(t).  (21b)

[0162] n_λb(t)=[ε_5,λbc₃+ε_6,λbc₄]x_3,4(t)+n_λb(t)  (21c)

[0163] where signals n_λa(t) and n_λb(t) are similar to the secondary signals n_λa(t) and n_λb(t) except for the omission of the 3, 4 layer.

[0164] Any signal portions whether primary or secondary, outside of a known bandwidth of interest, including the constant undesired secondary signal portion resulting from the generally constant absorption of the constituents when not under perturbation, should be removed to determine an approximation to either the primary signal or the secondary signal within the bandwidth of interest. This is easily accomplished by traditional band pass filtering techniques. As in the previous example, it is often the case that the total perturbation or change affecting the layers associated with the secondary signal components is caused by random or erratic forces, causing the thickness of each layer, or the optical path length of each layer, x_i(t), to change erratically, producing a random or erratic secondary signal component n_λa(t). Regardless of whether or not the secondary signal portion n_λa(t) is erratic, the secondary signal component n_λa(t) can be removed or derived via a correlation canceler, such as an adaptive noise canceler, having as one input a secondary reference n′(t) or a primary reference s′(t) determined by a processor of the present invention as long as the perturbation in layers other than the layer of constituents A₅and A₆is different than the perturbation in the layer of constituents A₅and A₆. Either the erratic secondary signal components n_λa(t) and n_λb(t) or the primary components s_λa(t) and s_λb(t) may advantageously be removed from equations (18) and (19), or alternatively equations (20) and (21), by a correlation canceler. The correlation canceler, again, requires a sample of either the primary reference s′(t) or the secondary reference n′(t) and a sample of either of the composite signals S_λa(t) or S_λb(t) of equations (18) and (19).

[0165] One method for determining reference signals s′(t) or n′(t) from the measured signals S_λa(t) and S_λb(t) in accordance with one aspect of the invention is what will be referred to as the constant saturation approach. In this approach, it is assumed that the saturation of A₅in the volume containing A₅and A₆and the saturation of A₃in the volume containing A₃and A₄remains relatively constant over some period of time, i.e.:

[0166] Saturation(A₅(t))=c₅(t)/[c₅(t)+c₆(t)]  (22a)

[0167] Saturation(A₃(t))=c₃(t)/[c₃(t)+c₄(t)]  (22b)

[0168] Saturation(A₅(t))={1+[c₆(t)/c₅(t)]}⁻¹  (23a)

[0169] Saturation(A₃(t))={1+[c₄(t)/c₃(t)]}⁻¹  (23b)

[0170] are substantially constant over many samples of the measured signals S_λaand S_λb. This assumption is accurate over many samples since saturation generally changes relatively slowly in physiological systems.

[0171] The constant saturation assumption is equivalent to assuming that:

[0172] c₅(t)/c₆(t)=constant₁  (24a)

[0173] c₃(t)/c₄(t)=constant₂  (24b)

[0174] since the only other term in equations (23a) and (23b) is a constant, namely the numeral 1.

[0175] Using this assumption, the proportionality constants r_aand r_vwhich allow determination of the secondary reference signal n′(t) and the primary reference signal s′(t) in the constant saturation method are: $\begin{array}{cc}{r}_a=\frac{{\epsilon }_{5,\lambda a}{c}_5{x}_{5,6}\left(t\right)+{\epsilon }_{6,\lambda a}{c}_6{x}_{5,6}\left(t\right)}{{\epsilon }_{5,\lambda b}{c}_5{x}_{5,6}\left(t\right)+{\epsilon }_{6,\lambda b}{c}_6{x}_{5,6}\left(t\right)}& \text{(25a)}\\ =s_{\lambda a}\left(t\right)/s_{\lambda b}\left(t\right)& \text{(26a)}\\ =\frac{{\epsilon }_{5,\lambda a}{c}_5+{\epsilon }_{6,\lambda a}{c}_6}{{\epsilon }_{5,\lambda b}{c}_5+{\epsilon }_{6,\lambda b}{c}_6}& \text{(27a)}\\ =\frac{{\epsilon }_{5,\lambda a}\left(c_5/c_6\right)+{\epsilon }_{6,\lambda a}}{{\epsilon }_{5,\lambda b}\left(c_5/c_6\right)+{\epsilon }_{6,\lambda b}}& \text{(28a)}\\ \approx s_{\lambda a}^{″}\left(t\right)/s_{\lambda b}^{″}\left(t\right)={\mathrm{constant}}_3;\mathrm{where}& \text{(29a)}\\ n_{\lambda a}\left(t\right)\ne r_a\left(t\right)n_{\lambda b}\left(t\right)\mathrm{and}& \text{(30a)}\\ r_v=\frac{{\epsilon }_{5,\lambda a}{c}_3{x}_{3,4}\left(t\right)+{\epsilon }_{6,\lambda a}{c}_4{x}_{3,4}\left(t\right)}{{\epsilon }_{5,\lambda b}{c}_3{x}_{3,4}\left(t\right)+{\epsilon }_{6,\lambda b}{c}_4{x}_{3,4}\left(t\right)}& \text{(25b)}\\ =n_{\lambda a}\left(t\right)/n_{\lambda b}\left(t\right)& \text{(26b)}\\ =\frac{{\epsilon }_{5,\lambda a}{c}_3+{\epsilon }_{6,\lambda a}{c}_4}{{\epsilon }_{5,\lambda b}{c}_3+{\epsilon }_{6,\lambda b}{c}_4}& \text{(27b)}\\ =\frac{{\epsilon }_{5,\lambda a}\left(c_3/c_4\right)+{\epsilon }_{6,\lambda a}}{{\epsilon }_{5,\lambda b}\left(c_3/c_4\right)+{\epsilon }_{6,\lambda b}}& \text{(28b)}\\ \approx n_{\lambda a}^{″}\left(t\right)/n_{\lambda b}^{″}\left(t\right)={\mathrm{constant}}_4;\mathrm{where}& \text{(29b)}\\ s_{\lambda a}\left(t\right)\ne r_v\left(t\right)s_{\lambda b}\left(t\right).& \text{(30b)}\end{array}$

[0176] In accordance with the present invention, it is often the case that both equations (26) and (30) can be simultaneously satisfied to determine the proportionality constants r_aand r_v. Additionally, the absorption coefficients at each wavelength ε_5,λa, ε_6,λa, ε_5,λb, and ε_6,λbare constant and the central assumption of the constant saturation method is that c₅(t)/c₆(t) and c₃(t)/c₄(t) are constant over many sample periods. Thus, new proportionality constants r_aand r_vmay be determined every few samples from new approximations to either the primary or secondary signal as output from the correlation canceler. Thus, the approximations to either the primary signals s_λa(t) and s_λb(t) or the secondary signals n_λa(t) and n_λb(t), found by the correlation canceler for a substantially immediately preceding set of samples of the measured signals S_λa(t) and S_λb(t) are used in a processor of the present invention for calculating the proportionality constants, r_aand r_v, for the next set of samples of the measured signals S_λa(t) and S_λb(t).

[0177] Multiplying equation (19) by r_aand subtracting the resulting equation from equation (18) yields a non-zero secondary reference signal:

[0178] n′(t)=S_λa(t)−r_aS_λb(t)=n_λa(t)−r_an_λb(t).  (31a)

[0179] Multiplying equation (19) by r_vand subtracting the resulting equation from equation (18) yields a non-zero primary reference signal:

[0180] s′(t)=S_λa(t)−r_vS_λb(t)=s_λa(t)−r_vs_λb(t).  (31b)

[0181] When using the constant saturation method in patient monitoring, initial proportionality coefficients can be determined as further explained below. It is not necessary for the patient to remain motionless even for an initialization period. With values for the proportionality coefficients r_aand r_vdetermined, a correlation canceler may be utilized with a secondary reference n′(t) or a primary reference s′(t).

[0182] In accordance with one aspect of the present invention, the reference processor 26 of FIG. 4aand FIG. 4bof the present invention may be configured to multiply the second measured assumed signal S_λb(t)=s_λb(t)+n_λb(t) by each of a plurality of signal coefficients r₁, r₂, . . . r_nand then subtract each result from the first measured signal S_λa(t)=s_λa(t)+n_λa(t) to obtain a plurality of reference signals

[0183] R′(r,t)=s_λa(t)−rs_λb(t)+n_λa(t)−rn_λb(t)  (32)

[0184] for r=r₁, r₂, . . . r_nas shown in FIG. 7a.In other words, a plurality of signal coefficients are chosen to represent a cross section of possible signal coefficients.

[0185] In order to determine either the primary reference s′(t) or the secondary reference n′(t) from the above plurality of reference signals of equation (32), signal coefficients r_aand r_vare determined from the plurality of assumed signal coefficients r₁, r₂, . . . r_n. The coefficients r_aand r_vare selected such that they cause either the primary signal portions s_λa(t) and s_λb(t) or the secondary signal portions n_λa(t) and n_λb(t) to cancel or nearly cancel when they are substituted into the reference function R′(r, t), e. g.

[0186] s_λa(t)=r_as_λb(t)  (33a)

[0187] n_λa(t)=r_vn_λb(t)  (33b)

[0188] n′(t)=R′(r_a,t)=n_λa(t)−r_an_λb(t)  (33c)

[0189] s′(t)=R′(r_v,t)=s_λa(t)−r_vs_λb(t).  (33d)

[0190] In other words, coefficients r_aand r_vare selected at values which reflect the minimum of correlation between the primary signal portions and the secondary signal portions. In practice, one does not usually have significant prior information about either the primary signal portions s_λa(t) and s_λb(t) or the secondary signal portions n_λa(t) and n_λb(t) of the measured signals S_λa(t) and S_λb(t). The lack of this information makes it difficult to determine which of the plurality of coefficients r₁, r₂, . . . r_ncorrespond to the signal coefficients r_a=s_λa(t)/s_λb(t) and r_v=n_λa(t)/n_λb(t).

[0191] One approach to determine the signal coefficients r_aand r_vfrom the plurality of coefficients r₁, r₂, . . . r_nemploys the use of a correlation canceler 27, such as an adaptive noise canceler, which takes a first input which corresponds to one of the measured signals S_λa(t) or S_λb(t) and takes a second input which corresponds to successively each one of the plurality of reference signals R′(r₁, t), R′(r₂, t), . . . , R′(r_n, t) as shown in FIG. 7a.For each of the reference signals R′(r₁, t), R′(r₂, t), . . . , R′(r_n, t) the corresponding output of the correlation canceler 27 is input to a “squares” operation 28 which squares the output of the correlation canceler 27. The output of the squares operation 28 is provided to an integrator 29 for forming a cumulative output signal (a summation of the squares). The cumulative output signal is subsequently input to an extremum detector 31. The purpose of the extremum detector 31 is to chose signal coefficients r_aand r_vfrom the set r₁, r₂, . . . r_nby observing which provide a maximum in the cumulative output signal as in FIGS. 7band 7c.In other words, coefficients which provide a maximum integrated output, such as energy or power, from the correlation canceler 27 correspond to the signal coefficients r_aand r_vwhich relate to a minimum correlation between the primary signal portions and the secondary signal portions in accordance with the signal model of the present invention. One could also configure a system geometry which would require one to locate the coefficients from the set r₁, r₂, . . . r_nwhich provide a minimum or inflection in the cumulative output signal to identify the signal coefficients r_aand r_v.

[0192] Use of a plurality of coefficients in the processor of the present invention in conjunction with a correlation canceler 27 to determine the signal coefficients r_aand r_vmay be demonstrated by using the properties of correlation cancellation. If x, y and z are taken to be any collection of three time varying signals, then the properties of some correlation cancelers C(x, y) may be defined as follows:

[0193] Property (1) C(x, y)=0 for x, ycorrelated  (34a)

[0194] Property (2) C(x, y)=xfor x, yuncorrelated  (34b)

[0195] Property (3) C(x+y, z)=C(x, z)+C(y, z)  (34c )

[0196] With properties (1), (2) and (3) it is easy to demonstrate that the energy or power output of a correlation canceler with a first input which corresponds to one of the measured signals S_λa(t) or S_λb(t) and a second input which corresponds to successively each one of a plurality of reference signals R′(r₁, t), R′(r₂, t), . . . , R′(r_n, t) can determine the signal coefficients r_aand r_vneeded to produce the primary reference s′(t) and secondary reference n′(t). If we take as a first input to the correlation canceler the measured signal S_λa(t) and as a second input the plurality of reference signals R′(r₁, t), R′(r₂, t), . . . , R′(r_n, t) then the outputs of the correlation canceler C(S_λa(t), R′(r_j, t)) for j=1, 2, . . . , n may be written as

[0197] C(s_λa(t)+n_λa(t),s_λa(t)−r_js_λb(t)+n_λa(t)−r_jn_λb(t))  (35)

[0198] where j=1, 2, . . . , n and we have used the expressions

[0199] R′(r,t)=S_λa(t)−rS_λb(t)  (36)

[0200] S_λa(t)=s_λa(t)+n_λa(t)  (37a)

[0201] S_λb(t)=s_λb(t)+n_λb(t).  (37b)

[0202] The use of property (3) allows one to expand equation (35) into two terms

[0203] C(S_λa(t),R′(r,t))=C(s_λa(t),s_λa(t)−rs_λb(t)+n_λa(t)−rn_λb(t))+C(n_λa(t),s_λa(t)−rs_λb(t)+n_λa(t)−rn_λb(t))  (38)

[0204] so that upon use of properties (1) and (2) the correlation canceler output is given by

[0205] C(S_λa(t),R′(r_j,t))=s_λa(t)δ(r_j−r_a)+n_λa(t)δ(r_j−r_v)  (39)

[0206] where δ(x) is the unit impulse function

[0207] δ(x)=0 if x≠0δ(x)=1 if x=0.  (40)

[0208] The time variable, t, of the correlation canceler output C(S_λa(t), R′(r_j, t)) may be eliminated by computing its energy or power. The energy of the correlation canceler output is given by

[0209] E_λa(r_j)=∫C²(S_λa(t),R′(r_j,t)dt=δ(r_j−r_a)∫s²_λa(t)dt+δ(r_j−r_v)∫n²_λa(t)dt.  (41a)

[0210] It should be understood that one could, equally well, have chosen the measured signal S_λb(t) as the first input to the correlation canceler and the plurality of reference signals R′(r₁, t), R′(r₂, t), . . . , R′(r_n, t) as the second input. In this event, the correlation canceler energy output is

[0211] E_λb(r_j)=∫C²(S_λb(t),R′(r,t)dt=δ(r_j−r_a)∫s²_λb(t)dt+δ(r_j−r_v)∫n²_λb(t)dt.  (41b)

[0212] It should also be understood that in practical situations the use of discrete time measurement signals may be employed as well as continuous time measurement signals. A system which performs a discrete transform (e.g., a saturation transform in the present example) in accordance with the present invention is described with reference to FIGS. 11-22. In the event that discrete time measurement signals are used, integration approximation methods such as the trapezoid rule, midpoint rule, Tick's rule, Simpson's approximation or other techniques may be used to compute the correlation canceler energy or power output. In the discrete time measurement signal case, the energy output of the correlation canceler may be written, using the trapezoid rule, as $\begin{array}{cc}\begin{array}{c}{E}_{\lambda a}\left(r_j\right)=\delta \left(r_j-r_a\right)\Delta t\left\{\sum _{i=0}^n{s}_{\lambda a}^2\left(t_i\right)-0.5\left(s_{\lambda a}^2\left(t_0\right)+s_{\lambda a}^2\left(t_n\right)\right)\right\}+\\ \delta \left(r_j-r_v\right)\Delta t\left\{\sum _{i=0}^n{n}_{\lambda a}^2\left(t_i\right)-0.5\left(n_{\lambda a}^2\left(t_0\right)+n_{\lambda a}^2\left(t_n\right)\right)\right\}\end{array}& \text{(42a)}\\ \begin{array}{c}{E}_{\lambda b}\left(r_j\right)=\delta \left(r_j-r_a\right)\Delta t\left\{\sum _{i=0}^n{s}_{\lambda b}^2\left(t_i\right)-0.5\left(s_{\lambda b}^2\left(t_0\right)+s_{\lambda b}^2\left(t_n\right)\right)\right\}+\\ \delta \left(r_j-r_v\right)\Delta t\left\{\sum _{i=0}^n{n}_{\lambda b}^2\left(t_i\right)-0.5\left(n_{\lambda b}^2\left(t_0\right)+n_{\lambda b}^2\left(t_n\right)\right)\right\}\end{array}& \text{(42b)}\end{array}$

[0213] where t_iis the i^thdiscrete time, t₀is the initial time, t_nis the final time and Δt is the time between discrete time measurement samples.

[0214] The energy functions given above, and shown in FIG. 7b,indicate that the correlation canceler output is usually zero due to correlation between the measured signal S_λa(t) or S_λb(t) and many of the plurality of reference signals R′(r₁, t), R′(r₂, t), . . . , R′(r_n, t). However, the energy functions are non zero at values of r_jwhich correspond to cancellation of either the primary signal portions s_λa(t) and s_λb(t) or the secondary signal portions n_λa(t) and n_λb(t) in the reference signal R′(r_j, t). These values correspond to the signal coefficients r_aand r_v.

[0215] It should be understood that there may be instances in time when either the primary signal portions s_λa(t) and s_λb(t) or the secondary signal portions n_λa(t) and n_λb(t) are identically zero or nearly zero. In these cases, only one signal coefficient value will provide maximum energy or power output of the correlation canceler.

[0216] Since there may be more than one signal coefficient value which provides maximum correlation canceler energy or power output, an ambiguity may arise. It may not be immediately obvious which signal coefficient together with the reference function R′(r, t) provides either the primary or secondary reference. In such cases, it is necessary to consider the constraints of the physical system at hand. For example, in pulse oximetry, it is known that arterial blood, whose signature is the primary plethysmographic wave, has greater oxygen saturation than venous blood, whose signature is the secondary erratic or random signal. Consequently, in pulse oximetry, the ratio of the primary signals due to arterial pulsation r_a=s_λa(t)/s_λb(t) is the smaller of the two signal coefficient values while the ratio of the secondary signals due to mainly venous blood dynamics r_v=n_λa(t)/n_λb(t) is the larger of the two signal coefficient values, assuming λa=660 nm and λb=910 nm.

[0217] It should also be understood that in practical implementations of the plurality of reference signals and cross correlator technique, the ideal features listed as properties (1), (2) and (3) above will not be precisely satisfied but will be approximations thereof. Therefore, in practical implementations of this embodiment of the present invention, the correlation canceler energy curves depicted in FIG. 7bwill not consist of infinitely narrow delta functions but will have finite width associated with them as depicted in FIG. 7c.

[0218] It should also be understood that it is possible to have more than two signal coefficient values which produce maximum energy or power output from a correlation canceler. This situation arises when the measured signals each contain more than two components each of which are related by a ratio as follows: $\begin{array}{cc}{S}_{\lambda a}\left(t\right)=\sum _{i=0}^n{f}_{\lambda a,i}\left(t\right)S_{\lambda b}\left(t\right)=\sum _{i=0}^n{f}_{\lambda b,i}\left(t\right)& \left(43\right)\end{array}$

[0219] where

[0220] f_λa,i(t)=r_if_λb,i(t) r_i≠r_j.

[0221] i=1, . . . , n

[0222] Thus, reference signal techniques together with a correlation cancellation, such as an adaptive noise canceler, can be employed to decompose a signal into two or more signal components each of which is related by a ratio.

[0223] Once either the secondary reference n′(t) or the primary reference s′(t) is determined by the processor of the present invention, the correlation canceler can be implemented in either hardware or software. The preferred implementation of a correlation canceler is that of an adaptive noise canceler using a joint process estimator.

[0224] The least mean squares (LMS) implementation of the internal processor 32 described above in conjunction with the adaptive noise canceler of FIG. 5aand FIG. 5bis relatively easy to implement, but lacks the speed of adaptation desirable for most physiological monitoring applications of the present invention. Thus, a faster approach for adaptive noise canceling, called a least-squares lattice joint process estimator model, is used in one embodiment. A joint process estimator 60 is shown diagrammatically in FIG. 8 and is described in detail in Chapter 9 of Adaptive Filter Theoryby Simon Haykin, published by Prentice-Hall, copyright 1986. This entire book, including Chapter 9, is hereby incorporated herein by reference.

[0225] The function of the joint process estimator is to remove either the secondary signal portions n_λa(t) or n_λb(t) or the primary signal portions s_λa(t) or s_λb(t) from the measured signals S_λa(t) or S_λb(t), yielding either a primary signal approximation s″_λa(t) or s″_λb(t) or a secondary signal approximation n″_λa(t) or n″_λb(t). Thus, the joint process estimator estimates either the value of the primary signals s_λa(t) or s_λb(t) or the secondary signals n_λa(t) or n_λb(t). The inputs to the joint process estimator 60 are either the secondary reference n′(t) or the primary reference s′(t) and the composite measured signal S_λa(t) or S_λb(t). The output is a good approximation to the signal S_λa(t) or S_λb(t) with either the secondary signal or the primary signal removed, i.e. a good approximation to either s_λa(t), s_λb(t), n_λa(t) or n_λb(t).

[0226] The joint process estimator 60 of FIG. 8 utilizes, in conjunction, a least square lattice predictor 70 and a regression filter 80. Either the secondary reference n′(t) or the primary reference s′(t) is input to the least square lattice predictor 70 while the measured signal S_λa(t) or S_λb(t) is input to the regression filter 80. For simplicity in the following description, S_λa(t) will be the measured signal from which either the primary portion s_λa(t) or the secondary portion n_λa(t) will be estimated by the joint process estimator 60. However, it will be noted that S_λb(t) could also be input to the regression filter 80 and the primary portion s_λb(t) or the secondary portion n_λb(t) of this signal could be estimated.

[0227] The joint process estimator 60 removes all frequencies that are present in both the reference n′(t) or s′(t), and the measured signal S_λa(t) The secondary signal portion n_λa(t) usually comprises frequencies unrelated to those of the primary signal portion s_λa(t). It is improbable that the secondary signal portion n_λa(t) would be of exactly the same spectral content as the primary signal portion s_λa(t). However, in the unlikely event that the spectral content of s_λa(t) and n_λa(t) are similar, this approach will not yield accurate results. Functionally, the joint process estimator 60 compares the reference input signal n′(t) or s′(t), which is correlated to either the secondary signal portion n_λa(t) or the primary signal portion s_λa(t), and input signal S_λa(t) and removes all frequencies which are identical. Thus, the joint process estimator 60 acts as a dynamic multiple notch filter to remove those frequencies in the secondary signal component n_λa(t) as they change erratically with the motion of the patient or those frequencies in the primary signal component s_λa(t) as they change with the arterial pulsation of the patient. This yields a signal having substantially the same spectral content and amplitude as either the primary signal s_λa(t) or the secondary signal n_λa(t). Thus, the output s″_λa(t) or n″_λa(t) of the joint process estimator 60 is a very good approximation to either the primary signal S_λa(t) or the secondary signal n_λa(t)

[0228] The joint process estimator 60 can be divided into stages, beginning with a zero-stage and terminating in an m^th-stage as shown in FIG. 8. Each stage, except for the zero-stage, is identical to every other stage. The zero-stage is an input stage for the joint process estimator 60. The first stage through the m^th-stage work on the signal produced in the immediately previous stage, i.e., the (m−1)^th-stage, such that a good primary signal approximation s″_λa(t) or secondary signal approximation n″_λa(t) is produced as output from the m^th-stage.

[0229] The least-squares lattice predictor 70 comprises registers 90 and 92, summing elements 100 and 102, and delay elements 110. The registers 90 and 92 contain multiplicative values of a forward reflection coefficient Γ_f,m(t) and a backward reflection coefficient Γ_b,m(t) which multiply the reference signal n′(t) or s′(t) and signals derived from the reference signal n′(t) or s′(t). Each stage of the least-squares lattice predictor outputs a forward prediction error f_m(t) and a backward prediction error b_m(t). The subscript m is indicative of the stage.

[0230] For each set of samples, i.e. one sample of the reference signal n′(t) or s′(t) derived substantially simultaneously with one sample of the measured signal S_λa(t), the sample of the reference signal n′(t) or s′(t) is input to the least-squares lattice predictor 70. The zero-stage forward prediction error f₀(t) and the zero-stage backward prediction error b₀(t) are set equal to the reference signal n′(t) or s′(t). The backward prediction error b₀(t) is delayed by one sample period by the delay element 110 in the first stage of the least-squares lattice predictor 70. Thus, the immediately previous value of the reference n′(t) or s′(t) is used in calculations involving the first-stage delay element 110. The zero-stage forward prediction error is added to the negative of the delayed zero-stage backward prediction error b₀(t−1) multiplied by the forward reflection coefficient value Γ_f,1(t) register 90 value, to produce a first-stage forward prediction error f₁(t). Additionally, the zero-stage forward prediction error f₀(t) is multiplied by the backward reflection coefficient Γ_b,1(t) register 92 value and added to the delayed zero-stage backward prediction error b₀(t−1) to produce a first-stage backward prediction error b₁(t). In each subsequent stage, m, of the least square lattice predictor 70, the previous forward and backward prediction error values, f_m−1(t) and b_m−1(t−1), the backward prediction error being delayed by one sample period, are used to produce values of the forward and backward prediction errors for the present stage, f_m(t) and b_m(t).

[0231] The backward prediction error b_m(t) is fed to the concurrent stage, m, of the regression filter 80. There it is input to a register 96, which contains a multiplicative regression coefficient value κ_{m, λa}(t). For example, in the zero-stage of the regression filter 80, the zero-stage backward prediction error b₀(t) is multiplied by the zero-stage regression coefficient κ_{0, λa}(t) register 96 value and subtracted from the measured value of the signal S_λa(t) at a summing element 106 to produce a first stage estimation error signal e_{1, λa}(t). The first-stage estimation error signal e_{1, λa}(t) is a first approximation to either the primary signal or the secondary signal. This first-stage estimation error signal e_{1, λa}(t) is input to the first-stage of the regression filter 80. The first-stage backward prediction error b₁(t), multiplied by the first-stage regression coefficient κ_{1, λa}(t) register 96 value is subtracted from the first-stage estimation error signal e_{1, λa}(t) to produce the second-stage estimation error e_{2, λa}(t). The second-stage estimation error signal e_{2, λa}(t) is a second, somewhat better approximation to either the primary signal s_λa(t) or the secondary signal n_λa(t).

[0232] The same processes are repeated in the least-squares lattice predictor 70 and the regression filter 80 for each stage until a good approximation e_{m, λa}(t), to either the primary signal s_λa(t) or the secondary signal n_λa(t) is determined. Each of the signals discussed above, including the forward prediction error f_m(t), the backward prediction error b_m(t), the estimation error signal e_{m, λa}(t), is necessary to calculate the forward reflection coefficient Γ_f,m(t), the backward reflection coefficient Γ_b,m(t), and the regression coefficient κ_{m, λa}(t) register 90, 92, and 96 values in each stage, m. In addition to the forward prediction error f_m(t) the backward prediction error b_m(t), and the estimation error e_{m, λa}(t) signals, a number of intermediate variables, not shown in FIG. 8 but based on the values labeled in FIG. 8, are required to calculate the forward reflection coefficient Γ_f,m(t) the backward reflection coefficient Γ_b,m(t) I and the regression coefficient κ_{m,, λa}(t) register 90,92, and 96 values.

[0233] Intermediate variables include a weighted sum of the forward prediction error. squares ℑ_m(t), a weighted sum of the backward prediction error squares β_m(t), a scalar parameter Δ_m(t), a conversion factor γ_m(t), and another scalar parameter ρ_{m, λa}(t) The weighted sum of the forward prediction errors ℑ_m(t) is defined as: $\begin{array}{cc}{ℱ}_m\left(t\right)=\sum _{i=1}^t{\lambda }^{t-i}{\left|f_m\left(i\right)\right|}^2;& \left(44\right)\end{array}$

[0234] where λ without a wavelength identifier, a or b, is a constant multiplicative value unrelated to wavelength and is typically less than or equal to one, i.e., λ≦1. The weighted sum of the backward prediction errors β_m(t) is defined as: $\begin{array}{cc}{ℬ}_m\left(t\right)=\sum _{i=1}^t{\lambda }^{t-i}{\left|b_m\left(i\right)\right|}^2& \left(45\right)\end{array}$

[0235] where, again, λ without a wavelength identifier, a or b, is a constant multiplicative value unrelated to wavelength and is typically less than or equal to one, i.e., λ≦1. These weighted sum intermediate error signals can be manipulated such that they are more easily solved for, as described in Chapter 9, § 9.3 of the Haykin book referenced above and defined hereinafter in equations (59) and (60).

[0236] The operation of the joint process estimator 60 is as follows. When the joint process estimator 60 is turned on, the initial values of intermediate variables and signals including the parameter Δ_m−1(t), the weighted sum of the forward prediction error signals ℑ_m−1(t), the weighted sum of the backward prediction error signals β_m−1(t), the parameter ρ_m,λa(t), and the zero-stage estimation error e_0,λa(t) are initialized, some to zero and some to a small positive number δ:

[0237] Δ_m−1(0)=0;  (46)

[0238] ℑ_m−1(0)=δ;  (47)

[0239] β_m−1(0)=δ;  (48)

[0240] ρ_m,λa(0)=0;  (49)

[0241] e_0,λa(t)=S_λa(t) for t≧0.  (50)

[0242] After initialization, a simultaneous sample of the measured signal S_λa(t) or S_λb(t) and either the secondary reference n′(t) or the primary reference s′(t) are input to the joint process estimator 60, as shown in FIG. 8. The forward and backward prediction error signals f₀(t) and b₀(t), and intermediate variables including the weighted sums of the forward and backward error signals ℑ₀(t) and β₀(t), and the conversion factor γ₀(t) are calculated for the zero-stage according to:

[0243] f₀(t)=b₀(t)=n′(t)  (51a)

[0244] ℑ₀(t)=β₀(t)=λℑ₀(t−1)+|n′(t)|²  (52a)

[0245] γ₀(t−1)=1  (53a)

[0246] if a secondary reference n′(t) is used or according to:

[0247] f₀(t)=b₀(t)=s′(t)  (51b)

[0248] ℑ₀(t)=β₀(t)=λℑ₀(t−1)+|s′(t)²  (52b)

[0249] γ₀(t−1)=1  (53b)

[0250] if a primary reference s′(t) is used where, again, λ without a wavelength identifier, a or b, is a constant multiplicative value unrelated to wavelength.

[0251] Forward reflection coefficient Γ_f,m(t), backward reflection coefficient Γ_b,m(t), and regression coefficient κ_m,λa(t) register 90, 92 and 96 values in each stage thereafter are set according to the output of the previous stage. The forward reflection coefficient Γ_f,1(t), backward reflection coefficient Γ_b,1(t), and regression coefficient κ_1,λa(t) register 90, 92 and 96 values in the first stage are thus set according to the algorithm using values in the zero-stage of the joint process estimator 60. In each stage, m≧1, intermediate values and register values including the parameter Δ_m−1(t); the forward reflection coefficient Γ_f,m(t) register 90 value; the backward reflection coefficient Γ_b,m(t) register 92 value; the forward and backward error signals f_m(t) and b_m(t); the weighted sum of squared forward prediction errors ℑ_f,m(t), as manipulated in §9.3 of the Haykin book; the weighted sum of squared backward prediction errors β_b,m(t), as manipulated in §9.3 of the Haykin book; the conversion factor γ_m(t); the parameter ρ_m,λa(t); the regression coefficient κ_m,λa(t) register 96 value; and the estimation error e_m+1λa(t) value are set according to:

[0252] Δ_m−1(t)=λγ_m−1(t−1)+{b_m−1(t−1)F*_m−1(t)/γ_m−1(t−1)}  (54)

[0253] Γ_f,m(t)=−{Δ_m−1(t)/β_m−1(t−1)}  (55)

[0254] Γ_b,m(t)=−{Δ*_m−1(t)/ℑ_m−1(t)}  (56)

[0255] f_m(t)=f_m−1(t)+Γ*_f,m(t)b_m−1(t−1)  (57)

[0256] b_m(t)=b_m−1(t−1)+Γ*_b,m(t)f_m−1(t)  (58)

[0257] ℑ_m(t)=ℑ_m−1(t)−{|Δ_m−1(t)|²/β_m−1(t−1)}  (59)

[0258] β_m(t)=β_m−1(t−1)−{|Δ_m−1(t)|²/ℑ_m−1(t)}  (60)

[0259] γ_m(t−1)=γ_m−1(t−1)−{|b_m−1(t−1)|²/β_m−1(t−)}  (61)

[0260] ρ_m,λa(t)=λρ_m,λa(t−1)+{b_m(t)ε*_m,λa(t)/γ_m(t)}  (62)

[0261] κ_m,λa(t)={ρ_m,λa(t)/β_m(t)}  (63)

[0262] ε_m+1,λa(t)=ε_m,λa(t)−κ*_m(t)b_m(t)  (64)

[0263] where a (*) denotes a complex conjugate.

[0264] These equations cause the error signals f_m(t), b_m(t), e_m,λa(t) to be squared or to be multiplied by one another, in effect squaring the errors, and creating new intermediate error values, such as Δ_m−1(t). The error signals and the intermediate error values are recursively tied together, as shown in the above equations (54) through (64). They interact to minimize the error signals in the next stage.

[0265] After a good approximation to either the primary signal s_λa(t) or the secondary signal n_λa(t) has been determined by the joint process estimator 60, a next set of samples, including a sample of the measured signal S_λa(t) and a sample of either the secondary reference n′(t) or the primary reference s′(t), are input to the joint process estimator 60. The re-initialization process does not re-occur, such that the forward and backward reflection coefficient Γ_f,m(t) and Γ_b,m(t) register 90, 92 values and the regression coefficient κ_m,λa(t) register 96 value reflect the multiplicative values required to estimate either the primary signal portion s_λa(t) or the secondary signal portion n_λa(t) of the sample of S_λa(t) input previously. Thus, information from previous samples is used to estimate either the primary or secondary signal portion of a present set of samples in each stage.

[0266] In a more numerically stable and preferred embodiment of the above described joint process estimator, a normalized joint process estimator is used. This version of the joint process estimator normalizes several variables of the above-described joint process estimator such that the normalized variables fall between −1 and 1. The derivation of the normalized joint process estimator is motivated in the Haykin text as problem 12 on page 640 by redefining the variables defined according to the following conditions: ${\stackrel{\_}{f}}_m\left(t\right)=\frac{f_m\left(t\right)}{\sqrt{{ℱ}_m\left(t\right){\gamma }_m\left(t-1\right)}}$ ${\stackrel{\_}{b}}_m\left(t\right)=\frac{f_m\left(t\right)}{\sqrt{{\beta }_m\left(t\right){\gamma }_m\left(t-1\right)}}$ ${\stackrel{\_}{\Delta }}_m\left(t\right)=\frac{f_m\left(t\right)}{\sqrt{{ℱ}_m\left(t\right){\gamma }_m\left(t-1\right)}}$

[0267] This transformation allows the conversion of Equations (54)-(64) to the following normalized equations:

[0268] {overscore (Δ)}_m−1(t)={overscore (Δ)}_m−1(t−1)[1−|f_m−1(t)|²]^½[1−|{overscore (b)}_m−1(t−1)|²]^½+{overscore (b)}_m−1(t−1){overscore (f)}_m−1(t) ${\stackrel{\_}{b}}_m\left(t\right)=\frac{\left[{\stackrel{\_}{b}}_{m-1}\left(t-1\right)-{\stackrel{\_}{\Delta }}_{m-1}\left(t\right){\stackrel{\_}{f}}_{m-1}\left(t\right)\right]}{{{\left[1-{\left|{\stackrel{\_}{\Delta }}_{m-1}\left(t\right)\right|}^2\right]}^{1/2}\left[1-{\left|{\stackrel{\_}{f}}_{m-1}\left(t\right)\right|}^2\right]}^{1/2}}$ ${\stackrel{\_}{f}}_m\left(t\right)=\frac{\left[{\stackrel{\_}{f}}_{m-1}\left(t-1\right)-{\stackrel{\_}{\Delta }}_{m-1}\left(t\right){\stackrel{\_}{b}}_{m-1}\left(t-1\right)\right]}{{{\left[1-{\left|{\stackrel{\_}{\Delta }}_{m-1}\left(t\right)\right|}^2\right]}^{1/2}\left[1-{\left|{\stackrel{\_}{b}}_{m-1}\left(t-1\right)\right|}^2\right]}^{1/2}}$  β_m(t)=[1−|{overscore (Δ)}_m−1(t)|²]β_m−1(t−1)

[0269] γ_m(t)=γ_m−1(t)[1−|{overscore (b)}_m−1(t)|²] ${\rho }_m\left(t\right)=\lambda ·{\left[\frac{{\gamma }_m\left(t\right){\beta }_m\left(y-1\right)}{{\gamma }_m\left(t-1\right){\beta }_m\left(t\right)}\right]}^{1/2}\rho \left(t-1\right)+{\stackrel{\_}{b}}_m\left(t\right){ϵ}_m\left(t\right)$  ε_m+1,λa(t)=ε_m,λa(t)−ρ_m(t){overscore (b)}_m(t)

[0270] Initialization of Normalized Joint Process Estimator

[0271] Let N(t) be defined as the reference noise input at time index n and U(t) be defined as combined signal plus noise input at time index t the following equations apply (see Haykin, p. 619):

[0272] 1. To initialize the algorithm, at time t=0 set

[0273] {overscore (Δ)}_m−1(0)=0

[0274] β_m−1(0)=δ=10⁻⁶

[0275] γ₀(0)=1

[0276] 2. At each instant t≧1, generate the various zeroth-order variables as follows:

[0277] γ₀(t−1)=1

[0278] β₀(t)=λβ₀(t−1)+N²(t) ${\stackrel{\_}{b}}_0\left(t\right)={\stackrel{\_}{f}}_0\left(t\right)=\frac{N\left(t\right)}{\sqrt{{\beta }_0\left(t\right)}}$

[0279] 3. For regression filtering, initialize the algorithm by setting at time index t=0

[0280] ρ_m(0)=0

[0281] 4. At each instant t≧1, generate the zeroth-order variable

[0282] ε₀(t)=U(t).

[0283] Accordingly, a normalized joint process estimator can be used for a more stable system.

[0284] In yet another embodiment, the correlation cancellation is performed with a QRD algorithm as shown diagrammatically in FIG. 8aand as described in detail in Chapter 18 of Adaptive Filter Theoryby Simon Haykin, published by Prentice-Hall, copyright 1986.

[0285] The following equations adapted from the Haykin book correspond to the QRD-LSL diagram of FIG. 8a(also adapted from the Haykin book).

[0286] Computations

[0287] a. Predictions: For time t=1, 2, . . . , and prediction order m =1, 2, . . . , M, where M is the final prediction order, compute:

[0288] β_m−1(t−1)=λβ_m−1(t−2)+|ε_b,m−1(t−1)|² $c_{b,m-1}\left(t+1\right)=\frac{{\lambda }^{1/2}{\beta }_{m-1}^{1/2}\left(t-2\right)}{{\beta }_{m-1}^{1/2}\left(t-1\right)}$ $s_{b,m-1}\left(t-1\right)=\frac{{\epsilon }_{b,m-1}^{*}\left(t-1\right)}{{\beta }_{m-1}^{1/2}\left(t-1\right)}$  ε_f,m(t)=c_b,m−1(t−1)ε_f,m−1(t)−s*_b,m−1(t−)λ^½π*_f,m−1(t−1)

[0289] π*_f,m−1(t)=c_b,m−1(t−1)λ^½π*_f,m−1(t−1)+s_b,m−1(t−)ε_f,m−1(t)

[0290] γ_m^½(t−1)=c_b,m−1(t−1)γ_m−1^½(t−1)

[0291] _m−1(t)=λ_m−1(t−1)+|ε_f,m−1(t)|² $c_{f,m-1}\left(t\right)=\frac{{\lambda }^{1/2}{ℱ}_{m-1}^{1/2}\left(t-1\right)}{{ℱ}_{m-1}^{1/2}\left(t\right)}$ $s_{f,m-1}\left(t\right)=\frac{{\epsilon }_{f,m-1}^{*}\left(t\right)}{{ℱ}_{m-1}^{1/2}\left(t\right)}$  ε_b,m(t)=c_f,m−1(t)ε_b,m−1(t−1)−s*_f,m−1(t)λ^½π*_b,m−1(t−)

[0292] π*_b,m−1(t)=c_f,m−1(t)λ^½π*_b,m−1(t−1)+s_f,m−1(t)ε_b,m−1(t−1)

[0293] b. Filtering: For order m=0, 1, . . . , M−1; and time t=1, 2, . . . , compute

[0294] β_m(t)=λβ_m(t−1)+|ε_b,m(t)|² $c_{b,m}\left(t\right)=\frac{{\lambda }^{1/2}{\beta }_m^{1/2}\left(t-1\right)}{{\beta }_m^{1/2}\left(t\right)}$ $s_{b,m}\left(t\right)=\frac{{\epsilon }_{b,m}^{*}\left(t\right)}{{\beta }_m^{1/2}\left(t\right)}$  ε_m+1(t)=c_b,m(t)ε_m(t)−s*_b,m(t)λ^½ρ*_m(t−1)

[0295] ρ*_m(t)=c_b,m(t)λ^½ρ*_m(t−1)+s_b,m(t)ε_m(t)

[0296] γ_m+1^½(t)=c_b,m(t)γ_m^½(t)

[0297] ε_m+1(t)=λ_m+1^½(t)ε_m+1(t)

[0298] 5. Initialization

[0299] a. Auxiliary parameter initialization: for order m=1, 2, . . . , M, set

[0300] π_f,m−1(0)=π_b,m−1(0)=0

[0301] p_m(0)=0

[0302] b. Soft constraint initialization: For order m=0, 1, . . . , M, set

[0303] β_m(−1)=δ

[0304] _m(0)=δ

[0305] where δ is a small positive constant.

[0306] c. Data initialization: For t=1, 2, . . . , compute

[0307] ε_f,0(t)=ε_b,0(t)=μ(t)

[0308] ε₀(t)=d(t)

[0309] γ₀(t)=1

[0310] where μ(t) is the input and d(t) is the desired response at time t.

[0311] In a signal processor, such as a physiological monitor incorporating a reference processor of the present invention to determine a reference n′(t) or s′(t) for input to a correlation canceler, a joint process estimator 60 type adaptive noise canceler is generally implemented via a software program having an iterative loop. One iteration of the loop is analogous to a single stage of the joint process estimator as shown in FIG. 8. Thus, if a loop is iterated m times, it is equivalent to an m stage joint process estimator 60.

[0312] A flow chart of a subroutine to estimate the primary signal portion s_λa(t) or the secondary signal portion n_λa(t) of a measured composite signal, S_λa(t) is shown in FIG. 9. The flow chart illustrates the function of a reference processor for determining either the secondary reference n′(t) or the primary reference s′(t). The flowchart for the joint process estimator is implemented in software.

[0313] A one-time initialization is performed when the physiological monitor is powered-on, as indicated by an “INITIALIZE NOISE CANCELER” action block 120. The initialization sets all registers 90, 92, and 96 and delay element variables 110 to the values described above in equations (46) through (50).

[0314] Next, a set of simultaneous samples of the composite measured signals S_λa(t) and S_λb(t) is input to the subroutine represented by the flowchart in FIG. 9. Then a time update of each of the delay element program variables occurs, as indicated in a “TIME UPDATE OF [Z⁻¹] ELEMENTS” action block 130. The value stored in each of the delay element variables 110 is set to the value at the input of the delay element variable 110. Thus, the zero-stage backward prediction error b₀(t) is stored as the first-stage delay element variable, and the first-stage backward prediction error b₁(t) is stored as the second-stage delay element variable, and so on.

[0315] Then, using the set of measured signal samples S_λa(t) and S_λb(t), the reference signal is obtained using the ratiometric or the constant saturation methods described above. This is indicated by a “CALCULATE REFERENCE [n′(t) or s′(t)] FOR TWO MEASURED SIGNAL SAMPLES” action block 140.

[0316] A zero-stage order update is performed next as indicated in a “ZERO-STAGE UPDATE” action block 150. The zero-stage backward prediction error b₀(t), and the zero-stage forward prediction error f₀(t) are set equal to the value of the reference signal n′(t) or s′(t). Additionally, the weighted sum of the forward prediction errors ℑ_m(t) and the weighted sum of backward prediction errors β_m(t) are set equal to the value defined in equations (47) and (48).

[0317] Next, a loop counter, m, is initialized as indicated in a “m=0” action block 160. A maximum value of m, defining the total number of stages to be used by the subroutine corresponding to the flowchart in FIG. 9, is also defined. Typically, the loop is constructed such that it stops iterating once a criterion for convergence upon a best approximation to either the primary signal or the secondary signal has been met by the joint process estimator 60. Additionally, a maximum number of loop iterations may be chosen at which the loop stops iteration. In a preferred embodiment of a physiological monitor of the present invention, a maximum number of iterations, m=6 to m=10, is advantageously chosen.

[0318] Within the loop, the forward and backward reflection coefficient Γ_f,m(t) and Γ_b,m(t) register 90 and 92 values in the least-squares lattice filter are calculated first, as indicated by the “ORDER UPDATE MTH CELL OF LSL-LATTICE” action block 170 in FIG. 9. This requires calculation of intermediate variable and signal values used in determining register 90, 92, and 96 values in the present stage, the next stage, and in the regression filter 80.

[0319] The calculation of regression filter register 96 value κ_m,λa(t) is performed next, indicated by the “ORDER UPDATE MTH STAGE OF REGRESSION FILTER(S)” action block 180. The two order update action blocks 170 and 180 are performed in sequence m times, until m has reached its predetermined maximum (in the preferred embodiment, m=6 to m=10) or a solution has been converged upon, as indicated by a YES path from a “DONE” decision block 190. In a computer subroutine, convergence is determined by checking if the weighted sums of the forward and backward prediction errors ℑ_m(t) and β_m(t) are less than a small positive number. An output is calculated next, as indicated by a “CALCULATE OUTPUT” action block 200. The output is a good approximation to either the primary signal or secondary signal, as determined by the reference processor 26 and joint process estimator 60 subroutine corresponding to the flow chart of FIG. 9. This is displayed (or used in a calculation in another subroutine), as indicated by a “TO DISPLAY” action block 210.

[0320] A new set of samples of the two measured signals S_λa(t) and S_λb(t) is input to the processor and joint process estimator 60 adaptive noise canceler subroutine corresponding to the flowchart of FIG. 9 and the process reiterates for these samples. Note, however, that the initialization process does not re-occur. New sets of measured signal samples S_λa(t) and S_λb(t) are continuously input to the reference processor 26 and joint process estimator adaptive noise canceler subroutine. The output forms a chain of samples which is representative of a continuous wave. This waveform is a good approximation to either the primary signal waveform s_λa(t) or the secondary waveform n_λa(t) at wavelength λa. The waveform may also be a good approximation to either the primary signal waveform s_λb(t) or the secondary waveform n″_λb(t) at wavelength λb.

[0321] A corresponding flowchart for the QRD algorithm of FIG. 8ais depicted in FIG. 9a,with reference numeral corresponding in number with an ‘a’ extension.

[0322] Physiological monitors may use the approximation of the primary signals s″_λa(t) or s″_λb(t) or the secondary signals n″_λa(t) or n″_λb(t) to calculate another quantity, such as the saturation of one constituent in a volume containing that constituent plus one or more other constituents. Generally, such calculations require information about either a primary or secondary signal at two wavelengths. For example, the constant saturation method requires a good approximation of the primary signal portions s_λa(t) and s_λb(t) of both measured signals S_λa(t) and S_λb(t). The arterial saturation is determined from the approximations to both signals, i.e. s″_λa(t) and s″_λb(t). The constant saturation method also requires a good approximation of the secondary signal portions n_λa(t) or n_λb(t). An estimate of the venous saturation may be determined from the approximations to these signals i. e. n″_λa(t) and n″_λb(t).

[0323] A joint process estimator 60 having two regression filters 80aand 80bis shown in FIG. 10. A first regression filter 80aaccepts a measured signal S_λa(t). A second regression filter 80baccepts a measured signal S_λb(t) for a use of the constant saturation method to determine the reference signal n′(t) or s′(t). The first and second regression filters 80aand 80bare independent. The backward prediction error b_m(t) is input to each regression filter 80aand 80b,the input for the second regression filter 80bbypassing the first regression filter 80a.

[0324] The second regression filter 80bcomprises registers 98, and summing elements 108 arranged similarly to those in the first regression filter 80a.The second regression filter 80boperates via an additional intermediate variable in conjunction with those defined by equations (54) through (64), i.e.:

[0325] ρ_m,λb(t)=λρ_m,λb(t−1)+{b_m(t)e*_m,λb(t)/γ_m(t)}; and  (65)

[0326] ρ_0,λb(0)=0.  (66)

[0327] The second regression filter 80bhas an error signal value defined similar to the first regression filter error signal values, e_m+1,λa(t), i.e.:

[0328] e_m+1,λb(t)=e_m,λb(t)−κ*_m,λb(t)b_m(t); and  (67)

[0329] e_0,λb(t)=S_λb(t) for t≧0.  (68)

[0330] The second regression filter has a regression coefficient κ_m,λb(t) register 98 value defined similarly to the first regression filter error signal values, i.e.:

[0331] κ_m,λb(t)={ρ_m,λb(t)/β_m(t)}; or  (69)

[0332] These values are used in conjunction with those intermediate variable values, signal values, register and register values defined in equations (46) through (64). These signals are calculated in an order defined by placing the additional signals immediately adjacent a similar signal for the wavelength λa.

[0333] For the constant saturation method, S_λb(t) is input to the second regression filter 80b.The output is then a good approximation to the primary signal s″_λb(t) or secondary signal s″_λb(t).

[0334] The addition of the second regression filter 80bdoes not substantially change the computer program subroutine represented by the flowchart of FIG. 9. Instead of an order update of the m^thstage of only one regression filter, an order update of the m^thstage of both regression filters 80aand 80bis performed. This is characterized by the plural designation in the “ORDER UPDATE OF m^thSTAGE OF REGRESSION FILTER(S)” activity block 180 in FIG. 9. Since the regression filters 80aand 80boperate independently, independent calculations can be performed in the reference processor and joint process estimator 60 adaptive noise canceler subroutine modeled by the flowchart of FIG. 9.

[0335] An alternative diagram for the joint process estimator of FIG. 10, using the QRD algorithm and having two regression filters is shown in FIG. 10a.This type of joint process estimator would be used for correlation cancellation using the QRD algorithm described in the Haykin book.

[0336] Once good approximations to the primary signal portions s″_λa(t) and s″_λb(t) or the secondary signal portion, n″_λa(t) and n″_λb(t), have been determined by the joint process estimator 60, the saturation of A₅in a volume containing A₅and A₆, for example, may be calculated according to various known methods. Mathematically, the approximations to the primary signals can be written in terms of λa and λb, as:

[0337] s″_λa(t)≈ε_5,λac₅x_5,6(t)+ε_6,λac₆x_5,6(t); and  (70)

[0338] s″_λb(t)≈ε_5,λbc₅x_5,6(t)+ε_6,λbc₆x_{5,6 (}t).  (71)

[0339] Equations (70) and (71) are equivalent to two equations having three unknowns, namely c₅(t), c₆(t) and x_5,6(t). The saturation can be determined by acquiring approximations to the primary or secondary signal portions at two different, yet proximate times t₁and t₂over which the saturation of A₅in the volume containing A₅and A₆and the saturation of A₃in the volume containing A₃and A₄does not change substantially. For example, for the primary signals estimated at times t₁and t₂:

[0340] s″_λa(t₁)≈ε_5,λac₅x_5,6(t₁)+ε_6,λac₆x_5,6(t₁)  (72)

[0341] s″_λb(t₁)≈ε_5,λbc₅x_5,6(t₁)+ε_6,λbc₆x_5,6(t₁)  (73)

[0342] s″_λa(t₂)≈ε_5,λac₅x_5,6(t₂)+ε_6,λac₆x_5,6(t₂)  (74)

[0343] s″_λb(t₂)≈ε_5,λbc₅x_5,6(t₂)+ε_6,λbc₆x_5,6(t₂)  (75)

[0344] Then, difference signals may be determined which relate the signals of equations (72) through (75), i.e.:

[0345] Δs_λa=s″_λa(t₁)−s″_λa(t₂)≈ε_5,λac₅Δx+ε_6,λac₆Δx;and  (76)

[0346] Δs_λb=s″_λb(t₁)−s″_λb(t₂)≈ε_5,λbc₅Δx+ε_,λbc₆Δx;  (77)

[0347] where Δx=x_5,6(t₁)−x_5,6(t₂). The average saturation at time t=(t₁+t₂)/2 is:

[0348] Saturation(t)=c₅(t)/[c₅(t)+c₆(t)]  (78)

[0349] $\begin{array}{cc}=\frac{{\epsilon }_{6,\lambda a}-{\epsilon }_{6,\lambda b}\left(\Delta s_{\lambda a}/{\Delta }_{\lambda b}\right)}{{\epsilon }_{6,\lambda a}-{\epsilon }_{5,\lambda a}-\left({\epsilon }_{6,\lambda b}-{\epsilon }_{5,\lambda b}\right)\left(\Delta s_{\lambda a}/\Delta s_{\lambda b}\right)}& \left(79\right)\end{array}$

[0350] It will be understood that the Ax term drops out from the saturation calculation because of the division. Thus, knowledge of the thickness of the primary constituents is not required to calculate saturation.

[0351] A specific example of a physiological monitor utilizing a processor of the present invention to determine a secondary reference n′(t) for input to a correlation canceler that removes erratic motion-induced secondary signal portions is a pulse oximeter. Pulse oximetry may also be performed utilizing a processor of the present invention to determine a primary signal reference s′(t) which may be used for display purposes or for input to a correlation canceler to derive information about patient movement and venous blood oxygen saturation.

[0352] A pulse oximeter typically causes energy to propagate through a medium where blood flows close to the surface for example, an ear lobe, or a digit such as a finger, a forehead or a fetus' scalp. An attenuated signal is measured after propagation through or reflected from the medium. The pulse oximeter estimates the saturation of oxygenated blood.

[0353] Freshly oxygenated blood is pumped at high pressure from the heart into the arteries for use by the body. The volume of blood in the arteries varies with the heartbeat, giving rise to a variation in absorption of energy at the rate of the heartbeat, or the pulse.

[0354] Oxygen depleted, or deoxygenated, blood is returned to the heart by the veins along with unused oxygenated blood. The volume of blood in the veins varies with the rate of breathing, which is typically much slower than the heartbeat. Thus, when there is no motion induced variation in the thickness of the veins, venous blood causes a low frequency variation in absorption of energy. When there is motion induced variation in the thickness of the veins, the low frequency variation in absorption is coupled with the erratic variation in absorption due to motion artifact.

[0355] In absorption measurements using the transmission of energy through a medium, two light emitting diodes (LED's) are positioned on one side of a portion of the body where blood flows close to the surface, such as a finger, and a photodetector is positioned on the opposite side of the finger. Typically, in pulse oximetry measurements, one LED emits a visible wavelength, preferably red, and the other LED emits an infrared wavelength. However, one skilled in the art will realize that other wavelength combinations could be used. The finger comprises skin, tissue, muscle, both arterial blood and venous blood, fat, etc., each of which absorbs light energy differently due to different absorption coefficients, different concentrations, different thicknesses, and changing optical pathlengths. When the patient is not moving, absorption is substantially constant except for the flow of blood. The constant attenuation can be determined and subtracted from the signal via traditional filtering techniques. When the patient moves, this causes perturbation such as changing optical pathlength due to movement of background fluids (e.g., venous blood having a different saturation than the arterial blood). Therefore, the measured signal becomes erratic. Erratic motion induced noise typically cannot be predetermined and/or subtracted from the measured signal via traditional filtering techniques. Thus, determining the oxygen saturation of arterial blood and venous blood becomes more difficult.

[0356] A schematic of a physiological monitor for pulse oximetry is shown in FIGS. 11-13. FIG. 11 depicts a general hardware block diagram of a pulse oximeter 299. A sensor 300 has two light emitters 301 and 302 such as LED's. One LED 301 emitting light of red wavelengths and another LED 302 emitting light of infrared wavelengths are placed adjacent a finger 310. A photodetector 320, which produces an electrical signal corresponding to the attenuated visible and infrared light energy signals is located opposite the LED's 301 and 302. The photodetector 320 is connected to front end analog signal conditioning circuity 330.

[0357] The front end analog signal conditioning circuitry 330 has outputs coupled to analog to digital conversion circuit 332. The analog to digital conversion circuitry 332 has outputs coupled to a digital signal processing system 334. The digital signal processing system 334 provides the desired parameters as outputs for a display 336. Outputs for display are, for example, blood oxygen saturation, heart rate, and a clean plethysmographic waveform.

[0358] The signal processing system also provides an emitter current control output 337 to a digital-to-analog converter circuit 338 which provides control information for light emitter drivers 340. The light emitter drivers 340 couple to the light emitters 301, 302. The digital signal processing system 334 also provides a gain control output 342 for the front end analog signal conditioning circuitry 330.

[0359] FIG 11aillustrates a preferred embodiment for the combination of the emitter drivers 340 and the digital to analog conversion circuit 338. As depicted in FIG 11a,the driver comprises first and second input latches 321, 322, a synchronizing latch 323, a voltage reference 324, a digital to analog conversion circuit 325, first and second switch banks 326, 327, first and second voltage to current converters 328, 329 and the LED emitters 301, 302 corresponding to the LED emitters 301, 302 of FIG. 11.

[0360] The preferred driver depicted in FIG. 11ais advantageous in that the present inventors recognized that much of the noise in the oximeter 299 of FIG. 11 is caused by the LED emitters 301, 302. Therefore, the emitter driver circuit of FIG. 11ais designed to minimize the noise from the emitters 301, 302. The first and second input latches 321, 324 are connected directly to the DSP bus. Therefore, these latches significantly minimizes the bandwidth (resulting in noise) present on the DSP bus which passes through to the driver circuitry of FIG. 11a.The output of the first and second input latches only changes when these latched detect their address on the DSP bus. The first input latch receives the setting for the digital to analog converter circuit 325. The second input latch receives switching control data for the switch banks 326, 327. The synchronizing latch accepts the synchronizing pulses which maintain synchronization between the activation of emitters 301, 302 and the analog to digital conversion circuit 332.

[0361] The voltage reference is also chosen as a low noise DC voltage reference for the digital to analog conversion circuit 325. In addition, in the present embodiment, the voltage reference has an lowpass output filter with a very low corner frequency (e.g., 1 Hz in the present embodiment). The digital to analog converter 325 also has a lowpass filter at its output with a very low corner frequency (e.g., 1 Hz). The digital to analog converter provides signals for each of the emitters 301, 302.

[0362] In the present embodiment, the output of the voltage to current converters 328, 329 are switched such that with the emitters 301, 302 connected in back-to-back configuration, only one emitter is active an any given time. In addition, the voltage to current converter for the inactive emitter is switched off at its input as well, such that it is completely deactivated. This reduces noise from the switching and voltage to current conversion circuitry. In the present embodiment, low noise voltage to current converters are selected (e.g., Op 27 Op Amps), and the feedback loop is configured to have a low pass filter to reduce noise. In the present embodiment, the low pass filtering function of the voltage to current converter 328, 329 has a corner frequency of just above 625 Hz, which is the switching speed for the emitters, as further discussed below. Accordingly, the preferred driver circuit of FIG. 11a,minimizes the noise of the emitters 301, 302.

[0363] In general, the red and infrared light emitters 301, 302 each emits energy which is absorbed by the finger 310 and received by the photodetector 320. The photodetector 320 produces an electrical signal which corresponds to the intensity of the light energy striking the photodetector 320. The front end analog signal conditioning circuitry 330 receives the intensity signals and filters and conditions these signals as further described below for further processing. The resultant signals are provided to the analog-to-digital conversion circuitry 332 which converts the analog signals to digital signals for further processing by the digital signal processing system 334. The digital signal processing system 334 utilizes the two signals in order to provide a what will be called herein a “saturation transform.” It should be understood, that for parameters other than blood saturation monitoring, the saturation transform could be better termed as a concentration transform, in-vivo transform, or the like, depending on the desired parameter. The term saturation transform is used to describe an operation which converts the sample data from time domain to saturation domain values as will be apparent from the discussion below. In the present embodiment, the output of the digital signal processing system 334 provides clean plethysmographic waveforms of the detected signals and provides values for oxygen saturation and pulse rate to the display 336.

[0364] It should be understood that in different embodiments of the present invention, one or more of the outputs may be provided. The digital signal processing system 334 also provides control for driving the light emitters 301, 302 with an emitter current control signal on the emitter current control output 337. This value is a digital value which is converted by the digital-to-analog conversion circuit 338 which provides a control signal to the emitter current drivers 340. The emitter current drivers 340 provide the appropriate current drive for the red emitter 301 and the infrared emitter 302. Further detail of the operation of the physiological monitor for pulse oximetry is explained below.

[0365] In the present embodiment, the light emitters are driven via the emitter current driver 340 to provide light transmission with digital modulation at 625 Hz. In the present embodiment, the light emitters 301, 302 are driven at a power level which provides an acceptable intensity for detection by the detector and for conditioning by the front end analog signal conditioning circuitry 330. Once this energy level is determined for a given patient by the digital signal processing system 334, the current level for the red and infrared emitters is maintained constant. It should be understood, however, that the current could be adjusted for changes in the ambient room light and other changes which would effect the voltage input to the front end analog signal conditioning circuitry 330. In the present invention, the red and infrared light emitters are modulated as follows: for one complete 625 Hz red cycle, the red emitter 301 is activated for the first quarter cycle, and off for the remaining three-quarters cycle; for one complete 625 Hz infrared cycle, the infrared light emitter 302 is activated for one quarter cycle and is off for the remaining three-quarters cycle. In order to only receive one signal at a time, the emitters are cycled on and off alternatively, in sequence, with each only active for a quarter cycle per 625 Hz cycle and a quarter cycle separating the active times.

[0366] The light signal is attenuated (amplitude modulated) by the pumping of blood through the finger 310 (or other sample medium). The attenuated (amplitude modulated) signal is detected by the photodetector 320 at the 625 Hz carrier frequency for the red and infrared light. Because only a single photodetector is used, the photodetector 320 receives both the red and infrared signals to form a composite time division signal.

[0367] The composite time division signal is provided to the front analog signal conditioning circuitry 330. Additional detail regarding the front end analog signal conditioning circuitry 330 and the analog to digital converter circuit 332 is illustrated in FIG. 12. As depicted in FIG. 12, the front end circuity 302 has a preamplifier 342, a high pass filter 344, an amplifier 346, a programmable gain amplifier 348, and a low pass filter 350. The preamplifier 342 is a transimpedance amplifier that converts the composite current signal from the photodetector 320 to a corresponding voltage signal, and amplifies the signal. In the present embodiment, the preamplifier has a predetermined gain to boost the signal amplitude for ease of processing. In the present embodiment, the source voltages for the preamplifier 342 are −15 VDC and +15 VDC. As will be understood, the attenuated signal contains a component representing ambient light as well as the component representing the infrared or the red light as the case may be in time. If there is light in the vicinity of the sensor 300 other than the red and infrared light, this ambient light is detected by the photodetector 320. Accordingly, the gain of the preamplifier is selected in order to prevent the ambient light in the signal from saturating the preamplifier under normal and reasonable operating conditions.

[0368] In the present embodiment, the preamplifier 342 comprises an Analog Devices AD743JR OpAmp. This transimpedance amplifier is particularly advantageous in that it exhibits several desired features for the system described, such as: low equivalent input voltage noise, low equivalent input current noise, low input bias current, high gain bandwidth product, low total harmonic distortion, high common mode rejection, high open loop gain, and a high power supply rejection ratio.

[0369] The output of the preamplifier 342 couples as an input to the high pass filter 344. The output of the preamplifier also provides a first input 346 to the analog to digital conversion circuit 332. In the present embodiment, the high pass filter is a single-pole filter with a corner frequency of about ½-1 Hz. However, the corner frequency is readily raised to about 90 Hz in one embodiment. As will be understood, the 625 Hz carrier frequency of the red and infrared signals is well above a 90 Hz corner frequency. The high-pass filter 344 has an output coupled as an input to an amplifier 346. In the present embodiment, the amplifier 346 comprises a unity gain amplifier. However, the gain of the amplifier 346 is adjustable by the variation of a single resistor. The gain of the amplifier 346 would be increased if the gain of the preamplifier 342 is decreased to compensate for the effects of ambient light.

[0370] The output of the amplifier 346 provides an input to a programmable gain amplifier 348. The programmable gain amplifier 348 also accepts a programming input from the digital signal processing system 334 on a gain control signal line 343. The gain of the programmable gain amplifier 348 is digitally programmable. The gain is adjusted dynamically at initialization or sensor placement for changes in the medium under test from patient to patient. For example, the signal from different fingers differs somewhat. Therefore, a dynamically adjustable amplifier is provided by the programmable gain amplifier 348 in order to obtain a signal suitable for processing.

[0371] The programmable gain amplifier is also advantageous in an alternative embodiment in which the emitter drive current is held constant. In the present embodiment, the emitter drive current is adjusted for each patient in order to obtain the proper dynamic range at the input of the analog to digital conversion circuit 332. However, changing the emitter drive current can alter the emitter wavelength, which in turn affects the end result in oximetry calculations. Accordingly, it would be advantageous to fix the emitter drive current for all patients. In an alternative embodiment of the present invention, the programmable gain amplifier can be adjusted by the DSP in order to obtain a signal at the input to the analog to digital conversion circuit which is properly within the dynamic range (+3 v to −3 v in the present embodiment) of the analog to digital conversion circuit 332. In this manner, the emitter drive current could be fixed for all patients, eliminating the wavelength shift due to emitter current drive changes.

[0372] The output of the programmable gain amplifier 348 couples as an input to a low-pass filter 350. Advantageously, the low pass filter 350 is a single-pole filter with a corner frequency of approximately 10 Khz in the present embodiment. This low pass filter provides anti-aliasing in the present embodiment.

[0373] The output of the low-pass filter 350 provides a second input 352 to the analog-to-digital conversion circuit 332. FIG. 12 also depicts additional defect of the analog-to-digital conversion circuit. In the present embodiment, the analog-to-digital conversion circuit 332 comprises a first analog-to-digital converter 354 and a second analog-to-digital converter 356. Advantageously, the first analog-to-digital converter 354 accepts input from the first input 346 to the analog-to-digital conversion circuit 332, and the second analog to digital converter 356 accepts input on the second input 352 to the analog-to-digital conversion circuitry 332.

[0374] In one advantageous embodiment, the first analog-to-digital converter 354 is a diagnostic analog-to-digital converter. The diagnostic task (performed by the digital signal processing system) is to read the output of the detector as amplified by the preamplifier 342 in order to determine if the signal is saturating the input to the high-pass filter 344. In the present embodiment, if the input to the high pass filter 344 becomes saturated, the front end analog signal conditioning circuits 330 provides a ‘0’ output. Alternatively, the first analog-to-digital converter 354 remains unused.

[0375] The second analog-to-digital converter 352 accepts the conditioned composite analog signal from the front end signal conditioning circuitry 330 and converts the signal to digital form. In the present embodiment, the second analog to digital converter 356 comprises a single-channel, delta-sigma converter. In the present embodiment, a Crystal Semiconductor CS5317-KS delta-sigma analog to digital converter is used. Such a converter is advantageous in that it is low cost, and exhibits low noise characteristics. More specifically, a delta-sigma converter consists of two major portions, a noise modulator and a decimation filter. The selected converter uses a second order analog delta-sigma modulator to provide noise shaping. Noise shaping refers to changing the noise spectrum from a flat response to a response where noise at the lower frequencies has been reduced by increasing noise at higher frequencies. The decimation filter then cuts out the reshaped, higher frequency noise to provide 16-bit performance at a lower frequency. The present converter samples the data 128 times for every 16 bit data word that it produces. In this manner, the converter provides excellent noise rejection, dynamic range and low harmonic distortion, that help in critical measurement situations like low perfusion and electrocautery.

[0376] In addition, by using a single-channel converter, there is no need to tune two or more channels to each other. The delta-sigma converter is also advantageous in that it is exhibits noise shaping, for improved noise control. An exemplary analog to digital converter is a Crystal Semiconductor CS5317. In the present embodiment, the second analog to digital converter 356 samples the signal at a 20 Khz sample rate. The output of the second analog to digital converter 356 provides data samples at 20 Khz to the digital signal processing system 334 (FIG. 11).

[0377] The digital signal processing system 334 is illustrated in additional detail in FIG. 13. In the present embodiment, the digital signal processing system comprises a microcontroller 360, a digital signal processor 362, a program memory 364, a sample buffer 366, a data memory 368, a read only memory 370 and communication registers 372. In the present embodiment, the digital signal processor 362 is an Analog Devices AD 21020. In the present embodiment, the microcontroller 360 comprises a Motorola 68HC05, with built in program memory. In the present embodiment, the sample buffer 366 is a buffer which accepts the 20 Khz sample data from the analog to digital conversion circuit 332 for storage in the data memory 368. In the present embodiment, the data memory 368 comprises 32 KWords (words being 40 bits in the present embodiment) of static random access memory

[0378] The microcontroller 360 is connected to the DSP 362 via a conventional JTAG Tap line. The microcontroller 360 transmits the boot loader for the DSP 362 to the program memory 364 via the Tap line, and then allows the DSP 362 to boot from the program memory 364. The boot loader in program memory 364 then causes the transfer of the operating instructions for the DSP 362 from the read only memory 370 to the program memory 364. Advantageously, the program memory 364 is a very high speed memory for the DSP 362.

[0379] The microcontroller 360 provides the emitter current control and gain control signals via the communications register 372.

[0380] FIGS. 14-20 depict functional block diagrams of the operations of the pulse oximeter 299 carried out by the digital signal processing system 334. The signal processing functions described below are carried out by the DSP 362 in the present embodiment with the microcontroller 360 providing system management. In the present embodiment, the operation is software/firmware controlled. FIG. 14 depicts a generalized functional block diagram for the operations performed on the 20 Khz sample data entering the digital signal processing system 334. As illustrated in FIG. 14, a demodulation, as represented in a demodulation module 400, is first performed. Decimation, as represented in a decimation module 402 is then performed on the resulting data. Certain statistics are calculated, as represented in a statistics module 404 and a saturation transform is performed, as represented in a saturation transform module 406, on the data resulting from the decimation operation. The data subjected to the statistics operations and the data subjected to the saturation transform operations are forwarded to saturation operations, as represented by a saturation calculation module 408 and pulse rate operations, as represented in a pulse rate calculation module 410.

[0381] In general, the demodulation operation separates the red and infrared signals from the composite signal and removes the 625 Hz carrier frequency, leaving raw data points. The raw data points are provided at 625 Hz intervals to the decimation operation which reduces the samples by an order of 10 to samples at 62.5 Hz. The decimation operation also provides some filtering on the samples. The resulting data is subjected to statistics and to the saturation transform operations in order to calculate a saturation value which is very tolerant to motion artifacts and other noise in the signal. The saturation value is ascertained in the saturation calculation module 408, and a pulse rate and a clean plethysmographic waveform is obtained through the pulse rate module 410. Additional detail regarding the various operations is provided in connection with FIGS. 15-21.

[0382] FIG. 15 illustrates the operation of the demodulation module 400. The modulated signal format is depicted in FIG. 15. One full 625 Hz cycle of the composite signal is depicted in FIG. 15 with the first quarter cycle being the active red light plus ambient light signal, the second quarter cycle being an ambient light signal, the third quarter cycle being the active infrared plus ambient light signal, and the fourth quarter cycle being an ambient light signal. As depicted in FIG. 15, with a 20 KHz sampling frequency, the single full cycle at 625 Hz described above comprises 32 samples of 20 KHz data, eight samples relating to red plus ambient light, eight samples relating to ambient light, eight samples relating to infrared plus ambient light, and finally eight samples related to ambient light.

[0383] Because the signal processing system 334 controls the activation of the light emitters 300, 302, the entire system is synchronous. The data is synchronously divided (and thereby demodulated) into four 8-sample packets, with a time division demultiplexing operation as represented in a demultiplexing module 421. One eight-sample packet 422 represents the red plus ambient light signal; a second eight-sample packet 424 represents an ambient light signal; a third eight-sample packet 426 represents the attenuated infrared light plus ambient light signal; and a fourth eight-sample packet 428 represents the ambient light signal. A select signal synchronously controls the demultiplexing operation so as to divide the time-division multiplexed composite signal at the input of the demultiplexer 421 into its four subparts.

[0384] A sum of the last four samples from each packet is then calculated, as represented in the summing operations 430, 432, 434, 436 of FIG. 15. In the present embodiment, the last four samples are used because a low pass filter in the analog to digital converter 356 of the present embodiment has a settling time. Thus, collecting the last four samples from each 8-sample packet allows the previous signal to clear. This summing operation provides an integration operation which enhances noise immunity. The sum of the respective ambient light samples is then subtracted from the sum of the red and infrared samples, as represented in the subtraction modules 438, 440. The subtraction operation provides some attenuation of the ambient light signal present in the data. In the present embodiment, it has been found that approximately 20 dB attenuation of the ambient light is provided by the operations of the subtraction modules 438, 440. The resultant red and infrared sum values are divided by four, as represented in the divide by four modules 442, 444. Each resultant value provides one sample each of the red and infrared signals at 625 Hz.

[0385] It should be understood that the 625 Hz carrier frequency has been removed by the demodulation operation 400. The 625 Hz sample data at the output of the demodulation operation 400 is sample data without the carrier frequency. In order to satisfy Nyquist sampling requirements, less than 20 Hz is needed (understanding that the human pulse is about 25 to 250 beats per minute, or about 0.4 Hz-4 Hz) Accordingly, the 625 Hz resolution is reduced to 62.5 Hz in the decimation operation.

[0386] FIG. 16 illustrates the operations of the decimation module 402. The red and infrared sample data is provided at 625 Hz to respective red and infrared buffer/filters 450, 452. In the present embodiment, thug red and infrared buffer/filters are 519 samples deep. Advantageously, the buffer filters 450, 452 function as continuous first-in, first-out buffers. The 519 samples are subjected to low-pass filtering. Preferably, the low-pass filtering has a cutoff frequency of approximately 7.5 Hz with attenuation of approximately −110 dB. The buffer/filters 450, 452 form a Finite Impulse Response (FIR) filter with coefficients for 519 taps. In order to reduce the sample frequency by ten, the low-pass filter calculation is performed every ten samples, as represented in respective red and infrared decimation by 10 modules 454, 456. In other words, with the transfer of each new ten samples into the buffer/filters 450, 452, a new low pass filter calculation is performed by multiplying the impulse response (coefficients) by the 519 filter taps. Each filter calculation provides one output sample for respective red and infrared output buffers 458, 460. In the present embodiment, the red and infrared output buffers 458, 460 are also continuous FIFO buffers that hold 570 samples of data. The 570 samples provide respective infrared and red samples or packets (also denoted “snapshot” herein) of samples. As depicted in FIG. 14, the output buffers provide sample data for the statistics operation module 404, saturation transform module 406, and the pulse rate module 410.

[0387] FIG. 17 illustrates additional functional operation details of the statistics module 404. In summary, the statistics module 404 provides first order oximetry calculations and RMS signal values for the red and infrared channels. The statistics module also provides a cross-correlation output which indicates a cross-correlation between the red and infrared signals.

[0388] As represented in FIG. 17, the statistics operation accepts two packets of samples (e.g., 570 samples at 62.5 Hz in the present embodiment) representing the attenuated infrared and red signals, with the carrier frequency removed. The respective packets for infrared and red signals are normalized with a log function, as represented in the Log modules 480, 482. The normalization is followed by removal of the DC portion of the signals, as represented in the DC Removal modules 484, 486. In the present embodiment, the DC removal involves ascertaining the DC value of the first one of the samples (or the mean of the first several or the mean of an entire snapshot) from each of the respective red and infrared snapshots, and removing this DC value from all samples in the respective packets.

[0389] Once the DC signal is removed, the signals are subjected to bandpass filtering, as represented in red and infrared Bandpass Filter modules 488, 490. In the present embodiment, with 570 samples in each packet, the bandpass filters are configured with 301 taps to provide a FIR filter with a linear phase response and little or no distortion. In the present embodiment, the bandpass filter has a pass band from 34 beats/minute to 250 beats/minute. The 301 taps slide over the 570 samples in order to obtain 270 filtered samples representing the filtered red signal and 270 filtered samples representing the filtered infrared signal. In an ideal case, the bandpass filters 488, 490 remove the DC in the signal. However, the DC removal operations 484, 486 assist in DC removal in the present embodiment.

[0390] After filtering, the last 120 samples from each packet (of now 270 samples in the present embodiment) are selected for further processing as represented in Select Last 120 Samples modules 492, 494. The last 120 samples are selected because, in the present embodiment, the first 150 samples fall within the settling time for the Saturation Transfer module 406, which processes the same data packets, as further discussed below.

[0391] Conventional saturation equation calculations are performed on the red and infrared 120-sample packets. In the present embodiment, the conventional saturation calculations are performed in two different ways. For one calculation, the 120-sample packets are processed to obtain their overall RMS value, as represented in the first red and infrared RMS modules 496, 498. The resultant RMS values for red and infrared signals provide input values to a first RED_RMS/IR_RMS ratio operation 500, which provides the RMS red value to RMS infrared value ratio as an input to a saturation equation module 502. As well understood in the art, the ratio of the intensity of red to infrared attenuated light as detected for known red and infrared wavelengths (typically λ_red=650 nm and λ_IR=910 nm) relates to the oxygen saturation of the patient. Accordingly, the saturation equation module 502 represents a conventional look-up table or the like which, for predetermined ratios, provides known saturation values at its output 504. The red and infrared RMS values are also provided as outputs of the statistics operations module 404.

[0392] In addition to the conventional saturation operation 502, the 120-sample packets are subjected to a cross-correlation operation as represented in a first cross-correlation module 506. The first cross-correlation module 506 determines if good correlation exists between the infrared and red signals. This cross correlation is advantageous for detecting defective or otherwise malfunctioning detectors. The cross correlation is also advantageous in detecting when the signal model (i.e., the model of Equations (1)-(3)) is satisfied. If correlation becomes too low between the two channels, the signal model is not met. In order to determine this, the normalized cross correlation can be computed by the cross-correlation module 506 for each snapshot of data. One such correlation function is as follows: $\frac{\sum S_1{S}_2}{\sqrt{\sum S_1^2\sum S_2^2}}$

[0393] If the cross correlation is too low, the oximeter 299 provides a warning (e.g., audible, visual, etc.) to the operator. In the present embodiment, if a selected snapshot yields a normalized correlation of less than 0.75, the snapshot does not qualify. Signals which satisfy the signal model will have a correlation greater than the threshold.

[0394] The red and infrared 120-sample packets are also subjected to a second saturation operation and cross correlation in the same manner as described above, except the 120 samples are divided into 5 equal bins of samples (i.e., 5 bins of 24 samples each). The RMS, ratio, saturation, and cross correlation operations are performed on a bin-by-bin basis. These operations are represented in the Divide Into Five Equal Bins modules 510, 512, the second red and infrared RMS modules 514, 516, the second RED-RMS/IR-RMS ratio module 518, the second saturation equation module 520 and the second cross correlation module 522 in FIG. 17.

[0395] FIG. 18 illustrates additional detail regarding the saturation transform module 406 depicted in FIG. 14. As illustrated in FIG. 18, the saturation transform module 406 comprises a reference processor 530, a correlation canceler 531, a master power curve module 554, and a bin power curve module 533. The saturation transform module 406 can be correlated to FIG. 7awhich has a reference processor 26 and a correlation canceler 27 and an integrator 29 to provide a power curve for separate signal coefficients as depicted in FIG. 7c.The saturation transform module 406 obtains a saturation spectrum from the snapshots of data. In other words, the saturation transform 406 provides information of the saturation values present in the snapshots.

[0396] As depicted in FIG. 18, the reference processor 530 for the saturation transform module 406 has a saturation equation module 532, a reference generator module 534, a DC removal module 536 and a bandpass filter module 538. The red and infrared 570-sample packets from the decimation operation are provided to the reference processor 530. In addition, a plurality of possible saturation values (the “saturation axis scan”) are provided as input to the saturation reference processor 530. In the present embodiment, 117 saturation values are provided as the saturation axis scan. In a preferred embodiment, the 117 saturation values range uniformly from a blood oxygen saturation of 34.8 to 105.0. Accordingly, in the present embodiment, the 117 saturation values provide an axis scan for the reference processor 530 which generates a reference signal for use by the correlation canceler 531. In other words, the reference processor is provided with each of the saturation values, and a resultant reference signal is generated corresponding to the saturation value. The correlation canceler is formed by a joint process estimator 550 and a low pass filter 552 in the present embodiment.

[0397] It should be understood that the scan values could be chosen to provide higher or lower resolution than 117 scan values. The scan values could also be non-uniformly spaced.

[0398] As illustrated in FIG. 18, the saturation equation module 532 accepts the saturation axis scan values as an input and provides a ratio “r_n” as an output. In comparison to the general discussion of FIGS. 7a-7c,this ratio “r_n” corresponds to the plurality of scan value discussed above in general. The saturation equation simply provides a known ratio “r” (red/infrared) corresponding to the saturation value received as an input.

[0399] The ratio “r_n” is provided as an input to the reference generator 534, as are the red and infrared sample packets. The reference generator 534 multiplies either the red or infrared samples by the ratio “r_n” and subtracts the value from the infrared or red samples, respectively. For instance, in the present embodiment, the reference generator 534 multiplies the red samples by the ratio “r_n” and subtracts this value from the infrared samples. The resulting values become the output of the reference generator 534. This operation is completed for each of the saturation scan values (e.g., 117 possible values in the present embodiment). Accordingly, the resultant data can be described as 117 reference signal vectors of 570 data points each, hereinafter referred to as the reference signal vectors. This data can be stored in an array or the like.

[0400] In other words, assuming that the red and infrared sample packets represent the red S_red(t) and infrared S_IR(t) measured signals which have primary s(t) and secondary n(t) signal portions, the output of the reference generator becomes the secondary reference signal n′(t), which complies with the signal model defined above, as follows:

[0401] n′(t)=S_ir(t)−r_nS_red(t)

[0402] In the present embodiment, the reference signal vectors and the infrared signal are provided as input to the DC removal module 536 of the reference processor 530. The DC removal module 536, like the DC removal modules 484, 486 in the statistics module 404, ascertains the DC value of the first of the samples for the respective inputs (or mean of the first several or all samples in a packet) and subtracts the respective DC baseline from the sample values. The resulting sample values are subjected to a bandpass filter 538.

[0403] The bandpass filter 538 of the reference processor 530 performs the same type of filtering as the bandpass filters 488, 490 of the statistics module 404. Accordingly, each set of 570 samples subjected to bandpass filtering results in 270 remaining samples. The resulting data at a first output 542 of the bandpass filter 538 is one vector of 270 samples (representing the filtered infrared signal in the present embodiment). The resulting data at a second output 540 of the bandpass filter 538, therefore, is 117 reference signal vectors of 270 data points each, corresponding to each of the saturation axis scan values provided to the saturation reference processor 530.

[0404] It should be understood that the red and infrared sample packets may be switched in their use in the reference processor 530. In addition, it should be understood that the DC removal module 536 and the bandpass filter module 538 can be executed prior to input of the data to the reference processor 530 because the calculations performed in the reference processor are linear. This results in a significant processing economy.

[0405] The outputs of the reference processor 530 provide first and second inputs to a joint process estimator 550 of the type described above with reference to FIG. 8. The first input to the joint process estimator 550 is the 270-sample packet representing the infrared signal in the present embodiment. This signal contains primary and secondary signal portions. The second input to the joint process estimator is the 117 reference signal vectors of 270 samples each.

[0406] The joint process estimator also receives a lambda input 543, a minimum error input 544 and a number of cells configuration input 545. These parameters are well understood in the art. The lambda parameter is often called the “forgetting parameter” for a joint process estimator. The lambda input 543 provides control for the rate of cancellation for the joint process estimator. In the present embodiment, lambda is set to a low value such as 0.8. Because statistics of the signal are non-stationary, a low value improves tracking. The minimum error input 544 provides an initialization parameter (conventionally known as the “initialization value”) for the joint process estimator 550. In the present embodiment, the minimum error value is 10⁻⁶. This initialization parameter prevents the joint process estimator 500 from dividing by zero upon initial calculations. The number of cells input 545 to the joint process estimator 550 configures the number of cells for the joint process estimator. In the present embodiment, the number of cells for the saturation transform operation 406 is six. As well understood in the art, for each sine wave, the joint process estimator requires two cells. If there are two sine waves in the 35-250 beats/minute range, six cells allows for the two heart beat sine waves and one noise sine wave.

[0407] The joint process estimator 550 subjects the first input vector on the first input 542 to a correlation cancellation based upon each of the plurality of reference signal vectors provided in the second input 540 to the correlation canceler 531 (all 117 reference vectors in sequence in the present embodiment). The correlation cancellation results in a single output vector for each of the 117 reference vectors. Each output vector represents the information that the first input vector and the corresponding reference signal vector do not have in common. The resulting output vectors are provided as an output to the joint process estimator, and subjected to the low pass filter module 552. In the present embodiment, the low pass filter 552 comprises a FIR filter with 25 taps and with a corner frequency of 10 Hz with the sampling frequency of 62.5 Hz (i.e., at the decimation frequency).

[0408] The joint process estimator 550 of the present embodiment has a settling time of 150 data points. Therefore, the last 120 data points from each 270 point output vector are used for further processing. In the present embodiment, the output vectors are further processed together as a whole, and are divided into a plurality of bins of equal number of data points. As depicted in FIG. 18, the output vectors are provided to a master power curve module 554 and to a Divide into five Equal Bins module 556. The Divide into Five Equal Bins module 556 divides each of the output vectors into five bins of equal number of data points (e.g., with 120 data points per vector, each bin has 24 data points). Each bin is then provided to the Bin Power Curves module 558.

[0409] The Master Power Curve module 554 performs a saturation transform as follows: for each output vector, the sum of the squares of the data points is ascertained. This provides a sum of squares value corresponding to each output vector (each output vector corresponding to one of the saturation scan values). These values provide the basis for a master power curve 555, as further represented in FIG. 22. The horizontal axis of the power curve represents the saturation axis scan values and the vertical axis represents the sum of squares value (or output energy) for each output vector. In other words, as depicted in FIG. 22, each of the sum of squares could be plotted with the magnitude of the sum of squares value plotted on the vertical “energy output” axis at the point on the horizontal axis of the corresponding saturation scan value which generated that output vector. This results in a master power curve 558, an example of which is depicted in FIG. 22. This provides a saturation transform in which the spectral content of the attenuated energy is examined by looking at every possible saturation value and examining the output value for the assumed saturation value. As will be understood, where the first and second inputs to the correlation canceler 531 are mostly correlated, the sum of squares for the corresponding output vector of the correlation canceler 531 will be very low. Conversely, where the correlation between the first and second inputs to the correlation canceler 531 are not significantly correlated, the sum of squares of the output vector will be high. Accordingly, where the spectral content of the reference signal and the first input to the correlation canceler are made up mostly of physiological (e.g., movement of venous blood due to respiration) and non-physiological (e.g., motion induced) noise, the output energy will be low. Where the spectral content of the reference signal and the first input to the correlation canceler are not correlated, the output energy will be much higher.

[0410] A corresponding transform is completed by the Bin Power Curves module 558, except a saturation transform power curve is generated for each bin. The resulting power curves are provided as the outputs of the saturation transform module 406.

[0411] In general, in accordance with the signal model of the present invention, there will be two peaks in the power curves, as depicted in FIG. 22. One peak corresponds to the arterial oxygen saturation of the blood, and one peak corresponds to the venous oxygen concentration of the blood. With reference to the signal model of the present invention, the peak corresponding to the highest saturation value (not necessarily the peak with the greatest magnitude) corresponds to the proportionality coefficient r_a. In other words, the proportionality coefficient r_acorresponds to the red/infrared ratio which will be measured for the arterial saturation. Similarly, peak that corresponds to the lowest saturation value (not necessarily the peak with the lowest magnitude) will generally correspond to the venous oxygen saturation, which corresponds to the proportionality coefficient r_vin the signal model of the present invention. Therefore, the proportionality coefficient r_vwill be a red/infrared ratio corresponding to the venous oxygen saturation.

[0412] In order to obtain arterial oxygen saturation, the peak in the power curves corresponding to the highest saturation value could be selected. However, to improve confidence in the value, further processing is completed. FIG. 19 illustrates the operation of the saturation calculation module 408 based upon the output of the saturation transform module 406 and the output of the statistics module 404. As depicted in FIG. 19, the bin power curves and the bin statistics are provided to the saturation calculation module 408. In the present embodiment, the master power curves are not provided to the saturation module 408 but can be displayed for a visual check on system operation. The bin statistics contain the red and infrared RMS values, the seed saturation value, aid a value representing the cross-correlation between the red and infrared signals from the statistics module 404.

[0413] The saturation calculation module 408 first determines a plurality of bin attributes as represented by the Compute Bin Attributes module 560. The Compute Bin Attributes module 560 collects a data bin from the information from the bin power curves and the information from the bin statistics. In the present embodiment, this operation involves placing the saturation value of the peak from each power curve corresponding to the highest saturation value in the data bin. In the present embodiment, the selection of the highest peak is performed by first computing the first derivative of the power curve in question by convolving the power curve with a smoothing differentiator filter function. In the present embodiment, the smoothing differentiator filter function (using a FIR filter) has the following coefficients:

[0414] 0.014964670230367

[0415] 0.098294046682706

[0416] 0.204468276324813

[0417] 2.717182664241813

[0418] 5.704485606695227

[0419] 0.000000000000000

[0420] −5.704482606695227

[0421] −2.717182664241813

[0422] −0.204468276324813

[0423] −0.098294046682706

[0424] −0.014964670230367

[0425] This filter performs the differentiation and smoothing. Next, each point in the original power curve in question is evaluated and determined to be a possible peak if the following conditions are met: (1) the point is at least 2% of the maximum value in the power curve; (2) the value of the first derivative changes from greater than zero to less than or equal to zero. For each point that is found to be a possible peak, the neighboring points are examined and the largest of the three points Ls considered to be the true peak.

[0426] The peak width for these selected peaks is also calculated. The peak width of a power curve in question is computed by summing all the points in the power curve and subtracting the product of the minimum value in the power curve and the number of points in the power curve. In the present embodiment, the peak width calculation is applied to each of the bin power curves. The maximum value is selected as the peak width.

[0427] In addition, the infrared RMS value from the entire snapshot, the red RMS value, the seed saturation value for each bin, and the cross correlation between the red and infrared signals from the statistics module 404 are also placed in the data bin. The attributes are then used to determine whether the data bin consists of acceptable data, as represented in a Bin Qualifying Logic module 562.

[0428] If the correlation between the red and infrared signals is too low, the bin is discarded. If the saturation value of the selected peak for a given bin is lower than the seed saturation for the same bin, the peak is replaced with the seed saturation value. If either red or infrared RMS value is below a very small threshold, the bins are all discarded, and no saturation value is provided, because the measured signals are considered to be too small to obtain meaningful data. If no bins contain acceptable data, the exception handling module 563 provides a message to the display 336 that the data is erroneous.

[0429] If some bins qualify, those bins that qualify as having acceptable data are selected, and those that do not qualify are replaced with the average of the bins that are accepted. Each bin is given a time stamp in order to maintain the time sequence. A voter operation 565 examines each of the bins and selects the three highest saturation values. These values are forwarded to a clip and smooth operation 566.

[0430] The clip and smooth operation 566 basically performs averaging with a low pass filter. The low pass filter provides adjustable smoothing as selected by a Select Smoothing Filter module 568. The Select Smoothing Filter module 568 performs its operation based upon a confidence determination performed by a High Confidence Test module 570. The high confidence test is an examination of the peak width for the bin power curves. The width of the peaks provides some indication of motion by the patient—wider peaks indicating motion. Therefore, if the peaks are wide, the smoothing filter is slowed down. If peaks are narrow, the smoothing filter speed is increased. Accordingly, the smoothing filter 566 is adjusted based on the confidence level. The output of the clip and smooth module 566 provides the oxygen saturation values in accordance with the present invention.

[0431] In the presently preferred embodiment, the clip and smooth filter 566 takes each new saturation value and compares it to the current saturation value. If the magnitude of the difference is less than 16 (percent oxygen saturation) then the value is pass. Otherwise, if the new saturation value is less than the filtered saturation value, the new saturation value is changed to 16 less than the filtered saturation value. If the new saturation value is greater than the filtered saturation value, then the new saturation value is changed to 16 more than the filtered saturation value.

[0432] During high confidence (no motion), the smoothing filter is a simple one-pole or exponential smoothing filter which is computed as follows:

[0433] y(n)=0.6*x(n)+0.4*y(n−1)

[0434] where x(n) is the clipped new saturation value, and y(n) is the filtered saturation value.

[0435] During motion condition, a three-pole IIR (infinite impulse response) filter is used. Its characteristics are controlled by three time constants t_a, t_b, and t_cwith values of 0.985, 0.900, and 0.94 respectively. The coefficients for a direct form I, IIR filter are computed from these time constants using the following relationships:

[0436] a₀=0

[0437] a₁=t_b+(t_c)(t_a+t_b)

[0438] a₂=(−t_b)(t_c)(t_a+t_b+(t_c)(t_a))

[0439] a₃=(t_b)²(t_c)²(t_a)