Spectrometer Means Employing Linear Synthesized RF Excitation

The present invention relates in general to spectrometers employing broadband RF excitation and more particularly to an improved method and apparatus for generating the broadband RF excitation by use of linear synthesis.

Heretofore, broadband RF excitation has been employed for exciting RF resonance of a plurality of spectral lines simultaneously. The simultaneously excited resonance spectral lines are detected to produce a composite resonance signal. The composite resonance signal is sampled at time displaced intervals in the time domain, converted to digital data, stored in a multichannel storage or memory and time-averaged to improve signal-to-noise ratio. The time-averaged data is read out of the storage, Fourier transformed from the time domain to the frequency domain to reconstitute a resonance spectrum of the sample under analysis. The reconstituted resonance spectrum is then displayed. Such a radio frequency spectrometer is disclosed and claimed in U.S. Pat. No. 3,475,680 issued Oct. 28, 1969.

The broadband (i.e., about 1000 Hz at 100 MHz) RF excitation has been obtained in a number of ways. In a first method, an RF carrier is pulse modulated with relatively short pulses, i.e., about 100.mu.s, at relatively low pulse repetition rates as of 1 Hz to produce phase coherent Fourier components in the sidebands of the carrier at 1 Hz spacings over a bandwidth, as of 1000 Hz, on opposite sides of the carrier.

It is also known that the peak power requirements of the transmitter used to generate the RF excitation can be greatly reduced by modulating the phase or pulse amplitude of the carrier or of the field modulation in accordance with a pseudorandom sequence. Such spectrometers are disclosed and claimed in U.S. Pat. Nos. 3,588,678 issued June 28, 1971, 3,581,191 issued May 25, 1971 and 3,681,680 issued Aug. 1, 1972.

Phase correlation of the detected resonance, as excited by a pseudorandom noise generator, has been achieved by synchronizing the pseudorandom sequence with the time displaced sampling points of the composite resonance signals. Such a spectrometer is disclosed and claimed in U.S. Pat. Nos. 3,581,191 issued May 25, 1971 and 3,681,680 issued Aug. 1, 1972.

It is also known from the prior art that broadband RF excitation for a Fourier transform spectrometer is obtainable by pulsing an RF carrier between two values to produce a train of pulses of variable phase, pulse width, or pulse spacing of the successive pulses in accordance with a pseudorandom sequence to generate a wideband RF excitation. In this system the RF receiver of the resonance detector is sequenced with the transmitter pulses to obtain time sharing such that the receiver is decoupled from the transmitter. Such a spectrometer is disclosed and claimed in copending U.S. Pat. application Ser. No. 300,929 now U.S. Pat. No. 3,786,341, filed Oct. 26, 1972 and assigned to the same assignee as that of the present invention.

A problem with the prior art Fourier transform spectrometers is the increased expense derived from the fact that certain of the associated hardware such as, pseudorandom generators, modulators, spin decoupling transmitters have been relatively complex and inflexible for performing certain different kinds of resonance experiments thereby requiring a very large investment in apparatus to obtain broad experimental capability. In addition the power spectrum of the wideband RF excitation has followed the (sin X/X).sup.2 law such that the power density of the excitation has tended to fall off with frequency deviation from the carrier frequency resulting in complicated instrumental equipment or data processing to correct for this effect.

An object of this invention is to provide improved method and means for rapid qualitative and quantative analysis of atoms by measuring the precessional frequency of the nuclei of atoms in a prescribed magnetic field. A principal object of the present invention is the provision of an improved Fourier transform nuclear resonance spectrometer.

A further object of the present invention is to provide desired broadband RF excitation for the spectrometer in a more flexible and less expensive manner by providing a computer to Fourier synthesize a selected excitation frequency spectrum into a modulation output in the time domain which when employed to modulate an RF carrier produces the desired RF excitation as a sideband of the modulated carrier signal.

In one feature of the present invention, a pseudorandom phase shift component is added into each of the Fourier frequency components of the desired broadband excitation, or programmed into a digital computer and the programmed randomly phase-shifted components are Fourier transformed by the Fourier synthesis program of the computer to derive the modulation output, whereby the phases of the simultaneously excited resonance spectral lines are scrambled, thereby eliminating the requirement of a separate pseudorandom sequence generator.

In another feature of the present invention, an offset value is introduced into the Fourier synthesis program for synthesizing the computer derived modulation to be applied to the RF carrier to generate the broadband RF excitation, whereby the phase of the modulated RF carrier remains of one sign.

In another feature of the present invention, either the pulse height or pulse width of the pulse modulated RF carrier is varied in accordance with the modulation output of the digital computer to generate the wideband RF excitation for the spectrometer.

In another feature of the present invention, the modulation output of the digital computer used to modulate the RF carrier to generate the wideband RF excitation comprises a complex function of time having both real and imaginary parts, whereby the sideband spectrum is separately controllable on both sides of the modulated carrier frequency.

In another feature of the present invention, the modulation output of the digital computer used to modulate the RF carrier to generate the wideband RF excitation comprises first and second modulation components, one component for generating a sideband spectrum for exciting resonance of only a selected portion of the spectrum of the sample under analysis and the second modulation component for generating a sideband spectrum for exciting resonance of another portion of the spectrum of the sample under analysis, whereby among other advantages detected resonance of strong spectral lines may be suppressed.

In another feature of the present invention, the wideband RF excitation consists of two parts, one derived by Fourier synthesis in a digital computer and one derived from a separate time varying function with a known and desirable frequency spectrum.

Other features and advantages of the present invention will become apparent upon a perusal of the following specification taken in connection with the accompanying drawings wherein:

FIG. 1 is a schematic block diagram of a gyromagnetic resonance spectrometer incorporating features of the present invention,

FIG. 2 is a functional block diagram of the spectrometer of FIG. 1,

FIG. 3 is a plot of the resonance excitation functions in the frequency and time domain. FIG. 4 is an enlarged detail view of a portion of that excitation function of FIG. 3(c) delineated by line 4--4,

FIG. 5 is a view similar to that of FIG. 4 showing an alternative form of excitation,

FIG. 6 is a plot of certain waveforms used in the spectrometer of FIG. 1.

FIG. 7A and FIG. 7B are flow charts of the synthesizing and excitation steps,

FIG. 8 is a flow chart of a spin system analysis step,

FIG. 9 is a block diagram of an analogue embodiment of the pulse amplitude modulation synthesizer and analogue Fourier transform analyzer according to this invention,

FIG. 10 is a functional block diagram of the apparatus to convert the pulse amplitude modulation of FIG. 9 to a pulse width modulation synthesizer, FIG. 11 is a block diagram of the system of FIG. 9 using a digital computer for performing a Fourier transformation and unscrambling, and

FIG. 12 is an alternative embodiment of the invention shown in FIG. 1.

Referring now to FIG. 1, there is shown a Fourier transform gyromagnetic resonance spectrometer 11 incorporating features of the present invention. The spectrometer 11 includes a probe 12 for containing a sample of matter to be analyzed and for immersing the sample in a homogeneous polarizing magnetic field H.sub.o. The probe 12 contains a conventional RF coil structure for applying an RF magnetic field to the sample with the RF magnetic field vector being applied with a substantial component thereof at right angles to the direction of the polarizing magnetic field vector H.sub.o for exciting gyromagnetic resonance of the sample under analysis.

The RF energy for the coil structure and resonance of the sample is derived by modulating in modulator 13 an RF carrier signal supplied from RF oscillator 14 with a time-varying modulation function f(t) derived from a computer 15, such as a model 620 f digital computer commercially available from Varian Associates of Palo Alto, Cal. Modulation of the RF carrier produces sidebands on the carrier. The modulation function f(t) is chosen such that the sideband energy has the desired power spectral density for exciting resonance of a plurality of spectral lines of the sample simultaneously. Although the desired power spectral density can vary greatly depending upon the sample to be investigated and the particular desired mode of operation of the spectrometer, a typical example of one type of power spectrum for the resonance exciting energy is as shown by spectral waveform (a) of FIG. 3.

More particularly, in waveform 3(a) the desired RF exciting spectrum is generally of uniform spectral density over a relatively wide bandwidth as of 1000 Hz on one side of a carrier frequency, as of 60 to 100 MHz, except for a relatively narrow portion of the spectrum over which excitation of resonance is undesired. This narrow portion of the spectrum may contain an especially intense spectral line of the sample, such as a solvent line resonance of which it is desired to suppress.

Accordingly, data is fed into the computer in the form of a Table which tells the computer the amplitude of the real and imaginary component of each frequency of a selected excitation frequency spectrum. For example, the computer 15 is provided with the desired resonance exciting spectrum in the frequency domain, i.e., waveform 3(a), by setting up a Table I, as shown below, consisting of 2N points where N is the number of discrete frequencies in the exciting spectrum. The data may be entered into a spectral input terminal 8 or edited in Table I by being read from a digital input terminal such as a card reader, a Teletype, or a typewriter, or from an analog input device such as devices employing a cathode ray tube light pen combination, a tablet, or joystick; examples of such devices are commercially available from IMLAC Corporation of Waltham, Mass., or the data in Table I may be computed or edited automatically from the data already stored in the computer.

Assuming N is 1024, Table I will contain 2048 rows, two for each frequency component of the 1024 bandwidth (except for k=0 and k=N) representing two orthogonal components of the vector for each frequency component. One row of each pair is for a digital value corresponding to [A.sub.k cos f.sub.k ] and the other is for a digital value corresponding to [A.sub.k sin f.sub.k ] where A.sub.k represents the amplitude to the frequency component and f.sub.k its phase value at t=0.

For the example of FIG. 3 (a), the amplitude of the cosine and sine values for that portion of the spectrum which is to have zero amplitude are assigned a value of zero in Table I, see the cos and sin values for N = 1100 to 1107 while all other values A.sub.k are equal.

For coherent phase, wideband excitation, all values f.sub.k are selected to be equal and the tabled data from Table I is Fourier transformed by the computer to the time domain by means of a conventional discrete Fourier transform program using, for example, the algorithms appearing in Communications of the Association for Computing Machinery, Vol. 11, No. 10, of October 1968, pages 703 and following, see in particular equations 1-7. This Fourier transformation results in obtaining N pairs of outputs, such transformation values G(t) being tabled in the computer, such as Table II below, where G(t).sub.n represents the amplitude of the excitation function in the time domain at the time t.sub.n.

The values of G(t) are read out of Table II with the time spacing as indicated in the time column to derive a modulation output function F(t) in the time domain which when employed to modulate the carrier signal in modulator 13 results in producing the desired sideband power density spectrum as previously programmed into Table I. A typical modulation output function F(t) to produce the power density spectrum of FIG. 3(a) is shown by the waveform of FIG. 3(c), and is essentially a pulse of short duration at relatively long time spacing plus some fine structure to achieve the net lack of excitation near the center of the power density spectrum.

In a preferred mode of operation, the modulator 13 pulse modulates the carrier signal with a train of pulses with a repetition rate of 1/500 .mu.s (pulse spacing of 500 .mu.s) and a pulse width of approximately 1/10 the pulse spacing or about 50 .mu.s. The pulse height or pulse width is modulated in accordance with the modulation output G(t) of Table II, as shown by waveforms 6(a) and 6(b), respectively.

Since the values of G(t) from Table II can have both positive and negative sign, a gated phase inverter 16 is provided at the output of modulator 13 for changing the sign, reversing the phase of the modulated carrier energy fed to the probe 12 in accordance with the sign of the modulation component G(t) read out of Table II.

Cross coupling of RF energy from the transmitter 17 to a receiver portion 18 of the spectrometer 11, other than through the desired resonance of the sample, is avoided by providing a gate 19 between the probe 12 and RF amplifier 21 employed to amplify RF resonance signals picked up by the conventional receiver coil in the probe 12. The gate 19 is synchronized by the computer 15 with the timing of the transmitter pulses to provide time sharing as indicated by receiver gate waveform 6(c) and the corresponding transmitter pulse waveform of FIGS. 6(a) or 6(b).

The output of the RF amplifier is fed to one input of an RF phase detector 22 for phase detection against a reference phase signal derived via phase shifter 23 from the RF oscillator 14. The output of the phase detector is an audio frequency composite resonance signal consisting of the simultaneously excited resonance spectral line signals emanating from the sample under analysis. The composite audio frequency resonance signal is amplified in audio amplifier 24 and thence fed to an analog-to-digital converter 25 which samples (FIG. 6d) the composite resonance signal once for each transmitter pulse near the end of the period during which the receiver is gated on, see FIG. 6(c). The composite resonance signal is sampled near the end of the receiver on time in order that undesired transient signals associated with the receiver being gated on and off have died out. In an alternate embodiment, not shown, the modulator 13 may also be responsive to the modulation output G(t) to modulate the phase of the RF excitation.

The digitized samples from the output of the A to D converter 25 are stored in successive channels of a multichannel storage and adder portion 26 memory of the computer 15 for time averaging the composite resonance signal. The sampling sequence is synchronized with the readout times t.sub.0 -t.sub.n of the modulation output of the computer 15 as used to generate the windband RF excitation f(.nu.). The sampling sequence repeats with each repeat of the modulation output sequence F(t).

The time-averaged resonance data is then read out of the storage 26 and Fourier transformed via the computer 15 as programmed by a conventional Fourier transform program 27 for transforming data in the time domain f(t) into the frequency domain f(.nu.) to obtain a resonance spectrum of the sample under analysis. The time-averaged resonance spectrum of the sample is then fed to a display for display to the operator and/or for recording. Pure absorption mode, pure dispersion mode, or combinations of absorption and dispersion mode resonance spectral data can be obtained after correction for instrumental effects by reading out the cosine terms of the Fourier transformed data, sine terms of the Fourier transformed data or by reading out combinations of cosine and sine data. The Fourier transformed data is tabled by the computer in a table similar to that of Table I.

One disadvantage to the coherent phase wideband excitation as exemplified by waveform of FIG. 3(c) is that narrow pulses of carrier energy require a relatively high intensity although the RF excitation is a relatively low average spectral power density. This also introduces a dynamic range problem in view of limited storage and modulator precision. Accordingly, in a preferred embodiment, the phases of the desired RF wideband excitation are scrambled in accordance with a pseudorandom sequence. This is achieved by adding a phase shift value pseudorandomly selected between 0 and 2.pi. onto each of the cosine and sine values of Table I. In a preferred embodiment the pseudorandom number sequence is provided by a suitable pseudorandom number sequence program 29 which is fed into the computer 15 via switch 31. Such a suitable pseudorandom number sequence program is to be found in an article published in Mathematics of Computations, Vol. 19, page 201, 1965 and in the same journal, Vol. 16, page 368, 1962. The program 29 takes the desired frequency domain spectrum table similar to that of Table I and performs the pseudorandom phase addition to generate a modified table as shown in Table III adjacent Table I above. This is accomplished by taking the values of cos f.sub.k and sin f.sub.k components for a given Fourier frequency component and performing the vector multiplication as follows A.sub.k.sup.. exp(if.sub.k). exp(i.phi..sub.k), where .phi..sub.k is the pseudorandom phase shift value of phase angle. The resultant cosine and sine terms are tabled in Table III. The sequence of values tabled in Table III is then Fourier transformed to Table II and read out as previously described to generate the modulation output function G(t) employed for generating the sideband RF excitation. The waveform of FIG. 3 (b) shows a typical modulation output for providing incoherent sideband RF excitation. Either pulse width, phase or pulse height of the pulsed RF oscillator or field modulation may be accomplished with G(t).

FIG. 2 shows the functional block diagram for the spectrometer system 11 of FIG. 1 employing phase scrambled RF excitation. The time-averaged and Fourier transformed spectral data will be tabled by the computer 15 in a table similar to that of Table III. This data is unscrambled in phase by subtracting the pseudorandom sequence of phase angles previously added to the data of Table I to arrive at the original data of Table III. The result is a Table of time-averaged resonance spectral data similar to that of Table 1 which is read out as previously described to obtain pure absorption mode, pure dispersion mode or combinations of abosrption and dispersion mode resonance spectral data. If only a power spectrum of the sample is desired the Fourier transformed data need not be unscrambled as to phase and may be read out and displayed.

FIGS. 7A and 7B are the flow diagrams of an embodiment of the invention describing steps taken by the computer in converting the operator selected frequency domain excitation spectrum into a the desired time domain modulation, for controlling the modulation of RF excitation pulses in amplitude or width, and for sampling and storing the response of the sample spin system. The data table in block 100 is determined by the operator as described hereinbefore in reference to Table I and is entered into memory in any convenient manner. Two orthogonal values a.sub.k,b.sub.k are defined for each of N+1 frequencies except for a.sub.o and a.sub.n which are defined at zero phase angle, hence b.sub.o =0 and b.sub.n =0.

Assuming the operator has determined in block 102 to scramble pieces for power handling considerations, each orthogonal vector a.sub.k, b.sub.k is rotated by a pseudorandomly determined phase angle .phi..sub.k and stored in a new table 107 as a'.sub.k, b'.sub.k. The scramble decision initiates block 101 selecting a.sub.1, b.sub.1 from block 100 table and causing a pseudorandom generator 104 to start, and to select a pseudorandom number p.sub.k (where 0.ltoreq.P.sub.k .ltoreq.1), block 105, which is converted to a phase angle block 106. In block 107 the vector a.sub.1 b.sub.1 is rotated by angle .phi..sub.1 and the resultant a.sub.1 ', b.sub.1 ' is stored in memory block 108. Next, the running index k is interrogated, block 109, and if it is shown to equal less than N-1, the next value a.sub.k, b.sub.k is taken from the Table 100 by incrementing k=k+1, block 110, and repeating the cycle for each k=1, 2. . . N-1. When k=N-1, block 109, the storage of a.sub.o '=a.sub.o and a.sub.N '=a.sub.N takes place, block 111, and the inverse Fourier transform of the function represented by a'.sub.k, b'.sub.k is taken and stored, block 112.

At this point, the data is now available for modulating the RF excitation appropriately. The decision as to the number of cycles C, block 114, is noted and the modulation process is commenced, block 113, by selecting the value G.sub.o from Table G.sub.n, block 115, generating the RF pulse for t.sub.o responsive to G.sub.o either in amplitude, or width, and sampling the response, block 117, and storing the received data, block 118. At the time n is set to zero, block 113, the data table D.sub.n, block 118, is set to all zeros. If less than 2N-1 pulses have been applied, block 119, n is incremented, block 120, and the next value G.sub.n is taken from the table to control the modulation of the next pulse and repeat the steps of blocks 116, 117, 118 and 119 until n=2N-1. When the value of n reaches 2N-1, a check on the number of cycles, C, is performed, blocks 121 and 122, to see if the number of cycles run equals the amount preselected by the operation, block 114. If C=0, the process, blocks 116, 117, 118 and 119 is repeated, block 123 until C=0 at which time pulsing is stopped, block 124.

With reference to FIG. 8, the data D.sub.n, Table 118, is Fourier transformed, block 125, and the orthogonal values e'.sub.k, f'.sub.k, N+1 different frequencies are calculated and stored, block 126. If the excitation was not scrambled, block 128, the Table block 126 is displayed, block 129, as the sample frequency spectrum. If the excitation was scrambled, block 128, the unscrambling process is commenced by rotating each vector e'.sub.k, f'.sub.k through the same pseudorandom angle .phi..sub.k corresponding to that frequency as in block 107, but in the opposite sense, block 133. The unscrambled vectors e.sub.k, f.sub.k are stored, block 134, and when all vectors have been counter-rotated, block 135, the e.sub.o and e.sub.N terms are stored, block 137, and the unscrambled spectrum is displayed, block 158.

Although the spectrometer 11 of FIG. 1 has thus far been described as employing a phase inverter 16 for inverting the phase of the modulated carrier in accordance with sign changes in the modulation output G(t), this is not a requirement as an offset d.c. value of G(t) can be introduced into F(t), as shown in FIG. 5. Such a phase reversal of the modulated carrier signal is therefore not required. Accordingly in this embodiment, the phase inverter 16 can be eliminated. However, this offset in the d.c. value of G(t) tends to increase the intensity of the carrier signal.

In the amplitude modulation system according to this invention, for uniform RF power excitation of a spin system gyromagnetic resonator it may be advantageous to increase the amplitude of the Fourier coefficients of the excitation function at higher frequencies to compensate for the reduction in effective power at the sample due to the finite width of the pulses being applied. In the prior art, using Amplitude modulated pulses of fixed width result in an amplitude of the frequency spectrum coefficients seen by a spin system being proportional to (sin .omega..tau.)/.omega..tau.. Therefore, the frequency spectrum produced at the sample is the product in the frequency domain of the frequency spectrum P.sub.1 of a single pulse and the synthesized excitation frequency spectrum P.sub.d. By further shaping the synthesized excitation as a function whose frequency spectrum is proportional to (.omega..tau./sin .omega..tau.), the effective frequency spectrum of the irradiation seen by the spins can be compensated for the effect of the pulse width and can be made flat over the observed bandwidth. This feature is useful for RF excitation of spectra spanning a wide frequency range.

Referring now to FIG. 9, there is shown a nuclear resonance spectrometer wherein the advantages of the invention are accomplished by an embodiment utilizing analogue techniques as opposed to the digital computer technique of FIG. 1. After having selected the desired excitation spectrum for the sample i.e., the amplitude of each frequency component, in the frequency domain, the operator would energize the appropriate switches 71 through 74, to provide the basic oscillator 40 output to the appropriate multiplier 41 through 44. The outputs of the selected multipliers are each connected to a phase shifter, 75, wherein each channel has a corresponding voltage controlled phase shifter and a corresponding amplitude adjustment 76-79. In the example of FIG. 9 only four channels are shown x1, x2, x3, xk but it is understood that any number of channels may be provided, one channel for each desired sideband. The phase shifters 45-48 are each provided with a voltage V.sub.k to control the phase shift angle. The voltage may be constant values for the experiment, which values are arbitrarily selected, or they may be derived from a pseudorandom number generator. For purposes of this explanation, it is assumed that they are constant. The outputs of the phase shifters of the operative channels are added together in mixer 49. The output of mixer 49 is a time domain signal synthesized from the individually selected amplitudes and frequencies selected by the operator. The phase inverter 60 and digitally controlled attenuator 59 are controlled by the ADC sample and storage 51 which samples the output of mixer 49 at fixed increments and stores a digital value representative of the polarity and magnitude of the adder 49 output at the instant of sampling. The clock 50 synchronizes the ADC 51 and through delay 54 the pulse generator 56. This permits the phase inverter 60 and attenuator 59 to set before the gate 61 is opened by the pulse from pulse generator 56. When gate 61 is opened, a pulse of RF from oscillator 65 at the carrier frequency as of 60 or 100 MHz is caused to excite the probe 58 in the phase and amplitude as controlled by the inverter 60 and attenuator 59, respectively. The sample probe 58 is located in the high value field H.sub.o of magnet 70 and induced into simultaneous resonance as determined by the sidebands generated in the carrier frequency by the amplitude modulation determined by synthesized time domain signal at the output of mixer 49. The resonance signal of the sample atoms in the probe 58 are received by gate 62 which is gated on by blanking generator 57 whenever the RF is exciting the sample. The output of gate 62 is amplified in receiver 63 and fed to a synchronous phase detector or mixer 64. The output of the detector 64 which has had the RF carrier frequency removed is now connected in parallel to a series of phase detectors 66-69 and integrating amplifiers 80-83. For example, the 1 Hz channel is fed to detector 66 which detects that portion of the output of detector 64 which has the frequency and phase f.sub.1 (.phi..sub.1). The output of phase detector 66 is then sent into integrator amplifier 80 where the gain is responsive to the amplitude of reference f.sub.1 (.phi..sub.1) and the output is sent to display 70. For example, assuming that it was desired to excite the 1 Hz sideband with a very small signal because it was known that the sample exhibits a large resonance at that frequency, the operator may have adjusted the attenuator 76 so that the f.sub.1 (.phi..sub.1) output of phase shifter 46 was very small.

Since the sample resonant signal of the sample would now exhibit a smaller resonance to 1 Hz than to another more strongly excited line, the gain of amplifier 80 could be inversely responsive to the reference f.sub.1 (.phi..sub.1 ) so that the 1 Hz would be returned to its appropriate amplitude for display as if it had been excited as strongly as the other lines. As was earlier explained with reference to Table I, it may be desirable that all excited lines are excited at a single excitation level and certain lines are not excited at all. In this case, all the attenuators 76-79 would be set to the same value, the switches for the non-excited channels 71-74 would be opened and the connection of the reference f.sub.k (.phi..sub.k) to the integrator amplifiers 80-83 would be unnecessary since gain of each frequency would be treated equally.

With reference to FIG. 10, the schematic block diagram is disclosed of the control circuit to enable pulse width modulation of the RF responsive to the output of the adder 49 of FIG. 9. For each pulse from gate 89 to the divider 7, a pulse having a width determined by the magnitude of the digital signal in ADC 51 is sent from divider 7 to gate 61. The phase of the RF signal is responsive to the sign bit 52 of the ADC output. Operation of the modulator is initiated by oscillator 84 which is divided down in 85 converted to properly shaped pulses in clock pulse generator 86. Each output of clock pulse generator 86 initiates a sampling by the ADC 51 of the output of adder 49. An output of clock generator 86 also is delayed by 87 and sets the flip-flop 88 so that the next cycle of the oscillator initiates the transmission of the modulation pulse from divider 88 to gate 61. After each pulse from divider 7 the flip-flop 88 is reset so as to restart the process only upon the next pulse from clock pulse generator 86. The receipt and analysis of the signal from pulse 58 is the same as described in FIG. 9.

With reference to FIG. 11, a spectrometer having the synthesizer 31 and pulse amplitude or pulse width modulation apparatus and receiver circuitry 30 is disclosed in conjunction with a Fourier coefficient division scheme for analyzing the data received from detector 64. The outputs 53 and 52 of ADC 51 in addition to exciting the sample are connected to a digital computer 99 containing a standard Fourier transformation program as hereinbefore described wherein the frequency domain spectrum of both the synthesized excitation output of adder 49 and the sample output of phase detector 64 and ADC 93 are synchronously taken and stored upon computer command 100. The computer is further caused to divide the vector coefficients at each frequency of the sample response y.sub.k by the vector coefficient at the same frequency of the excitation X.sub.k and displaying the quotient. The division of the Fourier coefficients is the equivalent of a cross correlation in the time domain.

The use of pulse modulation apparatus as shown in FIGS. 1, 9-12 provides a convenient means to isolate the receiver from direct excitation by the transmitter. However, pulse modulation is not an essential feature of the invention. If isolation of transmitter and receiver can be achieved in an alternate fashion, for example by the use of transmitter and receiver coils which are sufficiently orthogonal, the synthesized excitation may be applied to a phase sensitive amplitude modulator or a phase modulator as a continuous signal directly from the synthesizer 31 without an intermediate ADC 51 or from the digital values in the table G(t) through a D to A converter and smoothing filter. Alternatively such continuous signals may be used to modulate the magnetic field H.sub.o such that the field modulation sidebands cause excitation of the nuclear resonance signals. With continuous excitation, the response of the spin system may also be detected as a continuous signal.

The aforedescribed technique of suppressing unwanted resonances by providing a hole in the exciting spectrum may also be applied to the prevention of aliasing. If the analog audio frequency output of the spectrometer is sampled at a frequency .nu..sub.s, in accordance with well known sampling theory the maximum frequency which may be recovered unambiguously is half the sample frequency, .nu..sub.max = .nu..sub.s /2. Higher frequencies than .nu..sub.s /2 are aliased or folded back into the frequency range 0 to .nu..sub.max. Such aliased frequencies are normally attenuated by a low-pass filter before sampling but it is not possible to make an infinitely sharp cut-off filter, and large phase anomalies near the cut-off frequently make it inconvenient to place the cut-off frequency too close to the edge of the observed frequency range. However, an excitation function may be synthesized whose power spectrum is constant up to .nu..sub.max and zero from .nu..sub.max to 2.nu..sub.max. To double the irradiated frequency range, while keeping the sampling rate constant at 2.nu..sub.max requires that the pulsing frequency of the transmitter be doubled to 4.nu..sub.max. In principle then, twice as much storage is required for the exciting function as for the signal. If, however, the excitation is synthesized in the form of a coherent phase power spectrum, the amplitudes decay fairly rapidly and much of the excitation may be approximated by zero for example, see FIG. 3. Alternatively, since the time function needed is of the form (sin .omega..tau.)/.omega..tau., it may be computed as required, eliminating the need to store an excitation function. By combining this technique with the use of the usual low-pass filter, very effective suppression of aliased frequencies is possible.

The excitation functions in the examples which have been described so far have all been real functions of time for modulation control of a carrier frequency resulting in a power spectrum which is symmetric about the carrier frequency. In general, the Fourier synthesis of a function of frequency results in a complex function of time. This time function may be represented both in phase and amplitude by a carrier frequency which is the vector sum of two components in quadrature, the amplitudes or pulse widths of which are modulated according to the real and imaginary components of the excitation function. Use of this type of modulation permits the suppression of aliasing about zero frequency, analogous to the suppression of aliasing of high frequencies previously discussed. More generally, this form of excitation can also be used to generate any desired power spectra which is asymmetric with respect to the carrier frequency. An algorithm for Fourier synthesis of a complex function of time is described in an aritcle titled "An Algorithm For Machine Calculation of Complex Fourier Series" appearing in Math. Comp., Vol. 19, p. 297 (April 1965).

For homonuclear decoupling the synthesized RF excitation technique enjoys several distinct advantages over conventional decouplers. For the incremental cost of enough information storage to hold the excitation sequence, one obtains the capability to do homonuclear decoupling as well as other experiments requiring shaped power spectra. Any number of decoupling frequencies up to the number of observed frequencies may be used, in any intensity ratio desired within the dynamic range of the modulation technique, and the conventional field frequency lock for the observing channel automatically locks the decoupling channel. Conventional prior art decouplers usually require a separate provision to lock the decoupler oscillator to the magnetic field, and can irradiate only one frequency or frequency band at a time. For heteronuclear decoupling, a separate decoupler based on the synthesized excitation technique offers much flexibility in constructing decoupling fields.

In a number of applications, the excitation function may be divided into two parts. For example, in a homonuclear decoupling experiment, one or more frequency components have large intensities for perturbing the spin system while a wideband of frequency components with low intensity are provided to observe the non-linear response of the spin system to the perturbation. In general, all nuclear spin systems are non-linear. While a good number of experiments consider these systems as linear, there are classes of experiments in which the non-linear response is very important. It is convenient to adjust the composite excitation by adjusting the amplitudes of these two parts independently. Such an addition of separate parts is indicated in FIG. 1 by the alternative embodiment in dashed lines shown by the adder 10 whose inputs are the output from the Fourier synthesized table G(t) in the computer and the output from an analog synthesizer 31 and ADC 51, or from a pulse generator 9. The wide band frequency components for observing the response of the spin system may be provided by pulses at a low repeition rate while the perturbing excitation is synthesized in the computer from the desired frequency components. This composite excitation may also be realized by adding an appropriate value to the first entry in the table G(t) following Fourier synthesis.

For suppressing unwanted lines, the aforedescribed synthesized excitation technique is conceptually equivalent to placing one or more ideal notch filters between the probe and a generator providing an output with a constant power spectral density. This technique appears to have certain advantages over other methods. It does not introduce phase anomalies in the final spectrum, as do currently available analog notch filters. Any number of lines may be suppressed without loss of sensitivity at the unsuppressed frequencies compared to the steady state pulsed Fourier transform experiment. Suppression ratios attainable are not critically dependent on spin lattice relaxation times.

The synthesized excitation technique is also useful to implement most of the line suppression methods. It may be used to do the line suppression by saturation by using a synthesized RF excitation function having a very large amplitude at the frequency of the line to be suppressed (similar to the homonuclear decoupling experiment aforedescribed). It may also be used to generate a quasi "two-pulse" experiment which has some of the advantages of both the nonirradiation synthesized excitation and the two-pulse Fourier transform techniques. Such a hybrid experiment consists of a "first pulse" which is synthesized RF excitation pulse sequence designed to apply a 180.degree. pulse only to those frequencies to be suppressed. The "second pulse" consists of a synthesized pulse sequence designed to apply a 90.degree. pulse to all frequencies except those to be suppressed. This kind of experiment will have much greater sensitivity than the standard two pulse experiment because unsuppressed lines are not saturated by the "first pulse" and much greater line suppression because the suppressed lines are not irradiated at all by the second pulse.

Other "multiple pulse" experiments may be devised for studying the relaxation parameters of the spin system in which some "pulses" are synthesized RF excitation pulse sequences derived from the table G(t) in the computer, while others are applied directly from a pulse generator 9 or analog synthesizer 31. For example, a first "pulse" may be a Fourier synthesized pulse sequence, or part of a Fourier synthesized pulse sequence, designed to perturb particular resonance lines in a spectrum. The second pulse, applied after some time interval, may be a 90.degree. pulse, for the purpose of monitoring the non-equilibrium state of the spin system which results from the perturbation due to the first pulse and subsequent partial relaxation.

The synthesized excitation technique need not be used to completely suppress a line; it may also be used to compress the dynamic range of a spectrum to facilitate accurate comparison of strong and weak line intensities. A correction will have to be made, however, to account for the different degrees of saturation of the strong and weak lines due to nonuniform irradiation power spectrum.

An important advantage to use of the programmed computer for synthesizing the RF excitation to be employed for exciting resonance in an RF spectrometer is the flexibility obtained in that a large number of very different experiments can be conducted without changing the hardware. Program changes can effectuate changes in the character of the RF excitation. For example, merely by substituting one program for another, pulse Fourier transform or stochastic resonance experiments may be conducted with the same equipment. Homonuclear decoupling experiments may be conducted without employing separate RF decouplers. Moreover, the decoupling energy may be adjusted by means of the computer synthesized RF to a much higher level than the observing power level, i.e., 128 times the amplitude of the remaining position of the RF excitation, to suppress certain frequencies such as solvent lines. In addition, the computer generated RF excitation can provide a much flatter power spectrum without the requirement for special filters.

As used herein RF spectrometer is defined to include nuclear magnetic resonance spectrometers, electron spin spectrometers, quadrupole resonance spectrometers, microwave absorption spectrometers, RF mass spectrometers and other types of spectrometers employing RF excitation.

The basic program for programming the computer for practicing the present invention in assembly language is as follows: ##SPC1## ##SPC2## ##SPC3## ##SPC4## ##SPC5## ##SPC6## ##SPC7## ##SPC8## ##SPC9## ##SPC10##