Abstract:
A system for extracting the complex Fourier coefficients from an unknown RF signal to classify the RF signal is disclosed. The extraction system utilizes optical signal processing in combination with the generation of electronic timing and control signals. The system employs an optical processor comprising a Bragg cell to yield the Fourier coefficients including the amplitude, phase and frequency parameters thereof. The system further includes a parallel arrangement that provide for parallel processing to reduce the computational time needed to determine the complex Fourier coefficients including the amplitude, phase and frequency parameters thereof.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a system that performs the measurement of complex Fourier coefficients of RF signals. More particularly, the present invention relates to a system that performs complex Fourier coefficient measurements of RF signals using optical processing techniques, specifically, a technique that improves on the Bragg cell optical technique so as to yield the phase parameters along with the frequency coefficient amplitude parameters of the RF signals being characterized. 
     2. Description of the Prior Art 
     Digital signal processing techniques are currently employed to provide complex Fourier coefficient measurements of RF signals so as to classify such RF signals. The digital signal processing techniques begin with the digitizing of the RF signal and then electronically calculating the Fourier transform which, in turn, yields the Fourier coefficients. The existing techniques that calculate complex Fourier coefficients take in the order of 300 microseconds which is relatively slow for many applications and are especially slow for dense signal environments made up of many RF signals. It is desired that the measurement of the Fourier coefficient be accomplished by faster means than digital signal processing techniques, more particularly, by optical processing techniques based on Bragg cell spectrum analysis techniques. 
     OBJECTS OF THE INVENTION 
     It is a primary object of the present invention to provide an electronic/optical hybrid system that provides complex spectrum analysis of the signal modulation that yields Fourier coefficients and which builds on known Bragg cell spectrum analysis techniques. 
     It is another object of the present invention to provide for optical processing techniques that yield the determination of the Fourier coefficients, especially the phase parameter thereof. 
     It is another object of the present invention to provide for a system that yields the determination of complex Fourier coefficients, especially the phase parameter, with minimum processing time by employing speed of light and parallel signal processing techniques. 
     Further still, it is an object of the present invention to provide for various embodiments of optical processing techniques each yielding the accurate determination of the Fourier coefficients, including the phase parameter thereof. 
     Further, it is an object of the present invention to reduce, in certain cases, the amount of sampling of an unknown RF signal that is needed to determine the Fourier coefficients, for example, when the intensity of the unknown RF signal is a known quantity. 
     SUMMARY OF THE INVENTION 
     The present invention is directed to an apparatus for extracting Fourier coefficients from an RF signal of interest so as to characterize the RF signal. The RF signal has a fundamental frequency and harmonics thereof along with a leading edge and a carrier frequency which is modulated. The apparatus is adapted to permit interference between beams of the same frequency launched from two different Bragg cells and preferably extracts the Fourier coefficient by using parallel and optical processing techniques so as to provide a rapid determination thereof. 
     The apparatus comprises a generator, first and second Bragg cells, and means for receiving the outputs of the Bragg cells. The generator generates a signal having a predetermined spectrum that includes one of the fundamental and harmonic frequencies of the RF signal of interest. The first Bragg cell has means for receiving the RF signal and providing a representative output thereof. The second Bragg cell has means for receiving the signal generated by the generator and providing a representative output thereof. The means for receiving the outputs of the first and second Bragg cells allows for the outputs of the Bragg cells to interact with each other to produce an interference pattern that contains amplitude and relative phase information representative of the Fourier coefficients of the RF signal of interest. In one embodiment, the generator provides a frequency spectrum containing a frequency that corresponds to one of the fundamental and harmonic frequencies of the RF signal of interest. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     These and other objects, features and advantages of the invention, as well as the invention itself, become better understood by reference to the following detailed description when considered in conjunction with the accompanying drawings wherein like reference numbers designate identical or corresponding parts throughout and wherein: 
     FIG. 1 is a block diagram of the system of the present invention for extracting Fourier coefficients from RF signals. 
     FIG. 2 is a block diagram of the input electronics of FIG.  1 . 
     FIG. 3 is a diagram of a prior art device employing Bragg cell technology Fourier analysis but without the benefits of the present invention. 
     FIG. 4 is an isometric schematic of one embodiment of an optical processor of the present invention. 
     FIG. 5 is composed of FIGS. 5A and 5B respectively illustrating top and side projections related to the optical beams yielded by the embodiment of FIG.  4 . 
     FIG. 6 is a schematic of the fiber arrangement of the array of the fiber/sensor arrangement of the optical focal plane of FIG.  4 . 
     FIG. 7 is a schematic of the output electronics of FIG.  1 . 
     FIG. 8 is a Fourier plane schematic related to the present invention. 
     FIG. 9 is an alternate embodiment of an optical processor related to the present invention. 
     FIG. 10 is another alternate embodiment of the optical processor related to the present invention. 
     FIG. 11 is a still further alternate embodiment of the optical processor related to the present invention. 
     FIG. 12 is a further alternate embodiment of the optical processor related to the present invention. 
     FIG. 13 illustrates a test set-up in accordance with the practice of the present invention. 
     FIG. 14 schematically illustrates video monitoring displays yielded by the arrangement of FIG.  13 . 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Referring to the drawings, there is shown in FIG. 1 a system  10  for extracting complex Fourier coefficients of an RF signal of interest so as to characterize the RF signal. The system  10  for extracting the complex Fourier coefficients comprises a preprocessor  12 , input electronics  14 , an optical processor  16 , output electronics  18 , a central processing unit (CPU)  20 , and preferably a display  22 . The system  10  accepts input pulsed RF signals  24  and outputs the complex Fourier coefficients  26  of the modulation embodied in the RF signal  24 . The RF signal  24  has a fundamental frequency and harmonics thereof and a leading edge and a carrier frequency which is modulated. The RF signal  24  is applied to the preprocessor  12 . 
     The preprocessor  12  serves as means for receiving the RF signal  24  having the leading edge. The preprocessor  12 , in a manner known in the art, generates first and second timing signals on signal paths  28  and  30 , respectively routed to input electronics  14  and output electronics  18 , in response to the leading edge of the respective RF signal  24 . The preprocessor  12  downconverts and demodulates the RF signal  24  to a baseband so as to remove the carrier frequency, but leave the modulation. This demodulated baseband signal serves as the output of the preprocessor  12  and is routed, via signal path  32 , to the input electronics  14  which may be further described with reference to FIG.  2 . 
     The input electronics  14  serves as the means for generating the signal and reference waveforms to respectively excite the optical processor Bragg cell  34  having acoustic columns  36  and  38 , to be further described with reference to FIG.  4 . Although it is preferred that the input electronics  14  be used, other means may be provided so long as the generated signal and reference signals are developed in accordance with the teachings of the present invention. 
     The input electronics  14  preferably comprises first, second and third branches, with the first branch comprising means  40  for amplifying the modulation signal on signal path  32  and means  42  which is a time delay (τ) that delays the received signal by a predetermined amount, to be further described hereinafter. The first branch further comprises a mixer  44  having first and second inputs and an output on signal path  46  that provides the signal to acoustic column  36  of the Bragg cell  34 . The first input of mixer  44  is connected to the output of time delay  42 . 
     The second branch of the input electronics  14  comprises an oscillator  48  having an output that is routed to a pseudorandom noise (PRN) generator  50 . The PRN output is routed to mixer  52 . The oscillator  48  provides a signal with an exemplary frequency of 155 MHz. The mixer  52  also has an output applied to signal path  54  that supplies the reference signal to acoustic column  38  of the Bragg cell  34 . The mixer  52  has first and second inputs with the first input connected to the output of the PRN generator  50 . The PRN generator  50  provides a signal whose Fourier transform outputs, serving as spectral components, are at evenly spaced intervals representative of a comb spectrum that has a typical comb distribution of 5, 10 . . . 40 MHz. 
     The third branch of the input electronics  14  comprises a local oscillator  56  having two outputs with the first output connected to the second input of the mixer  44  and the second output connected to the input of the mixer  52 . The oscillator  56  provides an output signal having a typical frequency of 120 MHz. 
     The input electronics  14  receives the baseband, downconverted, demodulated signal on signal path  32 , and after a delay provided by time delay  42 , the received signal is upconverted by the interaction of the signal applied to mixer  44 , via time delay  42 , and the output signal of the local oscillator  56 . This upconverted RF signal, via signal path  46 , is applied to the signal Bragg cell acoustic column  36  of the Bragg cell  34 . The input electronics  14  has a mixer  52  which has as inputs: the PRN generator  50  and the output of local oscillator  56 . The output of mixer  52  provides the reference waveform applied to the acoustic column  38 . The PRN signal on signal path  54  is converted to a Bragg cell frequency (established by local oscillator  56 ) by the operation of mixer  52  and applied to the reference Bragg cell acoustic column  38 . The overall operation of the oscillator  48  and the PRN generator  50  are both responsive to the first timing signal on signal path  28 . More particularly, the first timing signal on signal path  28  activates and synchronizes the operations of the oscillator  48  and the PRN generator  50 . 
     The PRN generator  50  outputs a PRN code at a sub harmonic rate that is established by the oscillator  48 . The PRN code mixes with the Bragg cell local oscillator, that is, local oscillator  56 . The modulated carrier on signal path  54  drives the reference Bragg cell, that is, the acoustic column  38 . The baseband, downconverted, demodulated signal on signal path  32  passes through the delay line  42  which equalizes the timing in the signal and reference paths, that is, the first and second branches of the input electronics  14  and provides a baseband signal. The baseband signal at the output of the time delay  42  mixes with the Bragg cell local oscillator  56  and provides the upconverted baseband signal on path  46  to drive the signal Bragg cell, that is, the acoustic column  36  of the Bragg cell  34 . 
     The present invention utilizes an optical processor Fourier analyzer to determine the signal modulation spectral characteristics, that is, the RF signal  24  of FIG.  1 . The present invention computes both the amplitude and the phase parameters of the complex Fourier coefficients. 
     FIG. 3 illustrates a prior art arrangement  1000  comprised of a Bragg cell  1002  containing a linear and exemplary frequency chirp  1008 , a linear photodetector array  1004 , a signal path  1006  that carries a RF signal, similar to the RF signal  24  of FIG. 1, to be analyzed by the circuit arrangement of FIG. 3 so as to produce an acoustic response  1008  having a pulse length PL as shown in FIG.  3 . Bragg cells, as well as Fourier lenses, are well known in the art and are disclosed, for example, in U.S. Pat. Nos. 4,558,925; 4,725,774 and 4,802,149 all of which are herein incorporated by reference and reference thereto for a general discussion thereof may be found. 
     The arrangement  1000  also comprises a laser  58  having a light source beam width, W, shown in FIG. 3, and a collimator  60 , both also applicable to the present invention. The laser  58  provides a laser beam  64  which is received by the collimator  60  which, in turn, provides for a collimated laser beam  66 . The collimated laser beam  66  is applied to the input port  1110  of the Bragg cell  1002  which, in turn, develops signals at its output port  1112  shown in FIG. 3 as a pattern  68  of collimated beams diverging with respect to one another. 
     The pattern  68  is intercepted by a Fourier lens  62  that causes the intercepted pattern to be Fourier-transformed which, in turn, provides an output pattern  70  that impinges on the photodetector array  1004 . The output pattern  70  is yielded by Fourier lens  62 . 
     In operation, Bragg cell technology Fourier lens of FIG. 3, without the benefits of the present invention, analyzes signals, such as the RF signals on signal path  1006 , by deflecting the input collimated light or laser beam  66  produced by laser  58  and collimator  60  at angles corresponding to the RF signal spectral content. More particularly, the angles correspond to the spectral content of the unknown RF signal on signal path  1006  and, similarly, the Bragg cell used in the present invention produces similar angles corresponding to the spectral content of the RF signal  24  of FIG.  1 . The energy of unknown RF signal on signal path  1006  and that of RF signal  24  is spatially dispersed, in accordance with the corresponding angles, into different areas of each associated energy spectrum. The term “spatially dispersed” is interchangeably used herein with the term “demultiplexed.” For the embodiment of FIG. 3, the light deflected at these angles is generally illustrated by diverging pattern  68 . The Bragg cell  1002  has optical input ( 1110 ) and output ( 1112 ) ports and an electronic input port ( 1114 ). The electronic input port  1114  accepts the unknown RF signal on signal path  1006 . The RF signal is applied to the Bragg cell electronic input port  1114 . The Bragg cell  1002  upconverts the RF signal to optical frequencies in a manner more fully described in the previously mentioned U.S. Pat. Nos. 4,558,925; 4,725,774; and 4,802,149. The laser beam  66  having a width, W, enters the Bragg cell  1002  optical input port  1110 . The Bragg cell  1002  has an interaction length, l, which is related to the interaction of the beam  66  (in particular W) and acoustic signal response  1008  (in particular PL) and which has a value (to be further described) which is the lesser of the two quantities W and PL both generally illustrated in FIG.  3 . The Bragg cell  1002  analyzes the signal spectrum by optically deflecting portions (shown as pattern  68 ) of the incident collimated laser beam  66  through the output port  1112 . The RF input signal is shown as a linear frequency chirp acoustic pattern  1008  as an example. The sine of the deflection angle varies linearly with the RF signal frequency of signal  1008 . The deflected light intensity varies linearly with the spectral power in the input signal for low power RF signals. 
     The Fourier lens  62  focuses the angular spatially dispersed light onto a linear photodetector array  1004 . The angular spatially dispersed light has a separate spatially distinct beam for each Fourier spectral component of the RF signal on signal path  1006  of FIG. 3, as well as the RF signal of FIG. 1, as is known in the art. The focus position along the array  1004  depends on the deflection angle, i.e., the RF signal frequency. The electrical strength of the linear photodetector array  1004  response included in beam pattern  70  indicates signal intensity, that is, the amplitude of the RF signal on signal path  1006 . Two or more simultaneous input frequencies will correspondingly deflect two or more simultaneous output beams from the input laser beam  66 . Each of the deflected beams (generally illustrated as diverging beam pattern  68 ) propagates at the same angle and intensity as if each beam of the deflected beams was acting independently. The signal spectrum is, therefore, immediately produced at the output focal plane of the Fourier lens  62 , to be further described with reference to FIG.  5 . However, this spectral analysis prior art method provides only the signal power (intensity) spectrum, not the phase, which is important to the present invention. 
     The spatially dispersed light beams related to the prior art arrangement  1000  of FIG. 3 comprising the diverging beam pattern  68  are frequency and phase modulated by the signal frequency component of the RF signal on signal path  1006 . The frequency for a given spectral component can be recovered, in a manner known in the art, using a reference channel beam and a high bandwidth photodetector. The high bandwidth photodetector would produce an RF current (indicative of the amplitude of the RF signal on signal path  1006 ) by mixing the signal channel optical beam with a reference channel optical beam. In contrast, the phase information embodied in the unknown RF signal on signal path  1006  is difficult to recover because it is measured with respect to the phases of the other reference frequencies. The present invention recovers the phase information of the RF signal modulation and may be further described with reference to FIGS. 4 and 5, wherein FIG. 4 illustrates the arrangement of the optical processor  16  of FIG. 1, and FIG. 5 is composed of top and side projection illustrations of the optical outputs of the Bragg cell  34  and the Fourier lens  62  of the present invention. 
     In general, the optical processor  16  of FIG. 4 measures the signal amplitude and phase of the RF signal  24  of FIG. 1 at the code repetition harmonics established by pseudorandom noise (PRN) generator  50  of FIG.  2 . The optical processor  16  produces the signal Fourier transform at optical frequencies and displays the Fourier transform image at the output focal plane. Each harmonic is displayed as a spectral intensity sinusoid along a spectrally orientated light bar on the focal plane. The sinusoid amplitude varies with the coefficient modulus and the sinusoid phase varies with the coefficient phase. Thus, the optical processor  16  produces the amplitude (sinusoid amplitude) of the RF signal  24  of FIG.  1 . 
     FIG. 4 illustrates the arrangement of some of the elements previously discussed with reference to FIGS. 2 and 3. Laser and collimator  58  outputs a collimated light beam  64  which is split into two paths at beam splitter  60 . The output of beam splitter  60  produces laser beams  72  that intercept acoustic columns  36  and  38 . FIG. 4 further illustrates an orientation  74  having spatial phase and optical frequency directions respectively indicated by directional arrows  74 A and  74 B and a z axis, and an array  76  comprised of a plurality of spaced apart optical fibers  78   1 ,  78   2 , . . .  78   N . The plurality of optical fibers  78   1 ,  78   2 , . . .  78   N  is arranged to cover the predetermined region of the optical output of the Fourier lens  62  at the Fourier plane  96  (to be further discussed with reference to FIG.  5 ). The array  76  is shown to have impressed thereon a sinusoidal pattern generally illustrated by reference number  80 . The Bragg cell  34  produces beam patterns to be described with reference to FIG. 5 that intercept Fourier lens  62  which, in turn, produce beam patterns to be described with reference to FIG. 5 that intercept the array  76 . The beam patterns produced by the Bragg cell  34  and Fourier lens  62 , as well as the collimated laser beams  72 , may be further described with reference to FIG. 5 composed of FIGS.  5 (A) and  5 (B). 
     FIG.  5 (A) illustrates the beams&#39; interaction that primarily yields phase information of the complex Fourier coefficients analyzed by the present invention, whereas FIG.  5 (B) illustrates the beams&#39; interaction that primarily yields frequency information of the complex Fourier coefficient analyzed by the present invention. FIGS.  5 (A) and  5 (B) are illustrated so as to show the interrelationship between beams  82 A,  82 B,  83 A,  83 B,  84 A and  84 B (all impinging the Fourier lens  62 ); and  85 A,  85 B,  86 A,  86 B,  87 A and  87 B (all exiting from the Fourier lens  62 ). The Bragg cell  34 , in an operative relationship with the Fourier lens, produces a set of the beams  82 A,  82 B . . .  87 A and  87 B for each frequency of the RF signal  24  being analyzed. 
     The Bragg cells  36  and  38  and Fourier lens  62  are arranged so that for each frequency in the spectrum shared by the RF signal  24  and PRN generator  50  corresponds to that frequency that is deflected by the Fourier lens  62  to the same region of the photodetectors  78   1 ,  78   2  . . .  78   N  where the dispersed beams launched from the Bragg cells  36  and  38  form an interference pattern. 
     FIG.  5 (A) illustrates the acoustic columns  36  and  38  of Bragg cell  34  respectively producing beam patterns  82 A,  83 A,  84 A and  82 B,  83 B,  84 B which impinges on the Fourier lens  62  which, in turn, produces beam patterns  85 A,  85 B,  86 A,  86 B,  87 A, and  87 B. FIG.  5 (A) further illustrates an orientation  89  in which the phase direction along the Fourier plane  96  is indicated by a directional arrow  89 A, whereas FIG.  5 (B) illustrates an orientation  94  in which the frequency direction along the Fourier plane  96  is indicated by a directional arrow  94 A. Beam patterns  85 A,  85 B,  86 A,  86 B,  87 A, and  87 B of FIG.  5 (B) are focused in the frequency direction of the array  76 . The array  76  is arranged at the Fourier plane  96  in both the phase and frequency directions. Further, FIG.  5 (A) illustrates two focal lengths respectively identified by dimension lines  88  and  90  that meet at the centerline  92  of the Fourier lens  62 . The Fourier lens  62  is one focal length, indicated in FIG.  5 (A) by reference number  88 , behind the Bragg cell, and the fiber array  76  is one focal length, indicated in FIG.  5 (A) by reference number  90 , behind the Fourier lens  62  for true Fourier imaging, known in the art, sometimes referred to as telecentric imaging. Although it is preferred, the Bragg cell may be located, relative to the Fourier lens  62 , at lengths other than the focal length. 
     For both beams (such as  85 A and  85 B related to the signal and reference acoustic column  36  and  38 , respectively,) the Fourier lens  62  images the spatially dispersed frequency components as light bars along the phase direction in the Fourier plane  96 . The spatially dispersed frequency components are sometimes referred to as demultiplexed frequency components. For a given frequency, the signal and reference beams travel in parallel after the Bragg cell, the Fourier lens focuses these two beams to the same point at the Fourier planed because a property of the Fourier lens is that it focuses beams traveling in the same direction, to the same point in the Fourier plane. This causes signal and reference light bars to overlap at the Fourier plane. More particularly, the superimposed beams  85 A and  85 B form a light bar on the array  76  so as to create an interference pattern as previously mentioned. The acousto-optic interaction length, l, not shown in FIG. 5 but previously discussed with reference to FIG. 3, determines the frequency plane divergence 1/e 2  width, δΘ freq , as δΘ freq =λ/l where the subscript “freq” represents the frequency direction and λ is the optical wavelength of the deflected beam. The acoustic column interaction width along the phase direction, D, shown in reference FIG. 5A, determines the phase divergence δΘ p , as δΘ p =λ/D, where the subscript, p, represents the phase direction  89 A. Since the interaction length, l, of columns  36  and  38  of the Bragg cell  34  is usually much greater than the column width, D, thereof, each beam diverges much more along phase direction  89 A than along frequency direction  94 A. 
     The Fourier lens  62  images each signal frequency each having beams  82 A,  82 B . . .  87 A and  87 B, onto the Fourier plane  96  as a bar shaped beam  91  along the phase direction  89 A and shown in FIG.  5 (A) for the footprint of beam  85 A intercepting and overlapping beam  85 B. The light bar frequency resolution, δ, varies with the deflected beam frequency divergence as δ=fδΘfreq where f is the Fourier lens focal length. The bar length, BL, such as that of bar shaped beam  91 , varies with the deflected beam divergence along the phase direction  89 A and BL=fδΘ p . The bar position, Y along the frequency direction  94 A for both the beam signals associated with the column  36  and beam signals associated with the reference column  38 , depend on the RF frequency of the signal applied on signal path  46  (see FIG.  4 ). For a given frequency, Y is the same for both associated beams and may be expressed:              Y   =       f                     θ   B          (   ω   )         =       λ                 f                 ω       2      π                 v                 (   1   )                                
     where Θ B (ω) is the frequency dependent Bragg deflection angle and v is the acoustic velocity. At each RF frequency of the signal applied on signal path  46 , all of beams associated with the signal and reference columns produce a phase directed light bar across the Fourier plane  96 . The reference focal plane optical output is a regularly spaced pattern of light bars representing a frequency comb where all the frequency components are initially in a known relative phase (ideally zero phase). The comb spectrum contains frequencies at the center of each frequency channel to be further described. Representative light bars are to be further described hereinafter with reference to FIG.  14 . 
     The split collimated beams  72  (see FIG.  5 (A)) impinge on the Bragg cell  34 . The split collimated beams  72  impinge upon the Bragg cell  34  optical input face, and separately illuminate acoustic columns  36  and  38 . The upconverted signal waveform on signal path  46  (see FIG. 4) generates the acoustic column  36  induced weak diffraction grating that deflects the applied optical beam  72  to the Bragg cell output beams  82 A,  83 A, and  84 A. The acoustic column  36  spatially disperses or demultiplexes the frequency within the acoustic column  36  into deflected light beams  82 A,  83 A, and  84 A in a manner as generally shown in FIG.  5 (B). The deflected beams propagate at different angles in the frequency direction  94 A as shown in FIG.  5 (B). Each deflected beam  82 A,  83 A, and  84 A is modulated, in frequency and phase by the respective signal characteristics applied on signal path  46  in a manner as shown in FIG.  5 (A) (phase) and FIG.  5 (B) (frequency). 
     The reference upconverted PRN code waveform applied on signal path  54  (see FIG. 4) is transduced into the reference acoustic column  38  of the Bragg cell  34 . The reference acoustic induced diffraction grating of acoustic column  38  demultiplexes the reference PRN comb spectrum carried by path  54  as deflected beams  82 B,  83 B, and  84 B from the incident collimated beams  72 . The deflected light beams propagate into frequency dependent angles in the frequency direction  94 A. Each deflected beam is frequency and phase modulated by its PRN spectral component generated by the PRN generator  50  of FIG.  2 . The reference beam frequency modulations are all phase synchronous. 
     The light bar intensity such as that developed by the superimposed beams  85 A and  85 B of FIG.  5 (A), depends on the signal and reference channel drive powers, which, for the embodiment of FIG. 4, are the signal on signal path  46  and reference signal on reference signal path  54 . The reference illumination is constant since the reference beam power (PRN generator  50 ) is spectrally and temporally constant (when it is pulsed on). Conversely, the signal beam intensity provided by elements  40 ,  42 ,  44  and  56  of FIG.  2  and applied on signal path  46  varies with the received signal modulation power of RF signal  24  of FIG. 1 in the spectral component. If parts of the signal and reference light bars being emitted from the Fourier lens  62  of FIG. 4 overlap, they interfere to produce a phase-directed sinusoidal spatial intensity pattern along the overlap region. If the signal and reference bars are coherent they produce a static sinusoid. Both the static sinusoid and sinusoidal spatial intensity modulation are generally illustrated in FIG. 4 by reference number  80 . If the signal and reference beams being emitted from the Fourier lens  62  of FIG. 5 are not coherent, the phase of the sinusoid will drift in a manner determined by the frequency difference between the signal and reference beams. It is, therefore, important to sample the focal plane  96  interference pattern within the optical processor  16  of FIG. 4 coherence period. The modulation spatial period, Δx, is given by expression:                Δ                 x     ≈       f                 λ     d             (   2   )                                
     where d is the acoustic column separation between column  36  and  38  of the Bragg cell  34 . Δx depends only on f, λ and d. Here f is the Fourier lens focal length, λ is the optical wavelength. Δx is independent of RF frequency, and is frequency independent across the frequency channels. The interference modulation depth depends on the relative intensity between the signal and reference beams. If these two intensities are equal, the modulation depth is 100%. The sinusoid phase depends on the initial signal frequency component phase of the received RF signal  24  of FIG. 1 because all the reference comb signals produced by the PRN generator  50  are synchronous. 
     It should now be appreciated that the optical processor  16  of FIG. 4, as well as alternate embodiments of FIGS. 9-12 to be described hereinafter, has thus analyzed the spectrum of the unknown signal, that is, RF signal  24  of FIG.  1 . The optical processor  16  produces the Fourier coefficients&#39; amplitude and phase. As will be further described, the optical processors of FIGS.  4  and  9 - 12 , process all frequencies in parallel. The signal modulation frequency of the RF signal  24  excites channel outputs to respond with Fourier coefficient descriptors. The focal plane  96  sinusoid modulation depth indicates the signal Fourier component intensity modulation, and the sinusoid phase measures the relative phase between the signal and reference beams respectively produced by acoustic columns  36  and  38  of the Bragg cell  34 . Since the signal and reference beams are in phase, the sinusoid phase gives the signal phase modulation component. 
     The fiber array  76  samples the Fourier plane  96  and may be described with reference to FIG.  6 . FIG. 6 schematically illustrates the array  76  comprised of the plurality of optical fiber  78   1  . . .  78   N  arranged in a row-column matrix with the rows being identified by the nomenclature frequency channels indicated by directional arrow  98 , and the columns being identified by the nomenclature interference sinusoid indicated by directional arrow  100  and correlatable to the sinusoidal waveform  80  shown in FIG.  4 . 
     Each phase directed line corresponds to a different frequency channel that is spatially sampled as an interference sinusoid three times as shown by the three fiber arrangement in each row of FIG.  6 . FIG. 6 also shows the fiber  78   1  . . .  78   N  position in the fiber array  76 . Each fiber  78   1  . . .  78   N  addresses a separate photodetector, to be described with reference to FIG. 7, which converts the intercepted optical signal to an electrical signal. The output electronics  18  of FIG. 7 extracts this information and provides a digital pulse descriptor word therefor. 
     FIG. 7 illustrates the output electronics  18  which provide, in part, a means for receiving the pattern of intercepted optical signals and extracting therefrom the Fourier coefficients. The output electronics  18 , as shown in FIG. 7, is comprised of a plurality of elements identified in Table 1 by reference numbers and functional operations. 
     
       
         
               
               
               
             
           
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 REFERENCE NO. 
                 FUNCTION 
               
               
                   
                   
               
             
             
               
                   
                 102 
                 PULSE GENERATOR 
               
               
                   
                 104 1 , 104 2 , . . . 104 N   
                 PHOTODETECTOR 
               
               
                   
                 106 1 , 106 2 , . . . 106 N   
                 TRANSIMPEDANCE AMPLIFIERS 
               
               
                   
                 108 1 , 108 2 , . . . 108 N   
                 SAMPLE AND HOLD CIRCUITS 
               
               
                   
                 110 1 , 110 2 , . . . 110 N   
                 ANALOG/DIGITAL CONVERTERS 
               
               
                   
                 112 
                 INTERFACE NETWORK 
               
               
                   
                   
               
             
          
         
       
     
     In general, the output electronics  18  of FIG. 7 extracts the information from the output focal plane  96  of FIG. 5, digitize the signal at points on the focal plane  96 , and encode the complex Fourier coefficients thereof. The output electronics  18  spatially samples and digitizes each waveform at three points along the phase axis for each frequency (previously discussed with reference to FIG.  6 ). The preprocessor&#39;s  12  trigger, by way of the second timing signal, initiates the sampling of the contents of the digitized waveforms. 
     FIG. 7 shows the signal path  30  on which is the second timing signal generated by the preprocessor  12  of FIG. 1 is applied, as being routed to the pulse generator  102 . The pulse generator  102  determines the sampling rate of the data of the output electronics  18  by appropriately activating the sample and hold circuits  108   1  . . .  108   N . The photodetectors  104   1  . . .  104   N  respectively receive the outputs of the fibers  78   1  . . .  78   N  and provide a corresponding electrical signal to the transimpedance amplifiers  106   1  . . .  106   N . The transimpedance amplifiers  106   1  . . .  106   N  drive the sample and hold circuits  108   1  . . .  108   N  which contain the spatial sinusoidal amplitude values at the sample time established by the pulse generator  102 . The second timing signal on signal path  30  generated by the preprocessor  12  initiates the pulse generator  102  to establish the sample window, that is, the time duration in which the contents of the sample and hold circuits  108   1  . . .  108   N  are read out. Each sample and hold circuit  108   1  . . .  108   N  provides an output which drives a separate analog-to-digital converter  110   1  . . .  110   N , which, in turn, digitizes the signal from each fiber  78   1  . . .  78   N  shown in FIG.  4 . Each analog-to-digital converter provides an output, in parallel, that is passed to the CPU  20  by way of an interface network  112 , and each of these digitized signals is stored in a memory of the CPU  20 . The interface network  112  provides the protocol to allow the digital signals of the A/D converters  110   1  . . .  110   N  to be delivered to the CPU  20  in a manner known in the art. 
     The digitized data provided by A/D converters  110   1  . . .  110   N  from each photodetector  104   1  . . .  104   N  is stored in a memory array of the CPU  20 . Each photodetector row corresponds to a frequency channel, and each column corresponds to a periodic sample of the sinusoid (see FIG. 4 reference number  80 ) in a manner as described with reference to FIG.  6 . The technique for the periodic sampling may be that described in U.S. Pat. No. 5,682,238, assigned to the same assignee as the present invention, and herein incorporated by reference. The presence of a sinusoid at a given frequency indicates the presence of a signal modulation at the respective channel frequency. If no signal is present, a uniform bar along the phase axis is present for that frequency. The amplitude of the sinusoid for that frequency indicates signal modulation intensity. The signal Fourier coefficients&#39; phase is determined both by the photodetector  104   1  . . .  104   N  responses along the spatial sinusoid (see FIG. 4 reference number  80 ) and the fiber  78   1  . . .  78   N  spacing along the spatial sinusoid (see FIG. 4 reference number  80 ). If the fiber  78   1  . . .  78   N  samples are at points separated by  90  spatial degrees, the signal amplitude, A, and the signal phase, φ, are respectively given by expressions (3) and (4):              A   =       (           D1   2     +     D2   2     +     D3   2       2     -     D2        (     D1   +   D3     )         )               (   3   )               φ   =     a                   tan        (       D1   -   D3       D1   +   D3   -     2      D2         )                 (   4   )                                
     where D 1 , D 2  and D 3  are the responses of the first, second, and third fibers along the Fourier component spatial sinusoid. More particularly, with reference to FIG. 6, the first, second and third fibers are those of any three fibers along any row identified by directional arrow  98  (frequency channels). With regard to expression (4), any quadrant ambiguity of the atan (arc tan) quantity can be resolved by considering the sign of the numerator and the denominator of expression (4). 
     The computer, in particular CPU  20 , receives the digitized data, manipulates and assembles the Fourier coefficients&#39; amplitudes and phases and provides them in a pulse descriptor word (known in the art). For instance, the information could be output from the A/D converters  110  by N digital words on N parallel data busses. Each parallel bus would contain the amplitude and phase corresponding to one frequency and the parallel lines could provide for parallel processing of the data, thereby, reducing the required processing time to about 16 μsec, which is a substantial decrease of the prior digital processing art that took about 300 μsec. 
     The application program being run in CPU  20  should take into account critical parameters which are spectral sampling width, timing, throughput rate, and amplitude and phase offset. 
     Spectral sampling width: The spectral sampling width (SSW) is the segment width along the frequency direction that samples the Fourier coefficient and may be further described with reference to FIG. 8 which is a Fourier plane schematic  114  (known in the art) having x and y axis respectively identified as phase and frequency parameters previously discussed with reference to FIG.  5  and illustrating the reference beam (identified by the clear presentation  116 ) and signal beam (identified by the dark presentation  118 ) at different frequencies across frequency bandwidth. The reference beam is that produced by the acoustic column  38  of the Bragg cell  34 , whereas the signal beam is that produced by the acoustic column  36  of the Bragg cell  34 . FIG. 8 further illustrates a detector  104   1  width identified by dimensional lines  120  and  127 . 
     Optical processing by the system  10  of FIG. 1 of the RF signal  24  of FIG. 1 Fourier transforms the RF signal  24  along the focal plane  96  frequency direction (see FIG.  5 ). It is not the Fourier transform that is of interest to the present invention, but rather the Fourier coefficients of RF signal  24 , which are the Fourier transform values at harmonically related spectral positions provided by the PRN generator  50  of FIG.  2 . The SSW is somewhat limited by the smaller of the Fourier plane reference light band width (e.g., clear presentation  116 ) or the fiber diameter of optical fibers  78   1  . . .  78   N  of FIG.  4 . 
     There is a design trade-off for the selection of SSW. A wide SSW produces more power at the photodetector, such as photodetector  104   1  of FIG. 7, but also narrows the integration time window necessary to maintain coherence between signal and reference established by pulse generator  102 . The wider SSW increases the power by allowing the photodetectors  104   1  . . .  104   N  of FIG. 7 to accept more of the instantaneous signal spectrum developed by the RF signal  24  of FIG.  1 . But the wide SSW exhibits a short term decorrelation interval that limits the coherent integration period. More particularly, the wider the frequency separation between the SSW limit (established by the acoustic column  36  of the Bragg cell  34 ) and the reference tone (established by the acoustic column  38  of the Bragg cell  34 ) at the SSW center frequency, the faster the two (signal and reference) tones decorrelate. This limit bounds the integration time and limits the input energy available in the sample and hold circuits  108   1  . . .  108   N . On the other hand, a narrow SSW provides little signal power at the Fourier component and less coherence loss. The narrow SSW allows longer sinusoid sampling. More particularly, the narrow SSW allows for more time to sample the three fibers previously described with reference to FIG.  6 . The trade-off is between a wide spectral sampling width (SSW) which provides more power for a limited sampling time and a narrow spectral sampling width (SSW) which provides little power and a long integration time. 
     Timing: Precise timing is critical to both the input and output electronics of FIGS. 2 and 7 respectively. For the input electronics  14 , the waveforms in the signal and reference Bragg cells are synchronized, otherwise the phase of the measured sinusoids, generally illustrated in FIG. 4 with reference number  80 , are not consistently produced. The total reference waveform (such as beam  85 B of FIG.  5 (A)) is applied at the focal plane  96  before the signal waveform (such as beam  85 A of FIG.  5 (A)). The complete reference waveform (such as beam  85 B of FIG.  5 (A)) remains at the focal plane  96  until the signal (such as beam  85 A of FIG.  5 (A)) is completely transferred through the optical processor  16  to ensure a spatial sinusoid (represented by the sinusoidal  80  of FIG. 4) for the entire sample time. In the output electronics  18 , the sampling begins after the signal waveform enters the signal Bragg cell acoustic column  36 . More particularly, with reference to FIG. 4, the sampling begins after the signal produced by mixer  44  (also see FIG. 2) is applied on signal path  46  (see FIG.  4 ). The preprocessor  12  trigger signals on signal paths  28  and  30  of FIG. 1 initiates timing for both the PRN code of the PRN generator  50  of FIG.  2  and the sampling of FIG.  7 . Inserting appropriate delay lines, such as time delay  42  of FIG. 2, assures proper synchronization between the input ( 14 ) and output ( 18 ) electronics. 
     Throughput rate: Because of speed-of-light processing, the spectrum related to the RF signal  24  of FIG. 1 appears at the focal plane  96  of FIG. 4 substantially instantly. The focal plane  96  information quickly flows through the fibers  78   1  . . .  78   N , detectors  104   1  . . .  104   N  and transimpedance amplifiers  106   1  . . .  106   N  of FIG.  7 . The first sample function τ, of each waveform is integrated and digitized in an equivalent amount of time. The digitized information at the output of the A/D converters  110   1  . . .  110   N  of FIG. 7 then flows to the computer (CPU  20 ) where it takes up to 16 microseconds (previously discussed parallel processing) to compute the spectrum and encode it. 
     Amplitude, Phase and Bias Offsets: Three measurements are needed to solve for the three unknowns: amplitude, phase and bias offsets. In the process of calculating phase coefficients, the computation of an arc tangent function is needed. Since this would take several microseconds in software an arctan look-up table is used. 
     It should now be appreciated that the present invention comprises an electronic/optical hybrid system  10  that provides complex spectrum analysis that builds on Bragg cell spectrum analysis technology. The phase values obtained by the practice of the present invention are determined by referencing the spectrum lines to a phase matched set of local oscillators, that is, oscillator  56  of FIG.  2 . To accomplish this, phase matched local oscillators are provided from a PRN generator  50  initialized by the leading edge of the signal. 
     It should also be appreciated that the practice of the present invention provides a technique that is electronically synchronized to and triggered by the leading edge of the unknown RF signal  24  of FIG.  1 . 
     Further, it should be appreciated that the present invention generates the complex Fourier coefficients with a higher throughput rate than existing technologies and, in one embodiment, also uses a fiber array to sample a signal waveform. 
     In addition, it should be appreciated that the present invention in its analysis aspect uses concurrent measurements of multiple Fourier coefficients to, thereby, expedite and speed up the solution in a parallel processing manner. 
     Furthermore, it should be appreciated that the present invention extracts the complex Fourier coefficients. A large number of complex Fourier coefficients can be measured by the present invention with minimum processing time due to parallel signal processing. 
     Moreover, it should be recognized that, in certain cases, the required amount of sampling of the quantities related to the invention may be reduced. For example, if the intensity of the reference signal (column  38 ) of the Bragg cell  34  is known and the intensity of the signal (column  36 ) of the Bragg cell  34  is also known, then one may calculate amplitude and offset quantities without sampling thereof. In this case, only the phase needs to be measured and can be done so with two samples at each frequency. Without this known information (intensity), at least three samplings of the related quantities are needed. 
     Although the present invention preferably mixes the reference signal (output of the acoustic column  38  of Bragg cell  34 ) optically with the channelized signal (output of the acoustic column  36  of the Bragg cell  34 ) component (see FIG. 7) as described with reference to FIGS. 4 and 7, it should be recognized that the practice of the present invention envisions that the mixing of the reference signal with the channelized signal can be electronically accomplished. 
     FIG. 9 illustrates an alternate embodiment  16 A of the optical processor of the present invention. The alternate embodiment  16 A is quite similar to the optical processor  16  of FIG. 4, except that beam splitter  124  has been added and at least a three row arrangement  126  comprised of photodetector elements replaces the fiber optic  78   1  . . .  78   N  FIG. 4. A beamsplitter  124  divides the intercepted output of the Fourier lens  62  into at least three components and provides outputs thereof that are directed to the three row column arrangement  126 . The three components are phase displaced by a preferred amount of 90° in a manner previously discussed with reference to expressions (3) and (4) and the sampling thereof yields the needed information to determine the complex Fourier coefficients. 
     The row column arrangement  126  comprises at least three row columns  126 A,  126 B and  126 C of photodetector elements, such as  104   1  . . .  104   N  of FIG. 7. A review of FIG. 9 reveals that beamsplitter  124  generates three sets of beams,  86 A- 87 A;  86 B- 87 B; and  86 C- 87 C that respectively impinge columns  126 A,  126 B and  126 C. The photodetector elements  126 A,  126 B and  126 C are arranged respectively to receive the at least three output components of the beam splitter  124  and provides corresponding electrical output signals that represent the pattern of the intercepted focussed and combined optical output of the Fourier lens  62  which are processed in a manner as previously described with reference to FIG.  7 . 
     FIG. 10 illustrates another alternate embodiment of an optical processor  16 B which is quite similar to the optical processor  16  of FIG. 4 with the exception of the addition of the beam splitter  124 , previously discussed with reference to FIG. 9, and the linear detector array  126  also discussed with reference to FIG. 9, but in addition thereto, optical processor  16 B comprises lenses  128 A,  128 B, and  128 C. A review of FIG. 10 reveals that beam splitter  124 , in operative cooperation with the lenses  128 A,  128 B and  128 C, generates three sets of collimated focus beams,  86 A- 87 A (not shown);  86 B- 87 B; and  86 C- 87 C that respectively impinge columns  126 A,  126 B and  126 C each comprised of photodetector elements that provide electrical signals that are processed in a manner as described for FIG.  9 . In each linear array ( 126 A,  126 B or  126 C), one detector corresponds to one frequency component. 
     FIG. 11 illustrates a still further embodiment  16 C of an optical processor related to the present invention which is quite similar to the optical processor  16  of FIG. 4 with the exception that the fiber optics  78   1  . . .  78   N  have been replaced by a row-column arrangement  132  of photodetectors arranged to cover a predetermined region of the optical output of the Fourier lens  62  and provide corresponding electrical outputs that represent the pattern of the intercepted optical signals. The electrical signals are routed to the sample and hold circuits  108   1  . . .  108   N  of FIG. 7 for further processing thereof in a manner as previously described. 
     FIG. 12 illustrates a still further embodiment of an optical processor  16 D which is quite similar to the optical processor  16  of FIG. 4 with the exception that the beam splitter  60  is removed and laser  58  produces a beam  72  that overlaps and floods both acoustic columns  36  and  38  of the Bragg cell  34 . The removal of the beam splitter  60  from the embodiments of FIGS. 4,  9 ,  10  and  11  may also be accomplished in accordance with the practice of the present invention. 
     Although the embodiments of FIGS. 9,  10 ,  11  and  12  have been used to separate the focal plane  96  along the phase direction, it is contemplated that other graphic techniques may also be used. Further, it is contemplated that holographic, diffractive or other types of optical elements may be used to form two separate beams to illuminate the Bragg cell  34 , in particular its acoustic columns  36  and  38  of FIG.  4 . Further, it is contemplated that the sampling of the array, such as that described with reference to FIG. 7, may be accomplished at any period or nonperiodic spacing. Further, it is contemplated that the sampling may be accomplished by a number M of fiber optics  78   1  . . .  78   N  or equivalent optical detectors rather than the three samples along the spatial sinusoidal distribution described with reference to FIG.  6 . 
     Furthermore, it is contemplated that the sampling of the Fourier plane  96  may be accomplished by a single translated detector rather than an array. Moreover, it is contemplated that the hereinbefore given description of the phase and frequency directions  89 A and  94 A, respectively, discussed with reference to FIG. 5 may be reversed or the optical processor may be oriented at a random angle. In addition, it is anticipated that the separation of the Fourier lens and fiber array or the Bragg cell  34  all described with reference to FIG. 5 may be at any random distance other than those described with reference to FIG.  5 (A) that provide for telecentric imaging. 
     In addition, it is contemplated that the present invention may be practiced with or without a beam splitter interposed between the laser and the Bragg cell. 
     Moreover, it is contemplated that software may be provided to compensate for unequal reference power or unequal distribution of the fibers or inadequacies of the fiber detectors responses. The reference power or photodetector response may be held constant as a function of frequency or spatial wavelength position. Furthermore, software may be used to correct for inherent phase or amplitude differences in the digital information of the analog-to-digital converters  110   1  . . .  110   N  of FIG.  7 . 
     It is further contemplated that an additional pseudorandom PRN generator column frequency or PRN clock may be used as a reference to calibrate for phase differences. 
     In the practice of this invention tests were performed using the circuit arrangement of FIG.  13 . FIG. 13 illustrates an arrangement that includes a video camera  134 . The video camera  134  houses a photodetector array, preferably a CCD array, that detected the optical sinusoidal shown thereon as  134 A. A video monitor  22  may be used to display the video camera  134  output. 
     The arrangement of FIG. 13 utilized an 80 MHz clock oscillator  136  which drove the PRN generator  50  previously discussed with reference to FIG.  2 . The PRN generator  50  produced a PRN code with a spectrum comb: 5, 10 . . . 40 MHz. For the arrangement of FIG. 13 instead of an unknown signal, such as RF signal  24  of FIG. 1, the 80 MHz clock provided by oscillator  136  was routed to a counter  138  which counted down the 80 MHz clock to 20 MHz. Both the reference PRN waveform generated by the PRN generator 50 and the 20 MHz waveform generated by the counter  138  were upconverted by 2.5 GHz by the local oscillator  56  (not shown in FIG. 13 but shown in FIG. 2) to the Bragg cell  34  bandwidth. The reference PRN comb was applied directly to the reference Bragg cell acoustic column  38 . The upconverted 20 MHz signal was directed to a phase shifter  140  and then to the signal Bragg cell acoustic column  36  by way of a standard amplifier  142 . The results were displayed on the display  22  which may be further described with reference to FIG.  14 . 
     FIG. 14 illustrates an overall monitor display  144  comprised of displays  146  and  148 . Each of the displays  146  and  148  has a zero frequency  150 , a zero phase  152  identified by dimensional lines  154  all shown in FIG.  13 . FIG. 14 illustrates phase and frequency coordinates that correspond to the phase and frequency parameters of the Fourier coefficients of the signal being analyzed. 
     FIG. 14 schematically shows the observed video monitor displays  146  and  148  for the initial, zero phase conditions and a phase shifted condition respectively. Each of the displays  146  and  148  shows  16  lines  156   1  . . .  156   16  across the screen. These lines correspond to the light bars previously described with reference to FIG.  5 . The lines  156   1  . . .  156   16  correspond to the upconverted and downconverted reference comb spectra modulated into the 2.5 GHz Bragg cell drive signal with the upconverted and downconverted frequency being respectively above and below the zero frequency  150 . From FIG. 14 it should be noted that there is no line in the center ( 150 ) since this spatial signal corresponds to the carrier frequency which does not exist in double side-band conversion. The dash lines  156   5  and  156   12 , at +/−20 MHz, are the observed 20 MHz optical sinusoids. These sinusoids are the interference patterns, such as  80  of FIG. 4, created by the 20 MHz comb line (generated by the PRN generator  50 ) and the 20 MHz signal (generated by the counter  138 ). Two dashed lines representing sinusoids are shown in display  146  and display  148  because both signals are upconverted to the 2,500 MHz processor center frequency. From FIG. 14 it should be noted that the display  146  shows the initial optical sinusoid, whereas the display  148  shows the optical sinusoidal after a phase shift. The shift is indicated by the dash line  154  of display  148  being positioned differently with respect to dotted line  154  in displays  146  and  148 . 
     It should now be appreciated that the practice of the present invention provides for a system  10  that extracts the Fourier coefficients from the applied RF signal  24  in a rapid manner, such as less than 16 microseconds and allows for rapid identification and classification of the RF signal  24 . 
     It is understood that the invention is not limited to the specific embodiments herein illustrated and described but may be otherwise without departing in the spirit and scope of the invention.