Signal processing apparatus

[0001] This application is a continuation of U.S. patent application Ser. No. 10/779,033, filed Feb. 13, 2004, which is a continuation of U.S. patent application Ser. No. 09/111,604, filed Jul. 7, 1998, which is a continuation of U.S. patent application Ser. No. 08/943,511, filed Oct. 6, 1997, now U.S. Pat. No. 6,263,222, which is a continuation of U.S. patent application Ser. No. 08/572,488, filed Dec. 14, 1995, now U.S. Pat. No. 5,685,299, which is a continuation of U.S. application Ser. No. 08/132,812, filed on Oct. 6, 1993, now U.S. Pat. No. 5,490,505, which is a continuation-in-part of U.S. patent application Ser. No. 07/666,060, filed Mar. 7, 1991, now abandoned. The present application incorporates each of the foregoing disclosures herein by reference.

[0002] 1. Field of the Invention

[0003] 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 and a secondary signal, for the removal or derivation of either the primary or secondary signal when little is known about either of these components. The present invention also relates to the use of a novel processor which in conjunction with a correlation canceler, such as an adaptive noise canceler, produces primary and/or secondary signals. The present invention is especially useful for physiological monitoring systems including blood oxygen saturation.

[0004] 2. Description of the Related Art

[0005] 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. 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 could be used 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) exit at a fixed frequency(s).

[0006] 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 totally ineffective in extracting either the primary or secondary signal. If, however, a description of either the primary or secondary signal portion can be made available correlation canceling, such as adaptive noise canceling, can be employed to remove either the primary or secondary signal portion of the signal leaving the other portion available for measurement.

[0007] Correlation cancelers, such as adaptive noise cancelers, dynamically change their transfer function to adapt to and remove either the primary or secondary signal portions of a composite signal. Correlation cancelers require either a secondary reference or a primary reference which is correlated to either the secondary signal or the primary signal portions only. The reference signals are not necessarily a representation of the primary or secondary signal portions, but have a frequency spectrum which is similar to that of the primary or secondary signal portions. In many cases, it requires considerable ingenuity to determine a reference signal since nothing is usually known a priori about the secondary and/or primary signal portions.

[0008] One area where composite 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 apparatuses generally measure 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, heart rate, respiration rate, 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 breathalyzer testing, drug testing, cholesterol testing, glucose testing, arterial carbon dioxide testing, protein testing, and carbon monoxide testing, for example. Complications arising in these measurements are often due to motion of the patient, both external and internal (muscle movement, for example), during the measurement process.

[0009] Knowledge of physiological systems, such as the amount of oxygen in a patient's blood, can be critical, for example during surgery. These data can be determined by a lengthy invasive procedure of extracting and testing matter, such as blood, from a patient, or by more expedient, non-invasive measures. Many types of non-invasive measurements can be made by using the known properties of energy attenuation as a selected form of energy passes through a medium.

[0010] Energy is caused to be incident on a medium either derived from or contained within a patient and the amplitude of transmitted or reflected energy is then measured. The amount of attenuation of the incident energy caused by the medium is strongly dependent on the thickness and composition of the medium through which the energy must pass as well as the specific form of energy selected. Information about a physiological system can be derived from data taken from the attenuated signal of the incident energy transmitted through the medium if either the primary or secondary signal of the composite measurement signal can be removed. However, non-invasive measurements often do not afford the opportunity to selectively observe the interference causing either the primary or secondary signal portions, making it difficult to extract either one of them from the composite signal.

[0011] The primary and/or secondary signal portions often originate from both AC and/or DC sources. The DC portions are caused by transmission of the energy through differing media which are of relatively constant thickness within the body, such as bone, tissue, skin, blood, etc. These portions are easy to remove from a composite signal. The AC components are caused by physiological pulsations or when differing media being measured are perturbed and thus, change in thickness while the measurement is being made. Since most materials in and derived from the body are easily compressed, the thickness of such matter changes if the patient moves during a non-invasive physiological measurement. Patient movement, muscular movement and vessel movement, can cause the properties of energy attenuation to vary erratically. Traditional signal filtering techniques are frequently totally ineffective and grossly deficient in removing these motion induced effects from a signal. The erratic or unpredictable nature of motion induced signal components is the major obstacle in removing or deriving them. Thus, presently available physiological monitors generally become totally inoperative during time periods when the measurement site is perturbed.

[0012] 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 tissue 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 pressure or blood gas saturation measurements, for example. 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 waves in FIG. 1.

[0013] 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.

[0014] 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 hide the primary plethysmographic signal s. It is easy to see how even small variations in amplitude make it difficult to distinguish the primary signal s in the presence of a secondary signal component n.

[0015] A specific example of a blood gas monitoring apparatus is a pulse oximeter which 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. 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 signal portions mostly due to venous blood, or motion artifacts, to the plethysmographic waveform illustrated in FIG. 3. It is these motion artifacts which must be removed from the measured signal for the oximeter to continue the measurement of arterial blood oxygen saturation, even during periods when the patient moves. It is also these motion artifacts which must be derived from the measured signal for the oximeter to obtain an estimate of venous blood oxygen saturation. Once the signal components due to either arterial blood or venous blood is known, its corresponding oxygen saturation may be determined.

[0016] This invention is an improvement of U.S. patent application Ser. No. 07/666,060 filed Mar. 7, 1991 and entitled Signal Processing Apparatus and Method, which earlier application has been assigned to the assignee of the instant application. The invention is a signal processor which acquires a first signal and a second signal that is correlated to the first 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.

[0017] 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. The remaining secondary signal portions from the first and second measured signals are combined to form the secondary reference. This secondary reference is correlated to the secondary signal portion of each of the first and second measured signals.

[0018] The secondary reference is then 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. 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 a reference signal. The output of the correlation canceler is a good approximation to the desired signal with the undesired component removed.

[0019] 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 remaining primary signal portions from the first and second measured signals are combined to form the primary reference. 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.

[0020] Physiological monitors can often advantageously employ 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.

[0021] One physiological monitoring apparatus which can advantageously incorporate the features of 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 gas saturation measurements, etc. A specific example of such a use is in pulse oximetry which determines the saturation of oxygen in the blood. In this configuration, we define the primary portion of the signal to be 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. We define the secondary portion of the signal to be that which is usually considered to be noise. This portion of the signal is related to the venous blood contribution to attenuation of energy as it passes through the body. Patient movement causes this component to flow in an unpredictable manner, causing unpredictable attenuation and corrupting the otherwise periodic plethysmographic waveform. Respiration also causes secondary or noise component to vary, although typically at a much lower frequency than the patients pulse rate.

[0022] 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 and secondary 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.

[0023] Next, a processor 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 the 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.

[0024] 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.

[0025] One aspect of the present invention is a signal processor comprising a detector for receiving a first signal which travels along a first propagation path and a second signal which travels along a second propagation path wherein a portion of the first and second propagation paths are located in a propagation medium. The first signal has a first primary signal portion and a first secondary signal portion and the second signal has a second primary signal portion and a second secondary signal portion. The first and second secondary signal portions are a result of a change of the propagation medium. This aspect of the invention additionally comprises a reference processor having an input for receiving the first and second signals. The processor is adapted to combine the first and second signals to generate a secondary reference having a significant component which is a function of the first and said second secondary signal portions. The processor may also be adapted to combine the first and second signals to generate a primary reference having a significant component which is a function of the first and second primary signal portions

[0026] The above described aspect of the present invention may further comprise a signal processor for receiving the secondary reference signal and the first signal and for deriving therefrom an output signal having a significant component which is a function of the first primary signal portion of the first signal. Alternatively, the above described aspect of the present invention may further comprise a signal processor for receiving the secondary reference signal and the second signal and for deriving therefrom an output signal having a significant component which is a function of the second primary signal portion of the second signal. Alternatively, the above described aspect of the present invention may further comprise a signal processor for receiving the primary reference and the first signal and for deriving therefrom an output signal having a significant component which is a function of the first secondary signal portion of the signal of the first signal. Alternatively, the above described aspect of the present invention may further comprise a signal processor for receiving the primary reference and the second signal and for deriving therefrom an output signal having a significant component which is a function of the second secondary signal portion of the second signal. The signal processor may comprise a correlation canceler, such as an adaptive noise canceler. The adaptive noise canceler may comprise a joint process estimator having a least-squares-lattice predictor and a regression filter.

[0027] The detector in the aspect of the signal processor of the present invention described above may further comprise a sensor for sensing a physiological function. The sensor may comprise a light or other electromagnetic sensitive device. Additionally, the present invention may further comprise a pulse oximeter for measuring oxygen saturation in a living organism. The present invention may further comprise an electrocardiograph.

[0028] Another aspect of the present invention is a physiological monitoring apparatus comprising a detector for receiving a first physiological measurement signal which travels along a first propagation path and a second physiological measurement signal which travels along a second propagation path. A portion of the first and second propagation paths being located in the same propagation medium. The first signal has a first primary signal portion and a first secondary signal portion and the second signal has a second primary signal portion and a second secondary signal portion. The physiological monitoring apparatus further comprises a reference processor having an input for receiving the first and second signals. The processor is adapted to combine the first and second signals to generate a secondary reference signal having a significant component which is a function of the first and the second secondary signal portions. Alternatively, the processor may be adapted to combine the first and second signals to generate a primary reference having a component which is a function of the first and second primary signal portions.

[0029] The physiological monitoring apparatus may further comprise a signal processor for receiving the secondary reference and the first signal and for deriving therefrom an output signal having a significant component which is a function of the first primary signal portion of the first signal. Alternatively, the physiological monitoring apparatus may further comprise a signal processor for receiving the secondary reference and the second signal and for deriving therefrom an output signal having a significant component which is a function of the second primary signal portion of the second signal. Alternatively, the physiological monitoring apparatus may further comprise a signal processor for receiving the primary reference and the first signal and deriving therefrom an output signal having a significant component which is a function of the first secondary signal portion of the first signal. Alternatively, the physiological monitoring apparatus may further comprise a signal processor for receiving the primary reference and the second signal and deriving therefrom an output signal having a significant component which is a function of the second secondary signal portion of the second signal.

[0030] A further aspect of the present invention is an apparatus for measuring a blood constituent comprising an energy source for directing a plurality of predetermined wavelengths of electromagnetic energy upon a specimen and a detector for receiving the plurality of predetermined wavelengths of electromagnetic energy from the specimen. The detector produces electrical signals corresponding to the predetermined wavelengths in response to the electromagnetic energy. At least two of the electrical signals are used each having a primary signal portion and an secondary signal portion. Additionally, the apparatus comprises a reference processor having an input for receiving the electrical signals. The processor is configured to combine said electrical signals to generate a secondary reference having a significant component which is derived from the secondary signal portions. Alternatively, the processor may be configured to combine said signals to generate a primary reference having a significant component which is derived from the primary signal portions.

[0031] This aspect of the present invention may further comprise a signal processor for receiving the secondary reference and one of the two electrical signals and for deriving therefrom an output signal having a significant component which is a function of the primary signal portion of one of the two electrical signals. Another aspect of the present invention may further comprise a signal processor for receiving the primary reference and one of the two electrical signals and for deriving therefrom an output signal having a significant component which is a function of the secondary signal portion of one of the two electrical signals. This may be accomplished by use of a correlation canceler, such as an adaptive noise canceler, in the signal processor which may employ a joint process estimator having a least-squares-lattice predictor and a regression filter.

[0032] Yet another aspect of the present invention is a blood gas monitor for non-invasively measuring a blood constituent in a body comprising a light source for directing at least two predetermined wavelengths of light upon a body and a detector for receiving the light from the body. The detector, in response to the light from the body, produces at least two electrical signals corresponding to the at least two predetermined wavelengths of light. The at least two electrical signals each have a primary signal portion and a secondary signal portion. The blood oximeter further comprises a reference processor having an input for receiving the at least two electrical signals. The processor is adapted to combine the at least two electrical signals to generate a secondary reference with a significant component which is derived from the secondary signal portions. The blood oximeter may further comprise a signal processor for receiving the secondary reference and the two electrical signals and for deriving therefrom at least two output signals which are substantially equal, respectively, to the primary signal portions of the electrical signals. Alternatively, the reference processor may be adapted to combine the at least two electrical signals to generate a primary reference with a significant component which is derived from the primary signal portions. The blood oximeter may further comprise a signal processor for receiving the primary reference and the two electrical signals and for deriving therefrom at least two output signals which are substantially equivalent to the secondary signal portions of the electrical signal. The signal processor may comprise a joint process estimator.

[0033] The present invention also includes a method of determining a secondary reference from a first signal comprising a first primary signal portion and a first secondary portion and a second signal comprising a second primary signal portion and a second secondary portion. The method comprises the steps of selecting a signal coefficient which is proportional to a ratio of predetermined attributes of the first primary signal portion and predetermined attributes of the second primary signal portion. The first signal and the signal coefficient are input into a signal multiplier wherein the first signal is multiplied by the signal coefficient thereby generating a first intermediate signal. The second signal and the first intermediate signal are input into a signal subtractor wherein the first intermediate signal is subtracted from the second signal. This generates a secondary reference having a significant component which is derived from the first and second secondary signal portions.

[0034] The present invention also includes a method of determining a primary reference from a first signal comprising a first primary signal portion and a first secondary signal portion and a second signal comprising a second primary signal portion and a second secondary signal portion. The method comprises the steps of selecting a signal coefficient which is proportional to a ratio of the predetermined attributes of the first secondary signal portion and predetermined attributes of the second secondary signal portion. The first signal and the signal coefficient are input into a signal multiplier wherein the first signal is multiplied by the signal coefficient thereby generating a first intermediate signal. The second signal and the first intermediate signal are input into a signal subtractor wherein the first intermediate signal is subtracted from the second signal. This generates a primary reference having a significant component which is derived from the first and second primary signal portions. The first and second signals in this method may be derived from electromagnetic energy transmitted through an absorbing medium.

[0035] The present invention further embodies a physiological monitoring apparatus comprising means for acquiring a first signal comprising a first primary signal portion and a first secondary signal portion and a second signal comprising a second primary signal portion and a second secondary signal portion. The physiological monitoring apparatus of the present invention also comprises means for determining from the first and second signals a secondary reference. Additionally, the monitoring apparatus comprises a correlation canceler, such as an adaptive noise canceler, having a secondary reference input for receiving the secondary reference and a signal input for receiving the first signal wherein the correlation canceler, in real or near real time, generates an output signal which approximates the first primary signal portion. Alternatively, the physiological monitoring device may also comprise means for determining from the first and second signals a primary reference. Additionally, the monitoring apparatus comprises a correlation canceler having a primary reference input for receiving the primary reference and a signal input for receiving the first signal wherein the correlation canceler, in real or near real time, generates an output signal which approximates the first secondary signal portion. The correlation canceler may further comprise a joint process estimator.

[0036] A further aspect of the present invention is an apparatus for processing an amplitude modulated signal having a signal amplitude complicating feature, the apparatus comprising an energy source for directing electromagnetic energy upon a specimen. Additionally, the apparatus comprises a detector for acquiring a first amplitude modulated signal and a second amplitude modulated signal. Each of the first and second signals has a component containing information about the attenuation of electromagnetic energy by the specimen and a signal amplitude complicating feature. The apparatus includes a reference processor for receiving the first and second amplitude modulated signals and deriving therefrom a secondary reference which is correlated with the signal amplitude complicating feature. Further, the apparatus incorporates a correlation canceler having a signal input for receiving the first amplitude modulated signal, a secondary reference input for receiving the secondary reference, wherein the correlation canceler produces an output signal having a significant component which is derived from the component containing information about the attenuation of electromagnetic energy by the specimen. Alternatively, the apparatus may also include a reference processor for receiving the first and second amplitude modulated signals and deriving therefrom a primary reference which is correlated with the component containing information about the attenuation of electromagnetic energy by the specimen. Further, the apparatus incorporates a correlation canceler having a signal input for receiving the first amplitude modulated signal, a primary reference input for receiving the primary reference, wherein the correlation canceler produces an output signal having a primary component which is derived from the signal amplitude complicating feature.

[0037] Still another aspect of the present invention is an apparatus for extracting a plethysmographic waveform from an amplitude modulated signal having a signal amplitude complicating feature, the apparatus comprising a light source for transmitting light into an organism and a detector for monitoring light from the organism. The detector produces a first light attenuation signal and a second light attenuation signal, wherein each of the first and second light attenuation signals has a component which is representative of a plethysmographic waveform and a component which is representative of the signal amplitude complicating feature. The apparatus also includes a reference processor for receiving the first and second light attenuation signals and deriving therefrom a secondary reference. The secondary reference and the signal amplitude complicating feature each have a frequency spectrum. The frequency spectrum of the secondary reference is correlated with the frequency spectrum of the signal amplitude complicating feature. Additionally incorporated into this embodiment of the present invention is a correlation canceler having a signal input for receiving the first attenuation signal and a secondary reference input for receiving the secondary reference. The correlation canceler produces an output signal having a significant component which is derived from the component which is representative of a plethysmographic waveform. The apparatus may also include a reference processor for receiving the first and second light attenuation signals and deriving therefrom a primary reference. Additionally incorporated in this embodiment of the present invention is a correlation canceler having a signal input for receiving the first attenuation signal and a primary reference input for receiving the primary reference. The correlation canceler produces an output signal having a significant component which is derived from the component which is representative of the signal complicating feature.

[0038] The present invention also comprises a method of removing or determining a motion artifact signal from a signal derived from a physiological measurement wherein a first signal having a physiological measurement component and a motion artifact component and a second signal having a physiological measurement component and a motion artifact component are acquired. From the first and second signals a secondary reference which is a primary function of the first and second signals motion artifact components is derived. This method of removing a motion artifact signal from a signal derived from a physiological measurement may also comprise the step of inputting the secondary reference into a correlation canceler, such as an adaptive noise canceler, to produce an output signal which is a significant function of the physiological measurement component of the first or second signal. Alternatively, from the first and second signals a primary reference which is a significant function of the physiological measurement components of the first and second signals may be derived. This approach may also comprise the step of inputting the primary reference into a correlation canceler to produce an output signal which is a significant function of the first or second signal's motion artifact component.

[0078] The present invention is a processor which determines either a secondary reference n′(t) or a primary reference s′(t) for use in a correlation canceler, such as an adaptive noise canceler. A correlation canceler may estimate a good approximation s″(t) to a primary signal s(t) from a composite signal S(t)=s(t)+n(t) which, in addition to the primary portion s(t) comprises a secondary portion n(t). It may also be used to provide a good approximation n″(t) to the secondary signal n(t). The secondary portion n(t) may contain one or more of a constant portion, a predictable portion, an erratic portion, a random portion, etc. The approximation to the primary signal s″(t) or secondary signal n″(t) is derived by removing as many of the secondary portions n(t) or primary portions s(t) from the composite signal S(t) as possible. The constant portion and predictable portion 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, it is often the case that no information is known about the erratic portion of the noise. In this case, traditional filtering techniques are usually insufficient. Often no information about the erratic portion of the measured signal is known. Thus, a correlation canceler, such as an adaptive noise canceler may be utilized in the present invention to remove or derive the erratic portion.

[0079] 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.

[0080] A block diagram of a generic monitor incorporating a signal processor, or reference processor, according to the present invention, and a correlation canceler is shown in FIGS. 4a and 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 22a and 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 24a and 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. The signals S_λa(t) and S_λb(t) are input to a reference processor 26. The reference processor multiplies the second measured signal S_λb(t) by either a factor ω_a=s_λa(t)/s_λb(t) or a factor ω_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 ω_a and ω_v are determined to 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 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)−ω_a n_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)−ω_v s_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 approximation s″(t) or n″(t) to either the primary s(t) or the secondary n(t) signal components. The approximation s″(t) or n″(t) is displayed on the display 28.

[0081] An adaptive noise canceler 30, an example of which is shown in block diagram form in FIG. 5a, is employed 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, which performs the functions of a correlation canceler, in FIG. 5a has 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).

[0082] 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 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).

[0083] 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).

[0084] Referring to FIG. 5c, the transfer function of a multiple notch filter is shown. The notches, or dips in the amplitude of the transfer function, indicate frequencies which are attenuated or removed when a composite measured signal passes through the notch filter. The output of the notch filter is the composite signal having frequencies at which a notch was 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.

[0085] The adaptive noise canceler 30 shown in FIGS. 5a and 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(t) in FIG. 5a or c(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(t) of the internal processor 32 in FIG. 5a is 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(t) of the internal processor 32 in FIG. 5b is 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 n_λa(t) or n_λb(t), respectively.

[0086] 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 Processing by 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.

[0087] Adaptive processors 30 in FIGS. 5a and 5b have 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 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. The determination of a suitable reference signal n′(t) or s′(t) from measurements taken by a monitor incorporating a reference processor of the present invention is one aspect of the present invention.

[0088] 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):
S_λa(t)=s_λa(t)+n_λa(t)  (I)

[0089] where s_λa(t) is the primary signal and n_λa(t) is the secondary signal.

[0090] A similar measurement is taken simultaneously, or nearly simultaneously, at a different wavelength, λb, yielding:
S_λb(t)=s_λb(t)+n_λb(t)  (2)

[0091] 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), will be correlated because any random or erratic functions will affect each measurement in nearly the same fashion. The well behaved primary signal components, s_λa(t) and s_λb(t), will also be correlated to one another.

[0092] 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. One way of doing this is to find proportionality constants, ω_a and ω_v, between the primary signals s_λa(t) and s_λb(t) and secondary signals n_λa(t) and n_λb(t) such that:
s_λa(t)=ω_as_λb(t)
n_λa(t)=ω_vn_λb(t).  (3)

[0093] These proportionality relationships can be satisfied in many measurements, including but not limited to absorption measurements and physiological measurements. Additionally, in most measurements, the proportionality constants ω_a and ω_v can be determined such that:
n_λa(t)≠ω_an_λb(t)
s_λa(t)≠ω_vs_λb(t).  (4)

[0094] Multiplying equation (2) by ω_a and 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, leaving:
n′(t)=S_λa(t)−ω_aS_λb(t)=n_λa(t)−ω_an_λb(t);  (5a)

[0095] 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.

[0096] Multiplying equation (2) by ω_v and 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:
s′(t)=S_λa(t)−ω_vS_λb(t)=s_λa(t)−ω_vs_λb(t);  (5b)

[0097] 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.

[0098] 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.

[0099] A schematic N constituent absorbing material comprising a container 42 having N different absorbing constituents, labeled A₁, A₂, A₃, . . . A_N, is shown schematically in FIG. 6a. The constituents A₁ through A_N in FIG. 6a are 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:

[0100] $\begin{array}{cc}I=I_o\exp \left(-\sum _{i=1}^N{\in }_{i,\lambda a}{c}_i{x}_i\right)& \left(6\right)\end{array}$

[0101] 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.:

[0102] $\begin{array}{cc}{S}_{\lambda a}=\ln \left(I_o\text{/}I\right)=\sum _{i=1}^N{\in }_{i,\lambda a}{c}_i{x}_i& \left(7\right)\end{array}$

[0103] where I₀ is the incident light energy intensity; I is the transmitted light energy intensity; ε_i,λa is the absorption coefficient of the i^th constituent at the wavelength λa; x_i(t) is the optical path length of i^th layer, i.e., the thickness of material of the i^th layer through which optical energy passes; and c_i(t) is the concentration of the i^th constituent in the volume associated with the thickness x_i(t). The absorption coefficients ε₁ through ε_N are 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.

[0104] 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 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, should be 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 each other layer. 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.

[0105] 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 A₅ is affected by perturbations different than each of the layers of other constituents A₁ through A₄ and A₆ through A_N. An example of such a situation is when layer A₅ is 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 A₅ is 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 A₁ through A₄ and A₆ through A_N make 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 A₅ cause it to have different total perturbation than each of the other layers of constituents A₁ through A₄ and A₆ through A_N.

[0106] 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 A₅ is 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.

[0107] The correlation canceler utilized a sample of 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:

[0108] $\begin{array}{cc}{S}_{\lambda a}\left(t\right)={\in }_{5,\lambda a}{c}_5{x}_5\left(t\right)+\sum _{i=1}^4{\in }_{i,\lambda a}{c}_i{x}_i+\sum _{i=6}^N{\in }_{i,\lambda a}{c}_i{x}_i& \left(8\right)\\ S_{\lambda a\left(t\right)}={\varepsilon }_{5,\lambda a}{c}_5{x}_5\left(t\right)+n_{\lambda a}\left(t\right)& \left(9\right)\\ S_{\lambda b\left(t\right)}={\in }_{5,\lambda b}{c}_5{x}_5\left(t\right)+\sum _{i=1}^4{\in }_{i,\lambda b}{c}_i{x}_i+\sum _{i=6}^N{\in }_{i,\lambda b}{c}_i{x}_i& \left(10\right)\\ S_{\lambda b\left(t\right)}={\varepsilon }_{5,\lambda b}{c}_5{x}_5\left(t\right)+n_{\lambda b}\left(t\right)& \left(11\right)\end{array}$

[0109] Further transformations of the signals are the proportionality relationships defining ω_a and ω_v, similarly to equation (3), which allows determination of a noise reference n′(t) and a primary reference s′(t). These are:
ε_5,λa=ω_aε_5,λb  (12a)
n_λa=ω_vn_λb  (12b)
where
n_λa≠ω_an_λb  (13a)
ε_5,λa≠ω_vε_5,λb  (13b)

[0110] It is often the case that both equations (12) and (13) can be simultaneously satisfied. Multiplying equation (11) by ω_a and subtracting the result from equation (9) yields a non-zero secondary reference which is a linear sum of secondary signal components:

[0111] $\begin{array}{cc}{n}^{\prime }\left(t\right)=S_{\lambda a}\left(t\right)-{\omega }_a{S}_{\lambda b}\left(t\right)=n_{\lambda a}\left(t\right)-{\omega }_a{n}_{\lambda b}\left(t\right)& \left(14a\right)\\ =\sum _{i=1}^4{\in }_{i,\lambda a}{c}_i{x}_i\left(t\right)+\sum _{i=6}^N{\in }_{i,\lambda a}{c}_i{x}_i\left(t\right)-\sum _{i=1}^4{\omega }_a{\in }_{i,\lambda b}{c}_i{x}_i\left(t\right)+\sum _{i=6}^N{\omega }_a{\in }_{i,\lambda b}{c}_i{x}_i\left(t\right)& \left(15a\right)\\ =\sum _{i=1}^4{c}_i{x}_i\left(t\right)\left[{\in }_{i,\lambda a}-{\omega }_a{\in }_{i,\lambda b}\right]+\sum _{i=6}^N{c}_i{x}_i\left(t\right)\left[{\in }_{i,\lambda a}-{\omega }_a{\in }_{i,\lambda b}\right]& \left(16a\right)\end{array}$

[0112] Multiplying equation (11) by ω_v and subtracting the result from equation (9) yields a primary reference which is a linear sum of primary signal components:

[0113] $\begin{array}{cc}{s}^{\prime }\left(t\right)=S_{\lambda a}\left(t\right)-{\omega }_v{S}_{\lambda b}\left(t\right)=s_{\lambda a}\left(t\right)-{\omega }_v{s}_{\lambda b}\left(t\right)& \left(14b\right)\\ =c_5{x}_5\left(t\right){\varepsilon }_{5,\lambda a}-{\omega }_v{c}_5{x}_5\left(t\right){\varepsilon }_{5,\lambda b}& \left(15b\right)\\ =c_5{x}_5\left(t\right)\left[{\varepsilon }_{5,\lambda a}-{\omega }_v{\varepsilon }_{5,\lambda b}\right].& \left(16b\right)\end{array}$

[0114] 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. 5a and 5b and 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:
c₅(t)≈s″_λa(t)/ε_5,λax₅(t)c₅(t)≈s″_λb(t)/ε_5,λbx₅(t)  (17)

[0115] 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.

[0116] Referring to FIG. 6b, another material having N different constituents arranged in layers is shown. In this material, two constituents A₅ and A₆ are found within one layer having thickness x₅,6(t)=x₅(t)+x₆(t), located generally randomly within the layer. This is analogous to combining the layers of constituents A₅ and A₆ in FIG. 6a. A combination of layers, such as the combination of layers of constituents A₅ and 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.

[0117] 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.

[0118] 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 A₅ within a given volume which contains A₅ and A₆. In this case, the primary signals s_λa(t) and s_λb(t) comprise terms related to both A₅ and A₆ so that a determination of the concentration or saturation of A₅ or A₆ in the volume may be made. A determination of saturation is discussed herein. It will be understood that the concentration of A₅ in a volume containing both A₅ and A₆ could 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. Then measured signals S_λa(t) and S_λb(t) can be written (logarithm converted) as:

[0119] $\begin{array}{cc}{S}_{\lambda a}\left(t\right)={\varepsilon }_{5,\lambda a}{c}_5{x}_{5,6}\left(t\right)+{\varepsilon }_{6,\lambda a}{c}_6{x}_{5,6}\left(t\right)+n_{\lambda a}\left(t\right)& \left(18a\right)\\ =s_{\lambda a}\left(t\right)+n_{\lambda a}\left(t\right);& \left(18b\right)\\ S_{\lambda b}\left(t\right)={\varepsilon }_{5,\lambda b}{c}_5{x}_{5,6}\left(t\right)+{\varepsilon }_{6,\lambda b}{c}_6{x}_{5,6}\left(t\right)+m_{\lambda b}\left(t\right)& \left(19a\right)\\ =s_{\lambda b}\left(t\right)+n_{\lambda b}\left(t\right).& \left(19b\right)\end{array}$

[0120] 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 A₅ within a given volume which contains A₅ and A₆ as well as the concentration or saturation of A₃ within a given volume which contains A₃ and A₄, A₃ and A₄ having the same constituency as A₅ and A₆, respectively. In this case, the primary signals s_λa(t) and s_λb(t) again comprise terms related to both A₅ and A₆ and portions of the secondary signals n_λa(t) and n_λb(t) comprise terms related to both A₃ and A₄. The layers, A₃ and A₄, do not enter into the primary equation because they are assumed to be perturbed by 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,λa and ε_4,λb=ε_6,λb. Generally speaking, however, A₃ and A₄ will have different concentrations than A₅ and A₆ and 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:

[0121] $\begin{array}{cc}{s}_{\lambda a}\left(t\right)=\left[{\varepsilon }_{5,\lambda a}{c}_5+{\varepsilon }_{6,\lambda a}{c}_6\right]x_{5,6}\left(t\right)n_{\lambda a}\left(t\right)=\left[{\varepsilon }_{5,\lambda a}{c}_3+{\varepsilon }_{6,\lambda a}{c}_4\right]x_{3,4}\left(t\right)& \left(20a\right)\\ +\sum _{i=1}^2{\in }_{i,\lambda a}{c}_i{x}_i\left(t\right)+\sum _{i=7}^n{\in }_{i,\lambda a}{c}_i{x}_i\left(t\right)& \left(20b\right)\\ n_{\lambda a}\left(t\right)=\left[{\varepsilon }_{5,\lambda a}{c}_3+{\varepsilon }_{6,\lambda a}{c}_4\right]x_{3,4}\left(t\right)+n_{\lambda a}\left(t\right)& \left(20c\right)\\ s_{\lambda b}\left(t\right)=\left[{\varepsilon }_{5,\lambda b}{c}_5+{\varepsilon }_{6,\lambda b}{c}_6\right]x_{5,6}\left(t\right)n_{\lambda b}\left(t\right)=\left[{\varepsilon }_{5,\lambda b}{c}_3+{\varepsilon }_{6,\lambda b}{c}_4\right]x_{3,4}\left(t\right)& \left(21a\right)\\ +\sum _{i=1}^2{\in }_{i,\lambda b}{c}_i{x}_i\left(t\right)+\sum _{i=7}^N{\in }_{i,\lambda b}{c}_i{x}_i\left(t\right).& \left(21b\right)\\ n_{\lambda b}\left(t\right)=\left[{\varepsilon }_{5,\lambda b}{c}_3+{\varepsilon }_{6,\lambda b}{c}_4\right]x_{3,4}\left(t\right)+n_{\lambda b}\left(t\right)& \left(21c\right)\end{array}$

[0122] 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.

[0123] 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 A₅ and A₆ is different than the perturbation in the layer of constituents A₅ and 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).

[0124] Two methods which may be used by a processor of the present invention to determine either the secondary reference n′(t) or the primary reference s′(t) are a ratiometric method and a constant saturation method. One embodiment of a physiological monitor incorporating a processor of the present invention utilizes the ratiometric method wherein the two wavelengths λa and λb, at which the signals S_λa(t) and S_λb(t) are measured, are specifically chosen such that a relationship between the absorption coefficients ε_5,λa, ε_5,λb, ε_6,λa and ε_6,λb exists, i.e.:

[0125] $\begin{array}{cc}\frac{{\varepsilon }_{5,\lambda b}}{{\varepsilon }_{6,\lambda b}}=\frac{{\varepsilon }_{5,\lambda a}}{{\varepsilon }_{6,\lambda a}}& \left(22\right)\end{array}$

[0126] The measured signals S_λa(t) and S_λb(t) can be factored and written as:

[0127] $\begin{array}{cc}{S}_{{\lambda }_a}\left(t\right)={\varepsilon }_{6,\lambda a}\left[\left(\frac{{\varepsilon }_{5,\lambda a}}{{\varepsilon }_{6,\lambda a}}\right)c_5{x}_{5,6}\left(t\right)+c_6{x}_{5,6}\left(t\right)\right]+n{\lambda }_a\left(t\right)& \left(23a\right)\\ S_{{\lambda }_a}\left(t\right)={\varepsilon }_{6,\lambda a}\left[\begin{array}{c}\left(\frac{{\varepsilon }_{5,\lambda a}}{{\varepsilon }_{6,\lambda a}}\right)c_5{x}_{5,6}\left(t\right)+c_6{x}_{5,6}\left(t\right)+\\ \left(\frac{{\varepsilon }_{5,\lambda a}}{{\varepsilon }_{6,\lambda a}}\right)c_3{x}_{3,4}\left(t\right)+c_4{x}_{3,4}\left(t\right)\end{array}\right]+n{\lambda }_a\left(t\right)& \left(23b\right)\\ S_{{\lambda }_a}\left(t\right)=s_{{\lambda }_a}\left(t\right)+n_{{\lambda }_a}\left(t\right)& \left(23c\right)\\ S_{{\lambda }_b}\left(t\right)={\varepsilon }_{6,\lambda b}\left[\left(\frac{{\varepsilon }_{5,\lambda b}}{{\varepsilon }_{6,\lambda b}}\right)c_5{x}_{5,6}\left(t\right)+c_6{x}_{5,6}\left(t\right)\right]+n{\lambda }_b\left(t\right)& \left(24a\right)\\ S_{{\lambda }_b}\left(t\right)={\varepsilon }_{6,\lambda b}\left[\begin{array}{c}\left(\frac{{\varepsilon }_{5,\lambda b}}{{\varepsilon }_{6,\lambda b}}\right)c_5{x}_{5,6}\left(t\right)+c_6{x}_{5,6}\left(t\right)+\\ \left(\frac{{\varepsilon }_{5,\lambda b}}{{\varepsilon }_{6,\lambda b}}\right)c_3{x}_{3,4}\left(t\right)+c_4{x}_{3,4}\left(t\right)\end{array}\right]+n{\lambda }_b\left(t\right)& \left(24b\right)\\ S_{{\lambda }_b}\left(t\right)=s_{{\lambda }_b}\left(t\right)+n_{{\lambda }_b}\left(t\right)& \left(24c\right)\end{array}$

[0128] The wavelengths λa and λb, chosen to satisfy equation (22), cause the terms within the square brackets to be equal, thereby causing the terms other than n_λa(t) and n_λb(t) to be linearly dependent. Then, proportionality constants ω_av and ω_e may be found for the determination of a non-zero primary and secondary reference
ε_6,λn=ω_avε_6,λb  (25a)
n_λn(t)=ω_en_λb(t)  (25b)
ε_6,λn≈ω_eε_6,λb  (25a)
n_λn(t)≈ω_avn_λb(t)  (26b)

[0129] It is often the case that both equations (25) and (26) can be simultaneously satisfied. Additionally, since the absorption coefficients of each constituent are constant with respect to wavelength, the proportionality constants ω_av and ω_e can be easily determined. Furthermore, absorption coefficients of other constituents A₁ through A₂ and A₇ through A_N are generally unequal to the absorption coefficients of A₃, A₄, A₅ and A₆. Thus, the secondary components n_λa and n_λb are generally not made linearly dependent by the relationships of equations (22) and (25).

[0130] Multiplying equation (24) by ω_av and subtracting the resulting equation from equation (23), a non-zero secondary reference is determined by:
n(t)=S_λa(t)−ω_avS_λb(t)=n_λa(t)−ω_avn_λb(t).  (27a)

[0131] Multiplying equation (24) by ω_e and subtracting the resulting equation from equation (23), a non-zero primary reference is determined by:
s(t)=S_λa(t)−ω_eS_λb(t)=s_λa(t)−ω_es_λb(t).  (27b)

[0132] An alternative method for determining reference signals from the measured signals S_λa(t) and S_λb(t) using a processor of the present invention is the constant saturation approach. In this approach, it is assumed that the saturation of A₅ in the volume containing A₅ and A₆ and the saturation of A₃ in the volume containing A₃ and A₄ remains relatively constant over some period of time, i.e.:
Saturation(A₅(t))=c₅(t)/[c₅(t)+c₆(t)]  (28a)
Saturation(A₃(t))=c₃(t)/[c₃(t)+c₄(t)]  (28b)
Saturation(A₅(t))={1+[c₆(t)/c₅(t)]}⁻¹  (29a)
Saturation(A₃(t))={1+[c₄(t)/c₃(t)]}⁻¹  (29b)

[0133] are substantially constant over many samples of the measured signals S_λa and S_λb. This assumption is accurate over many samples since saturation generally changes relatively slowly in physiological systems.

[0134] The constant saturation assumption is equivalent to assuming that:
c₅(t)/c₆(t)=constant₁  (30a)
c₃(t)/c₄(t)=constant₂  (30b)

[0135] since the only other term in equations (29a) and (29b) is a constant, namely the numeral 1.

[0136] Using this assumption, the proportionality constants ω_a and ω_v which allow determination of the secondary reference signal n′(t) and the primary reference signal s′(t) in the constant saturation method are:

[0137] $\begin{array}{cc}{\omega }_v=\frac{{\varepsilon }_{5,\lambda a}{c}_5{x}_{5,6}\left(t\right)+{\varepsilon }_{6,\lambda a}{c}_6{x}_{5,6}\left(t\right)}{{\varepsilon }_{5,\lambda b}{c}_5{x}_{5,6}\left(t\right)+{\varepsilon }_{6,\lambda b}{c}_6{x}_{5,6}\left(t\right))}& \left(31a\right)\\ =s_{\lambda a}\left(t\right)/s_{\lambda b}\left(t\right)& \left(32a\right)\\ =\frac{{\varepsilon }_{5,\lambda a}{c}_5+{\varepsilon }_{6,\lambda a}{c}_6}{{\varepsilon }_{5,\lambda b}{c}_5+{\varepsilon }_{6,\lambda b}{c}_6}& \left(33a\right)\\ =\frac{{\varepsilon }_{5,\lambda a}\left(c_5/c_6\right)+{\varepsilon }_{6,\lambda a}}{{\varepsilon }_{5,\lambda b}\left(c_5/c_6\right)+{\varepsilon }_{6,\lambda b}}& \left(34a\right)\\ \approx s_{\lambda a}^{″}\left(t\right)/s_{\lambda b}^{″}\left(t\right)={\mathrm{constant}}_3;\mathrm{where}& \left(35a\right)\\ n_{\lambda a}\left(t\right)\ne {\omega }_a\left(t\right)n_{\lambda b}\left(t\right)\mathrm{and}& \left(36a\right)\\ {\omega }_v=\frac{{\varepsilon }_{5,\lambda a}{c}_3{x}_{3,4}\left(t\right)+{\varepsilon }_{6,\lambda a}{c}_4{x}_{3,4}\left(t\right)}{{\varepsilon }_{5,\lambda b}{c}_3{x}_{3,4}\left(t\right)+{\varepsilon }_{6,\lambda b}{c}_4{x}_{3,4}\left(t\right))}& \left(31b\right)\\ =n_{\lambda a}\left(t\right)/n_{\lambda b}\left(t\right)& \left(32b\right)\\ =\frac{{\varepsilon }_{5,\lambda a}{c}_3+{\varepsilon }_{6,\lambda a}{c}_4}{{\varepsilon }_{5,\lambda b}{c}_3+{\varepsilon }_{6,\lambda b}{c}_4}& \left(33b\right)\\ =\frac{{\varepsilon }_{5,\lambda a}\left(c_3/c_4\right)+{\varepsilon }_{6,\lambda a}}{{\varepsilon }_{5,\lambda b}\left(c_3/c_4\right)+{\varepsilon }_{6,\lambda b}}& \left(34b\right)\\ \approx n_{\lambda a}^{″}\left(t\right)/n_{\lambda b}^{″}\left(t\right)={\mathrm{constant}}_4;\mathrm{where}& \left(35b\right)\\ s_{\lambda a}\left(t\right)\ne {\omega }_v\left(t\right)s_{\lambda b}\left(t\right).& \left(36b\right)\end{array}$

[0138] It is often the case that both equations (32) and (36) can be simultaneously satisfied to determine the proportionality constants ω_a and ω_v. Additionally, the absorption coefficients at each wavelength ε_5,λa, ε_6,λa, ε_5,λb, and ε_6,λb are 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 ω_a and ω_v may 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, ω_a and ω_v, for the next set of samples of the measured signals S_λa(t) and S_λb(t).

[0139] Multiplying equation (19) by ω_a and subtracting the resulting equation from equation (18) yields a non-zero secondary reference signal:
n′(t)=S_λa(t)−ω_aS_λb(t)=n_λa(t)−ω_an_λb(t).  (37a)

[0140] Multiplying equation (19) by ω_v and subtracting the resulting equation from equation (18) yields a non-zero primary reference signal:
s′(t)=S_λa(t)−ω_vS_λb(t)=s_λa(t)−ω_vs_λb(t).  (37b)

[0141] When using the constant saturation method, it is not necessary for the patient to remain motionless for a short period of time such that an accurate initial saturation value can be determined by known methods other than correlation canceling. With no erratic, motion-induced signal portions, a physiological monitor can very quickly produce an initial value of the saturation of A₅ in the volume containing A₅ and A₆. An example of a saturation calculation is given in the article “SPECTROPHOTOMETRIC DETERMINATION OF OXYGEN SATURATION OF BLOOD INDEPENDENT OF THE PRESENT OF INDOCYANINE GREEN” by G. A. Mook, et al., wherein determination of oxygen saturation in arterial blood is discussed. Another article discussing the calculation of oxygen saturation is “PULSE OXIMETRY: PHYSICAL PRINCIPLES, TECHNICAL REALIZATION AND PRESENT LIMITATIONS” by Michael R. Neuman. Then, with values for the coefficients ω_a and ω_v determined, a correlation canceler may be utilized with a secondary reference n′(t) or a primary reference s′(t) determined by the constant saturation method.

[0142] The reference processor 26 of FIG. 4a and FIG. 4b of the present invention may be configured to multiply the second measured signal S_λb(t)=s_λb(t)+n_λb(t) by a plurality of signal coefficients ω₁, ω₂, . . . ω_n and 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
r′(ω,t)=s_λa(t)−ωs_λb(t)+n_λa(t)−ωn_λb(t)  (38)

[0143] for ω=ω₁, ω₂, . . . ω_n as shown in FIG. 7a.

[0144] 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 (38), signal coefficients ω_a and ω_v must be determined from the plurality of signal coefficients ω₁, ω₂, . . . ω_n. The coefficients ω_a and ω_v are 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′(ω, t), e.g.
s_λa(t)=ω_as_λb(t)  (39a)
n_λa(t)=rω_vn_λb(t)  (39b)
n′(t)=r′(ω_a,t)=n_λa(t)−ω_an_λb(t)  (39c)
s′(t)=r′(ω_v,t)=s_λa(t)−ω_vs_λb(t).  (39d)

[0145] 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 ω₁, ω₂, . . . ω_n correspond to the signal coefficients ω_a=s_λa(t)/s_λb(t) and ω_v=n_λa(t)/n_λb(t). Herein the preferred approach to determine the signal coefficients ω_a and ω_v from the plurality of coefficients ω₁, ω₂, . . . ω_n employs 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′(ω₁,t), r′(ω₂, t), . . . , r′(ω_n, t) as shown in FIG. 7a. For each of the reference signals r′(ω₁, t), r′(ω₂, t), . . . , r′(ω_n, t) the corresponding output of the correlation canceler 27 is input to an integrator 29 for forming a cumulative output signal. The cumulative output signal is subsequently input to an extremum detector 31. The purpose of the extremum detector 31 is to chose signal coefficients ω_a and ω_v from the set ω₁, ω₂, . . . ω_n by observing which provide a maximum in the cumulative output signal as in FIGS. 7b and 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 ω_a and ω_v. One could also configure a system geometry which would require one to locate the coefficients from the set ω₁, ω₂, . . . ω_n which provide a minimum or inflection in the cumulative output signal to identify the signal coefficients ω_a and ω_v.

[0146] 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 ω_a and ω_v may 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 a generic correlation canceler C(x, y) may be defined as follows:
Property(1)C(x,y)=0 for x, y correlated
Property(2)C(x,y)=x for x, y uncorrelated
Property(3)C(x+y,z)=C(x,z)+C(y,z)  (40)

[0147] 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′(ω₁, t), r′(ω₂, t), . . . r′(ω_n, t) can determine the signal coefficients ω_a and ω_v needed 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′(ω₁, t), r′(ω₂, t), . . . , r′(ω_n, t) then the outputs of the correlation canceler C(S_λa(t), r′(ω_j,t)) for j=1, 2, . . . , n may be written as
C(s_λa(t)+n_λa(t),s_λa(t)−ω_js_λb(t)+n_λa(t)−r_jn_λb(t))  (41)

[0148] where j=1, 2, . . . , n and we have used the expressions
r′(ω,t)=S_λa(t)−ωS_λb(t)  (42)
S_λa(t)=s_λa(t)+n_λa(t)  (43a)
S_λb(t)=s_λb(t)+n_λb(t).  (43b)

[0149] The use of property (3) allows one to expand equation (41) into two terms
C(S_λa(t),r′(ω,t))=C(s_λa(t),s_λa(t)−ωs_λb(t)+n_λa(t)−ωn_λb(t))+C(n_λa(t),s_λa(t)−ωs_λb(t)+n_λa(t)−ωn_λb(t))  (44)

[0150] so that upon use of properties (1) and (2) the correlation canceler output is given by
C(S_λa(t),r′(ω_j,t))=s_λa(t)δ(ω_j−ωa)+n_λa(t)δ(ω_j−ω_v)  (45)

[0151] where δ(x) is the unit impulse function
δ(x)=0 if x≠0
δ(x)=1 if x=0.  (46)

[0152] The time variable, t, of the correlation canceler output C(S_λa(t), r′(ω_j, t)) may be eliminated by computing its energy or power. The energy of the correlation canceler output is given by

[0153] $\begin{array}{cc}\begin{array}{c}{E}_{\lambda a}\left({\omega }_j\right)=\int c^2(s_{\lambda a}\left(t\right),r^{\prime }\left({\omega }_j,t\right)dt\\ =\delta \left(\omega -{\omega }_a\right)\int s_{\lambda a}^2\left(t\right)dt+\delta \left(\omega -{\omega }_v\right)\int n_{\lambda b}^2\left(t\right)dt.\end{array}& \left(47a\right)\end{array}$

[0154] It must 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′(ω₁, t), r′(ω₂, t), . . . , r′(ω_n, t) as the second input. In this event, the correlation canceler energy output is

[0155] $\begin{array}{cc}\begin{array}{c}{E}_{\lambda b}\left(\omega \right)=\int c^2(s_{\lambda b}\left(t\right),r^{\prime }\left(\omega ,t\right)dt\\ =\delta \left(\omega -r_a\right)\int s_{\lambda b}^2\left(t\right)dt+\delta \left({\omega }_j-{\omega }_v\right)\int n_{\lambda b}^2\left(t\right)dt.\end{array}& \left(47b\right)\end{array}$

[0156] It must also be understood that in practical situations the use of discrete time measurement signals may be employed as well as continuous time measurement signals. 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

[0157] $\begin{array}{cc}{E}_{\lambda a}\left(\omega \right)=\delta \left(\omega -{\omega }_a\right)\Delta t\left\{\sum _{i=0}^n{s}_{\lambda a}^2\left(t_i\right)-0.5\left(s_{\lambda a}^2\left(t_0\right)+s_{\lambda a}^2\left(t_n\right)\right)\right\}+\delta \left(\omega -{\omega }_v\right)\Delta t\left\{\sum _{i=0}^n{n}_{\lambda a}^2\left(t_i\right)-0.5\left(n_{\lambda a}^2\left(t_0\right)+n_{\lambda a}^2\left(t_n\right)\right)\right\}& \left(48a\right)\\ E_{\lambda b}\left(\omega \right)=\delta \left(\omega -{\omega }_a\right)\Delta t\left\{\sum _{i=0}^n{s}_{\lambda b}^2\left(t_i\right)-0.5\left(s_{\lambda b}^2\left(t_0\right)+s_{\lambda b}^2\left(t_n\right)\right)\right\}+\delta \left(\omega -{\omega }_v\right)\Delta t\left\{\sum _{i=0}^n{n}_{\lambda b}^2\left(t_i\right)-0.5\left(n_{\lambda b}^2\left(t_0\right)+n_{\lambda b}^2\left(t_n\right)\right)\right\}& \left(48b\right)\end{array}$

[0158] where t_i is the i^th discrete time, t₀ is the initial time, t_n is the final time and Δt is the time between discrete time measurement samples.

[0159] 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′(ω₁, t), r′(ω₂, t), . . . , r′(ω_n, t)r′(ω, t). However, the energy functions are non zero at values of ω_j which 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′(ω_j, t). These values correspond to the signal coefficients ω_a and ω_v.

[0160] It must 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.

[0161] 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′(ω, 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 ω_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 ω_v=n_λa(t)/n_λb(t) is the larger of the two signal coefficient values, assuming λa=660 nm and λb=940 nm.

[0162] It must 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 the present invention, the correlation canceler energy curves depicted in FIG. 7b will not consist of infinitely narrow delta functions but will have finite width associated with them as depicted in FIG. 7c.

[0163] 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 will arise when the measured signals each contain more than two components each of which are related by a ratio as follows:

[0164] $\begin{array}{cc}{s}_{\lambda a}\left(t\right)=\sum _{i=1}^n{f}_{\lambda a,i}\left(t\right)s_{\lambda b}\left(t\right)=\sum _{i=1}^n{f}_{\lambda b,i}\left(t\right)\mathrm{where}{f}_{\lambda a,i}\left(t\right)=\omega f_{\lambda b,i}\left(t\right)i=1,\dots ,n{\omega }_i\ne {\omega }_j.& \left(49\right)\end{array}$

[0165] The ability to employ reference signal techniques together with a correlation cancellation, such as an adaptive noise canceler, to decompose a signal into two or more signal components each of which is related by a ratio is a further aspect of the present invention.

[0166] Once either the secondary reference n′(t) or the primary reference s′(t) is determined by the processor of the present invention using either the above described ratiometric or constant saturation methods, 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.

[0167] The least mean squares (LMS) implementation of the internal processor 32 described above in conjunction with the adaptive noise canceler of FIG. 5a and FIG. 5b is 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 preferably used. A joint process estimator 60 is shown diagrammatically in FIG. 8 and is described in detail in Chapter 9 of Adaptive Filter Theory by Simon Haykin, published by Prentice-Hall, copyright 1986. This entire book, including Chapter 9, is hereby incorporated herein by reference. 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 signal s″_λa(t) or s″_λb(t) or a signal n″_λa(t) or n″_λb(t) which is a good approximation to either the primary signal s_λa(t) or s_λb(t) or the secondary signal 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).

[0168] 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 equally well 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 equally well be estimated.

[0169] 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 highly 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 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). 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 approximation to either the primary signal s″_λa(t) or the secondary signal n″_λa(t) is produced as output from the m^th-stage.

[0170] 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.

[0171] 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 value 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).

[0172] 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).

[0173] 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), and the regression coefficient κ_m,λa(t) register 90,92, and 96 values.

[0174] Intermediate variables include a weighted sum of the forward prediction error squares J_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 J_m(t) is defined as:

[0175] $\begin{array}{cc}{m}_{}\left(t\right)=\sum _{i=1}^t{\lambda }^{t-i}{f_m\left(i\right)}^2;& \left(50\right)\end{array}$

[0176] 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:

[0177] $\begin{array}{cc}{\beta }_m\left(t\right)=\sum _{i=1}^t{\lambda }^{t=i}{b_m\left(i\right)}^2& \left(51\right)\end{array}$

[0178] 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, and defined hereinafter in equations (65) and (66).

[0179] 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 J_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:
Δ_m−1(0)=0;  (52)
_m−1(0)=6;  (53)
β_m−1(0)=6;  (54)
ρ_m,λa(0)=0;  (55)
e_0,λa(t)=S_λa(t) for t≧0.  (56)

[0180] 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 J₀(t) and β₀(t), and the conversion factor γ₀(t) are calculated for the zero-stage according to:
f₀(t)=b₀(t)=n′(t)  (57a)
J₀(t)=β₀(t)=λJ₀(t−1)+|n′(t)|²  (58a)
γ₀(t−1)=1  (59a)

[0181] if a secondary reference n′(t) is used or according to:
f₀(t)=b₀(t)=s′(t)  (57b)
J₀(t)=β₀(t)=λJ₀(t−1)+|s′(t)|²  (58b)
β₀(t−1)=1  (59b)

[0182] 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.

[0183] 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 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 J_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:
Δ_m−1(t)=λΔ_m−1(t−1)+{b_m−1(t−1)f*_m−1(t)/γ_m−1(t−1)}  (60)
Γ_f,m(t)=−{Δ_m−1(t)/β_m−1(t−1)}  (61)
Γ_b,m(t)=−{Δ*_m−1(t)/J_m−1(t)}  (62)
f_m(t)=f_m−1(t)+Γ*_f,m(t)b_m−1(t−1)  (63)
b_m(t)=b_m−1(t−1)+Γ*_b,m(t)f_m−1(t)  (64)
J_m(t)=J_m−1(t)−{|Δ_m−1(t)|²/β_m−1(t−1)}  (65)
β_m(t)=β_m−1(t−1)−{|Δ_m−1(t)|²/J_m−1(t)}  (66)
γ_m(t−1)=γ_m−1(t−1)−{|b_m−1(t−1)|²/β_m−1(t−1)}  (67)
ρ_m,λa(t)=λρ_m,λa(t−1)+{b_m(t)ε*_m,λa(t)/γ_m(t)}  (68)
κ_m,λa(t)={ρ_m,λa(t)/β_m(t)}  (69)
ε_m+1,λa(t)=ε_m,λa(t)−κ*_m(t)b_m(t)  (70)

[0184] where a(*) denotes a complex conjugate.

[0185] 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 (60) through (70). They interact to minimize the error signals in the next stage.

[0186] 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 reoccur, 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.

[0187] 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.

[0188] 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 signal, S_λa(t) is shown in FIG. 9. The flow chart describes how the action of a reference processor for determining either the secondary reference or the primary reference and the joint process estimator 60 would be implemented in software.

[0189] A one-time only initialization is performed when the physiological monitor is turned on, as indicated by an “INITIALIZE NOISE CANCELER” box 120. The initialization sets all registers 90, 92, and 96 and delay element variables 110 to the values described above in equations (52) through (56).

[0190] Next, a set of simultaneous samples of the 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” box 130, wherein 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 in the first-stage delay element variable, the first-stage backward prediction error b₁(t) is stored in the second-stage delay element variable, and so on.

[0191] Then, using the set of measured signal samples S_λa(t) and S_λb(t), the reference signal is calculated according to the ratiometric or the constant saturation method described above. This is indicated by a “CALCULATE REFERENCE [n′(t) or s′(t)] FOR TWO MEASURED SIGNAL SAMPLES” box 140.

[0192] A zero-stage order update is performed next as indicated in a “ZERO-STAGE UPDATE” box 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 J_m(t) and the weighted sum of backward prediction errors β_m(t) are set equal to the value defined in equations (53) and (54).

[0193] Next, a loop counter, m, is initialized as indicated in a “m=0” box 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.

[0194] 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” box 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.

[0195] 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)” box 180. The two order update boxes 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 box 190. In a computer subroutine, convergence is determined by checking if the weighted sums of the forward and backward prediction errors J_m(t) and β_m(t) are less than a small positive number. An output is calculated next, as indicated by a “CALCULATE OUTPUT” box 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” box 210.

[0196] 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 60 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.

[0197] 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) Then, 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). Then an estimate of the venous saturation may be determined from the approximations to these signals i.e. n″_λa(t) and n″_λb(t).

[0198] In other physiological measurements, information about a signal at a third wavelength is necessary. For example, to find the saturation using the ratiometric method, signals S_λa(t) and S_λb(t) are used to find the reference signal n′(t) or s′(t). But as discussed previously, λa and λb were chosen to satisfy a proportionality relationship like that of equation (22). This proportionality relationship forces the two primary signal portions s_λa(t) and s_λb(t) of equations (23c) and (24c) to be linearly dependent. Generally, linearly dependent mathematical equations cannot be solved for the unknowns. Analogously, some desirable information cannot be derived from two linearly dependent signals. Thus, to determine the saturation using the ratiometric method, a third signal is simultaneously measured at wavelength λc. The wavelength λc is chosen such that the primary portion s_λc(t) of the measured signal S_λc(t) is not linearly dependent with the primary portions s_λa(t) and s_λb(t) of the measured signals S_λa(t) and S_λb(t). Since all measurements are taken substantially simultaneously, the secondary reference signal n′(t) is correlated to the secondary signal portions n_λa, n_λb, and n_λc of each of the measured signals S_λa(t), S_λb(t), and S_λc(t) and can be used to estimate approximations to the primary signal portions s_λa(t), s_λb(t), and s_λc(t) for all three measured signals S_λa(t), S_λb(t), and S_λc(t). Using the ratiometric method, estimation of the ratio of signal portions s_λa(t) and s_λc(t) of the two measured signals S_λa(t) and S_λc(t), chosen correctly, is usually satisfactory to determine most physiological data.

[0199] A joint process estimator 60 having two regression filters 80a and 80b is shown in FIG. 10. A first regression filter 80a accepts a measured signal S_λa(t). A second regression filter 80b accepts a measured signal S_λb(t) or S_λc(t), depending whether the constant saturation method or the ratiometric method is used to determine the reference signal n′(t) or s′(t) for the constant saturation method or, n′(t) or s′(t) for the ratiometric method. The first and second regression filters 80a and 80b are independent. The backward prediction error b_m(t) is input to each regression, filter 80a and 80b, the input for the second regression filter 80b bypassing the first regression filter 80a.

[0200] The second regression filter 80b comprises registers 98, and summing elements 108 arranged similarly to those in the first regression filter 80a. The second regression filter 80b operates via an additional intermediate variable in conjunction with those defined by equations (60) through (70), i.e.:
ρ_m,λb(t)=λρ_m,λb(t−1)+{b_m(t)e*_m,λb(t)/γ_m(t)}; or  (71)
ρ_m,λc(t)=λρ_m,λc(t−1)+{b_m(t)e*_m,λc(t)/γ_m(t)}; and  (72)
ρ_0,λb(0)=0; or  (73)
ρ_0,λc(0)=0.  (74)

[0201] The second regression filter 80b has an error signal value defined similar to the first regression filter error signal values, e_m+1,λa(t), i.e.:
e_m+1,λb(t)=e_m,λb(t)−κ*_m,λb(t)b_m(t); or  (75)
e_m+1,λc(t)=e_m,λc(t)−κ*_m,λb(t)b_m(t); and  (76)
e_0,λb(t)=S_λb(t) for t≧0; or  (77)
e_0,λc(t)=S_λc(t) for t≧0.  (78)

[0202] 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.:
κ_m,λb(t)={ρ_m,λb(t)/β_m(t)}; or  (79)
κ_m,λc(t)={ρ_m,λc(t)/β_m(t)}.  (80)

[0203] These values are used in conjunction with those intermediate variable values, signal values, register and register values defined in equations (52) through (70). These signals are calculated in an order defined by placing the additional signals immediately adjacent a similar signal for the wavelength λa.

[0204] For the ratiometric method, S_λc(t) is input to the second regression filter 80b. The output of the second regression filter 80b is then a good approximation to the primary signal s″_λc(t) or secondary signal n″_λc(t). 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).

[0205] The addition of the second regression filter 80b does not substantially change the computer program subroutine represented by the flowchart of FIG. 9. Instead of an order update of the m^th in stage of only one regression filter, an order update of the m^th stage of both regression filters 80a and 80b is performed. This is characterized by the plural designation in the “ORDER UPDATE OF min STAGE OF REGRESSION FILTER(S)” box 180 in FIG. 9. Since the regression filters 80a and 80b operate 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.

[0206] Once good approximations to the primary signal portions, s″_λa(t) and s″_λc(t) or the secondary signal portions n″_λa(t) and n″_λc(t) for the ratiometric method and s″_λa(t) and s″_λb(t) or n″_λa(t) and n″_λc(t) for the constant saturation method, have been determined by the joint process estimator 60, the saturation of A₅ in a volume containing A₅ and A₆, for example, may be calculated according to various known methods. Mathematically, the approximations to the primary signals can be written:
s″_λa(t)≈ε_5,λac₅x_5,6(t)+ε_6,λac₆x_5,6(t)+ε_5,λac₃x_3,4(t)+ε_6,λac₃x_3,4(t)  (81a)
s″_λc(t)≈ε_5,λcc₅x_5,6(t)+ε_6,λcc₆x_5,6(t)+ε_5,λcc₃x_3,4(t)+ε_6,λcc₃x_3,4(t)  (82a)

[0207] for the ratiometric method using wavelengths λa and λc, and assuming that the secondary reference n′(t) is uncorrelated with x_3,4(t) and x_5,6(t). Terms involving x_3,4(t) and x₅,6(t) may then be separated using the constant saturation method. It is important to understand that if n′(t) is uncorrelated with x_3,4(t) and x_5,6(t), use of the ratiometric method followed by use of the constant saturation method results in a more accurate computation of the saturation of A₃ in the layer x_3,4 then by use of the ratiometric or constant saturation methods alone. In the event that n′(t) and x_3,4(t) are correlated the ratiometric method yields
s″_λa(t)≈ε_5,λcc₅x_5,6(t)+ε_6,λac₆x_5,6(t); and  (81b)
s″_λc(t)≈ε_5,λcc₅x_5,6(t)+ε_6,λcc₆x_5,6(t).  (82b)

[0208] For the constant saturation method, the approximations to the primary signals can be written, in terms of λa and λb, as:
s″_λa(t)≈ε_5,λac₅x_5,6(t)+ε_6,λcc₆x_5,6(t); and  (83)
s″_λb(t)≈ε_5,λbc₅x_5,6(t)+ε_6,λbc₆x_5,6(t).  (84)

[0209] Equations (81b), (82b), (83) and (84) are equivalent to two equations having three unknowns, namely c₅(t), c₆(t) and x₅,6(t). In both the ratiometric and the constant saturation cases, the saturation can be determined by acquiring approximations to the primary or secondary signal portions at two different, yet proximate times t₁ and t₂ over which the saturation of A₅ in the volume containing A₅ and A₆ and the saturation of A₃ in the volume containing A₃ and A₄ does not change substantially. For example, for the primary signals estimated by the ratiometric method, at times t₁ and t₂:
s″_λa(t₁)≈ε_5,λac₅x_5,6(t₁)+ε_6,λac₆x_5,6(t₁)  (85)
s″_λc(t₁)≈ε_5,λcc₅x_5,6(t₁)+ε_6,λcc₆x_5,6(t₁)  (86)
s″_λa(t₂)≈ε_5,λac₅x_5,6(t₂)+ε_6,λac₆x_5,6(t₂)  (87)
s″_λc(t₂)≈ε_5,λcc₅x_5,6(t₂)+ε_6,λcc₆x_5,6(t₂)  (88)

[0210] Then, difference signals may be determined which relate the signals of equations (85) through (88), i.e.:
Δs_λa=s″_λa(t₁)−s″_λa(t₂)≈ε_5,λac₅Δx+ε_6,λac₆Δx; and  (89)
Δs_λc=s″_λc(t₁)−s″_λc(t₂)≈ε_5,λcc₅Δx+ε_,λcc₆Δx.  (90)

[0211] where Δx=x_5,6(t₁)−x_5,6(t₂). The average saturation at time t=(t₁+t₂)/2 is:

[0212] $\begin{array}{cc}\mathrm{Saturation}\left(t\right)=c_5\left(t\right)/\left[c_5\left(t\right)+c_6\left(t\right)\right]& \left(91\right)\\ =\frac{{\varepsilon }_{6,\lambda a}-{\varepsilon }_{6,\lambda c}\left(\Delta s_{\lambda a}/\Delta s_{\lambda c}\right)}{{\varepsilon }_{6,\lambda a}-{\varepsilon }_{5,\lambda a}-\left({\varepsilon }_{6,\lambda a}-{\varepsilon }_{5,\lambda a}\right)\left(\Delta s_{\lambda a}/\Delta s_{\lambda c}\right)}& \left(92\right)\end{array}$

[0213] It will be understood that the Δx 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.

[0214] 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.

[0215] 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, or a forehead. An attenuated signal is measured after propagation through or reflected from the medium. The pulse oximeter estimates the saturation of oxygenated blood.

[0216] 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.

[0217] 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.

[0218] 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.

[0219] 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, and different thicknesses. 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, the absorption 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.

[0220] A schematic of a physiological monitor for pulse oximetry is shown in FIG. 11. Two LED's 300 and 302, one LED 300 emitting red wavelengths and another LED 302 emitting 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 300 and 302. The photodetector 320 is connected to a single channel of common processing circuitry including an amplifier 330 which is in turn connected to a band pass filter 340. The band pass filter 340 passes it output signal into a synchronized demodulator 350 which has a plurality of output channels. One output channel is for signals corresponding to visible wavelengths and another output channel is for signals corresponding to infrared wavelengths.

[0221] The output channels of the synchronized demodulator for signals corresponding to both the visible and infrared wavelengths are each connected to separate paths, each path comprising further processing circuitry. Each path includes a DC offset removal element 360 and 362, such as a differential amplifier, a programmable gain amplifier 370 and 372 and a low pass filter 380 and 382. The output of each low pass filter 380 and 382 is amplified in a second programmable gain amplifier 390 and 392 and then input to a multiplexer 400.

[0222] The multiplexer 400 is connected to an analog-to-digital converter 410 which is in turn connected to a microprocessor 420. Control lines between the microprocessor 420 and the multiplexer 400, the microprocessor 420 and the analog-to-digital converter 410, and the microprocessor 420 and each programmable gain amplifier 370, 372, 390, and 392 are formed. The microprocessor 420 has additional control lines, one of which leads to a display 430 and the other of which leads to an LED driver 440 situated in a feedback loop with the two LED's 300 and 302.

[0223] The LED's 300 and 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 surface. The amplifier 330 amplifies this electrical signal for ease of processing. The band pass filter 340 then removes unwanted high and low frequencies. The synchronized demodulator 350 separates the electrical signal into electrical signals corresponding to the red and infrared light energy components. A predetermined reference voltage, V_ref, is subtracted by the DC offset removal element 360 and 362 from each of the separate signals to remove substantially constant absorption which corresponds to absorption when there is no motion induced signal component. Then the first programmable gain amplifiers 370 and 372 amplify each signal for ease of manipulation. The low pass filters 380 and 382 integrate each signal to remove unwanted high frequency components and the second programmable gain amplifiers 390 and 392 amplify each signal for further ease of processing.

[0224] The multiplexer 400 acts as an analog switch between the electrical signals corresponding to the red and the infrared light energy, allowing first a signal corresponding to the red light to enter the analog-to-digital converter 410 and then a signal corresponding to the infrared light to enter the analog-to-digital converter 410. This eliminates the need for multiple analog-to-digital converters 410. The analog-to-digital converter 410 inputs the data into the microprocessor 420 for calculation of either a primary or secondary reference signal via the processing technique of the present invention and removal or derivation of motion induced signal portions via a correlation canceler, such as an adaptive noise canceler. The microprocessor 420 centrally controls the multiplexer 400, the analog-to-digital converter 410, and the first and second programmable gain amplifiers 370 and 390 for both the red and the infrared channels. Additionally, the microprocessor 420 controls the intensity of the LED's 302 and 304 through the LED driver 440 in a servo loop to keep the average intensity received at the photodetector 320 within an appropriate range. Within the microprocessor 420 a reference signal n′(t) or s′(t) is calculated via either the constant saturation method or the ratiometric method, as described above, the constant saturation method being generally preferred. This signal is used in an adaptive noise canceler of the joint process estimator type 60, as described above.

[0225] The multiplexer 400 time multiplexes, or sequentially switches between, the electrical signals corresponding to the red and the infrared light energy. This allows a single channel to be used to detect and begin processing the electrical signals. For example, the red LED 300 is energized first and the attenuated signal is measured at the photodetector 320. An electrical signal corresponding to the intensity of the attenuated red light energy is passed to the common processing circuitry. The infrared LED 302 is energized next and the attenuated signal is measured at the photodetector 320. An electrical signal corresponding to the intensity of the attenuated infrared light energy is passed to the common processing circuitry. Then, the red LED 300 is energized again and the corresponding electrical signal is passed to the common processing circuitry. The sequential energization of LED's 300 and 302 occurs continuously while the pulse oximeter is operating.

[0226] The processing circuitry is divided into distinct paths after the synchronized demodulator 350 to ease time constraints generated by time multiplexing. In the preferred embodiment of the pulse oximeter shown in FIG. 11, a sample rate, or LED energization rate, of 625 Hz is advantageously employed. Thus, electrical signals reach the synchronized demodulator 350 at a rate of 625 Hz. Time multiplexing is not used in place of the separate paths due to settling time constraints of the low pass filters 380, 382, and 384.