Two dimensional transform utilizing ultrasonic dispersive delay line
FIELD OF THE INVENTION 
     This invention relates to compressive receivers and more particularly, to a two-dimensional compressive receiver that simultaneously determines the frequency and direction of arrival of an incoming signal. 
     BACKGROUND OF THE INVENTION 
     Man has engaged in war on the land, in the sea, in the air and in the electromagnetic spectrum. The electromagnetic spectrum has been used by the military for improved communications, guidance of aircraft and missiles and the navigation of ships and planes. A nation seeks control of the electromagnetic spectrum because of the military&#39;s increasing dependency on its use for surveillance of potential enemy forces, communications between military units, detection of enemy military forces and the guidance and control of airplanes and missiles. With a mastery of the electromagnetic spectrum, one adversary could achieve an indispensable ingredient for conquering an enemy or discouraging a potential aggressor. 
     One of the most important problems in electronic surveillance involves the recognition of a signal in a multisignal environment and the determination of its direction of arrival. In the past, it has been common to use a one-dimensional compressive receiver or spectrum analyzer, which decomposed the frequency of the electromagnetic spectrum into bins. If a signal appeared in a bin in which it was not previously present, a new signal would have arrived. This new signal now had to be investigated, i.e., what kind of modulation is on it, what is its direction of arrival, in order to determine if the signal was produced by a friend or a foe. Some disadvantages of the foregoing was that this procedure was a time consuming, sequential process that used: a compressive receiver for rapidly sweeping a given band of frequencies to determine the presence or existence of a signal and its frequency; a plurality of analysis receivers for analyzing the kind of modulation that is on the signal, one analysis receiver being assigned to a bin that just received a new signal and some antenna receivers that acted as an interferometer by determining the direction of arrival of the incoming signal by detecting the signal&#39;s phase shifts. 
     The analysis receivers that were used in the aforementioned system required a large amount of space and were expensive. Hence, there was a limited number of analysis receivers, i.e., six (6) that were utilized in prior art systems. Thus, if the new signal birth rate was too high, there would not be enough analysis receivers to process all of the incoming signals. 
     SUMMARY OF THE INVENTION 
     This invention overcomes the disadvantages of the prior art by providing a Two-Dimensional Compressive Receiver that simultaneously determines the frequency spectrum and direction of arrival of incoming signals. By immediately knowing the direction of arrival of all detected signals, this system does not have to analyze all of the incoming signals for the reason that the location of the signals produced by friendly ships, tanks, airplanes, etc. are known. Thus, the foregoing system has the ability to filter signals by permitting the system to concentrate the search effort in certain sectors where intelligence believes there is the largest enemy concentration. 
     In essence, the apparatus of this invention is an ultrasonic layered half space dispersive delay line or lamb wave dispersive delay line which is utilized as a beam forming element in a compressive receiver. The compressive receiver performs a Fourier transform on a time function via the chirp transform algorithm. The beam forming delay line transmits the output of the compressive receiver so that the compressed pulse appears at the end of the delay line (at a time which corresponds to the frequency of the incoming wave), and the position of the compressed pulse along the edge of the delay line is related to the direction of arrival of the incoming signal. The width in frequency (time) and the width in direction of arrival (X) of the pulse depend upon the length of the delay line and the length of the antenna array. For the normal case of signals on many different frequencies and from many different directions of arrivals, the pattern on the output edge of the delay line is a two-dimensional transform of the input time-space (element) domain with the frequency coordinate readout in time and the direction of arrival coordinate readout along the delay line edge (X). 
     It is an object of this invention to provide a new and improved Two-Dimensional Fourier Transform device that simultaneously determines the frequency spectrum and direction of arrival of incoming signals. 
    
    
     Other objects and advantages of this invention will become apparent as the following description proceeds, with description should be considered together with the accompanying drawings. 
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a block diagram of the apparatus of this invention. 
     FIG. 2 is a perspective diagram of the layered half space surface acoustic wave beam forming delay line 17 of FIG. 1 shown in greater detail. 
     FIG. 3 is a perspective diagram of the lamb wave beam forming dispersive delay line 17 of FIG. 1 shown in greater detail. 
    
    
     DESCRIPTION OF A PREFERRED EMBODIMENT 
     Referring now to the drawings in detail, and more particularly to FIG. 1, the reference character 11 represents an M element linear antenna array, having a first element 1 and an N th  element N, with one of many possible incident wavefronts 12 that arrive at different times at the input of elements 1 through M at an angle of φ 0 . The output of antennas 11 are coupled to the inputs of a plurality of band pass filters 30 in order to limit the input bandwidth. The output of filters 30 are coupled to one of the inputs of an M element plurality of mixers 13. The corresponding number of each antenna element 11 being connected to the corresponding number of each filter element 30 and the corresponding number of each filter element 30 being connected to the corresponding number of each mixer element 13. The second input to mixer 13 is the output of a variable frequency swept oscillator or chirp 14. 
     Oscillator 14 is swept in a periodic fashion. The outputs of mixers 13 are applied to the respective inputs of M conventional weighting network 15. Network 15 reduces the compressed pulse time side lobes of its input signals, thus, removing any false signals that appear to exist in any bins. The outputs of networks 15 are respectively coupled to the inputs of a plurality of edge mounted transducers 16. The corresponding number of each network element 15 is coupled to the corresponding number of each transducer element 16. Transducer 16 converts the electrical energy of mixers 15 into acoustic energy. Transducers 16 are connected to the forward edge of delay line 17 and generate acoustic waves that travel through delay line 17. Delay line 17 has a length 1 and a width X. The waves that propagate through delay line 17 form an interference pattern within line 17 which produces a plurality of pulses 18 that dart out along edge 19 of line 17. Each pulse 18 represents a different waveform that was received by antennas 11. Pulses 18 are detected by a plurality of edge mounted output transducers 20. Transducers 20 are mounted to the back edge of line 17 and convert the acoustic energy contained in space 17 into electrical energy. The position of a particular transducer 20 along edge 19 that detects the pulse 18 at a given time is related to the direction of arrival of wavefront 12. The time that pulse 18 has arrived at detector 20 determines the frequency of the energy received by the antennas. Thus, the direction of arrival and frequency of incoming signals is determined at the same time. In order to improve the focusing at edge 19 a slight convex curvature should be placed on the forward edge of space 17. The detected pulse 18 at a given time may be represented by the following equation: ##EQU1## where V=voltage of pulse 18 as detected by detector 20 
     C=a constant 
     
         ψ=2πd.sub.λ φ-ψ.sub.o 
    
     
         γ=k.sup.2 /β.sup.2 
    
     d.sub.λ is the transducer spacing in acoustic wavelengths at F L  (center frequency). 
     M=Number of input transducers 16 
     β=1/2/T (weighting factor for 50 dB side lobes) 
     T=differential delay 
     k=time delay slope 
     φ o  =angle that wavefront 12 is traveling relative to antennas 11 
     ψ o  =2πS.sub.λ sin φ o  where S.sub.λ is the antenna array 11 spacing 
     φ=tan-1 X&#39;/l 
     l=length of layered half space 17 
     X&#39;=the location along the X axis that the pulse 18 was detected in a given time or the distance of the detector 20, that detected the pulse 18 in a given time from the edge of layered half space 17 having width X. 
     The frequency f, of the detected pulse 18 is represented by the following equation: 
     
         f=Kt+f.sub.o 
    
     where 
     f o  is the frequency of the pulse that arrives at t=o 
     t=time of pulse arrival 
     K=time delay slope 
     Thus, by knowing the time of arrival of pulse 18 at the output of detector 20, one may determine the frequency of pulse 18. 
     FIG. 2 shows the delay line 17 as a layered half space delay line 17 with transducers 20 and transducers 16 (not shown) of FIG. 1 in greater detail. Space 17 comprises two layers, a bottom layer 25 and a top layer 26. Bottom layer 25 is a sapphire substrate and top layer 26 may be any number of thin films, i.e., Quartz (SiO 2 ), Zinc Selenide (ZnSe), Gallium Arsenide (GaAs) and Zinc Oxide (ZnO). Layer 26 is deposited on layer 25 by procedures similar to the ones described in the book entitled &#34;Thin Film Process&#34;, Ed. by John L. Vossen and Werner Kern, Pub. 1978, by Academic Press, Inc. Layer 26 is contoured and the shape of contour 27 is dependent upon which one of the aforementioned materials is selected for layer 26. Contour 27 insures that a linear time delay vs. frequency characteristic will exist for space 17. The method for determining a linear time delay vs. frequency characteristics is described in an article by D. P. Morgan entitled &#34;Acoustic-Surface-wave Dispersive Delay Line&#34;. The aforementioned article was published in July, 1969 in the Proceedings of the Institution of Electrical Engineers, Vol. 116, No. 7. 
     FIG. 3 shows an alternate and preferred embodiment of the delay line 17. Delay line 17 in the preferred embodiment is a lamb wave dispersive delay line with transducers 20 and transducers 16 (not shown) of FIG. 1 in greater detail. Delay line 17 is a tapered slab of material 38. Material 38 may be quartz or sapphire. Material 38 is tapered and the shape of the taper is dependent upon which one of the aforementioned materials is selected for material 38. The taper on material 38 insures that a linear time delay vs. frequency characteristic will exist for line 17. The method for determining a linear time delay vs. frequency characteristics is described in an article by A. H. Fitch which appears in Vol. 35 of The Journal of the Acoustical Society of America, pages 709-714, published in 1963. 
     The above specification describes a new and improved two dimensional Fourier transform. It is realized that the above description may indicate to those skilled in the art additional ways in which the principles of this invention may be used without departing from its spirit. It is, therefore, intended that this invention be limited only by the scope of the appended claims.