Contains research objectives and reports on two research projects.Joint Services Electronics Programs (U. S. Army, U. S. Navy, and U. S. Air Force) under Contract DA 28-043-AMC-02536(E

Bose, A. G.

Bourne, J. B.

Bruce, J. D.

Nelsen, D. E.

Oppenheim, Alan V.

Searle, Campbell L.

Stockwell, R. K.

Zimmermann, Henry J.

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XXV. SIGNAL PROCESSINGAcademic and Research StaffProf. A. G. Bose Prof. D. E. Nelsen Prof. H. J. ZimmermannProf. J. D. Bruce Prof. A. V. Oppenheim Dr. M. V. CerrilloProf. C. L. SearleGraduate StudentsJ. B. Bourne D. A. Feldman J. R. Samson Jr.M. Bruce-Lockhart R. M. Mersereau L. M. SivertsonM. F. Davis T. L. Rhyne R. E. StewartRESEARCH OBJECTIVESThis research relates to the recording, processing, and reproduction of acousticand visual signals. Included are studies that consider nonlinear and time-variantfiltering, using analog or digital techniques.Various experiments conducted over many years have indicated that small changesin physical signals apparently yield relatively large changes in perceptual response.Attempts are being made to obtain more quantitative measures of these effects. Theresults of these studies are potentially important to the improvement of performancein communication systems.1. Digital Processing of Analog SignalsThis research concerns the development and application of techniques for processinganalog signals using a general-purpose digital computer and special-purpose digitalhardware. Signal processing using digital hardware is playing an increasingly importantrole, because of the inherent flexibility and reliability of digital processing coupled withlowering cost and size resulting from the development of integrated circuit technology.Applications for digital processing techniques can be drawn from a variety of areasincluding speech-waveform processing, radar signal processing, and enhancement ofimages such as photographs and medical x-rays. In particular, we shall consider thefollowing topics.a. Design of nonrecursive digital filters.b. The effect of finite register length in digital filtering and spectrum analysis.c. Implementation of two-dimensional Fourier transforms.d. Applications to speech processing and x-ray enhancement.2. Signals and PerceptionFurther consideration of the experiments made by Dr. M. V. Cerrillo with accousti-cal and visual signals has led to three areas of research: time-variant linear pro-cessing of music signals, removal of multipath echoes from a signal by window-functionprocessing, and computer generation of visual patterns by exploitation of symmetry.A multichannel music system has been constructed to examine the subjective effectsof modifying certain parameters of the "envelope" of a music signal. By modifying theThis work is supported by the Joint Services Electronics Programs (U. S. Army,U. S. Navy, and U. S. Air Force) under Contract DA 28-043-AMC-02536(E).QPR No. 100 239(XXV. SIGNAL PROCESSING)amplitude, first derivative, and second derivative of the signal envelope appropriately,it is possible to influence the contrast, the attack, and the percussive effects in themusic. Current work is directed toward design of an improved detector system.The problem of echo-removal provides an interesting example of the application ofCerrillo's linear systems synthesis methods using window functions. 1 We are nowundertaking computer studies of the advantages and limitations of echo-removal systemssynthesized in this manner. Preliminary work indicates that the method has potentialapplications to some practical signal-processing problems. Further work is necessary,however, to establish meaningful comparisons with other methods.More than a decade ago, Cerrillo performed experiments which, in effect, consti-tuted plausibility arguments for explaining various functions of the brain in terms ofspecific system models. One of these studies considered the type of information theeye-mind system extracts from a visual scene in order for a person to recognize thescene and store it in his memory. In one aspect of this study he used generalizedsymmetry considerations to generate visual patterns. His purpose was to show that theperceptual mechanism tends to seek symmetries in patterns. He used an apparentlyrandom arrangement of dots which actually contained symmetries. The construction ofsuch patterns by Dr. Cerrillo was a time-consuming process. During the past year aMaster's thesis student succeeded in generating similar patterns using a computerdisplay system. This technique permits rapid generation of dot patterns that can beconveniently varied to study perceptual effects. This work clearly indicates thatsymmetries play an important role in the perception of visual images. For example,Smith was able to generate crude facial images using a single topological transformand an image grid that had been devised by Cerrillo.These studies can now be extended in several ways. Parameters, such as thespacing, size, and number of dots, should be varied to obtain a better understanding ofthe relationship between pattern elements and the underlying symmetries. Furthermore,the use of curvilinear geometries as topological transforms would remove some of thelimitations imposed by the use of linear transforms.3. Signals, Noise, and SystemsTwo students who have had extensive industrial experience with the Loran-C navi-gation system have initiated studies of several practical problems encountered in con-nection with it. The questions involve such matters as appropriate criteria forspecification and design of the receiver when interference is non-Gaussian natural andman-made noise, the application of digital filtering techniques in the receiver design,and the possibility of using various nonlinear filter techniques. Most of the questionsbeing studied have implications for systems other than Loran-C.4. Noise in Switching CircuitsMechanisms contributing to switching-time jitter in regenerative bistable devicesand circuits have been the subject of investigation for several years. Models relatingtime jitter to more fundamental shot, thermal, and 1/f noise processes in the circuitcomponents have been found for the tunnel diode switch and for a class of Schmidttrigger circuits.Work on this problem continues. A family of nonlinear, dynamic differentialequations relating dynamic switching variables to circuit noise is being studied. Theseequations are interesting, in that regeneration in the physical switch corresponds to thesolution's infinity. In control problems this kind of divergence is classified as aninstability, and is generally not considered further. Much of this investigation is beingcarried out with the aid of a digital computer. In some regions of operation, theQPR No. 100 240(XXV. SIGNAL PROCESSING)solutions of these equations approach those of the classic first-passage time problem,involving the determination of statistics of the first zero passage of a ramp on whichstationary noise has been superposed.A. G. Bose, J. D. Bruce, D. E. Nelsen, A. V. OppenheimC. L. Searle, H. J. ZimmermannReferences1. M. V. Cerrillo, "On the Mode of Convergence and Its Correction by Methods ofLinear Summability," Technical Report 269, Research Laboratory of Electronics,M. I. T., Cambridge, Mass., May 3, 1950; see Appendix.2. J. F. Smith, "A Computer Investigation of Symmetry in Images," S.M. Thesis,Department of Electrical Engineering, M. I. T., August 1970.A. FREQUENCY- AND TIME-DOMAIN ANALYSIS OFWINDOW ARRAYSWe have been studying in detail the time-domain and frequency-domain characteris-tics of certain "window function" operators, as developed by M. V. Cerrillo. Theresults have been published in a Master's thesis.2 In this thesis, the general operator,constructed of evenly spaced impulse windows, is derived in the time domain, and gen-eral techniques are developed for singularity analysis and transfer-function frequencyresponse analysis. These techniques are used to analyze the four basic operators: puretransmission, differentiation, delay, and prediction. Numerical examples for each oper-ator are included, as well as computer programs written in APL, which were used toobtain numerical results; these results are compared with ideal operators. Two othertopics are considered briefly: operators with perturbed window areas, and operatordetermination from zero constellations.R. K. StockwellReferences1. M. V. Cerrillo, "On the Mode of Convergence and Its Correction by Methods ofLinear Summability," Technical Report 269, Research Laboratory of Electronics,M.I.T., Cambridge, Mass., May3, 1950, pp. 122-147.2. R. K. Stockwell, "Frequency and Time Domain Analysis of Window Arrays,"S. M. Thesis, Department of Electrical Engineering, M. I. T., January 1970.B. APPLICATION OF WINDOW FUNCTIONS TO THE DETECTIONOF A SIGNAL IN THE PRESENCE OF ECHOESTo extract a transmitted signal f(t) from a received signal g(t) corrupted by echoes,QPR No. 100 241241(XXV. SIGNAL PROCESSING)g(t) = f(t) + blf(t-T 1 ) + b f(t-T 2 ) + ... , (1)it is necessary to pass g(t) through a filter with transfer function1H(s) = -sT -sT (2)1 2l +bl e +b2e + ...Synthesis of this transfer function is being investigated, with the use of the techniquesdeveloped by M. V. Cerrillo in his theory of window functions. Initial work is con-cerned with the simpler case of removal of a single echo using the transfer function1H(s) = -sT (3)1+beIn general, a frequency function H(s) can be realized as a window function byexpanding H(s) as a Taylor series about s = 0, which together with a specification of theimpulse spacing 6 can be used to determine the weights a. of the impulses in the win-1dow function. Cerrillo has shown that the weights a. for the echo-removal transfer1function depend only on the number of impulses, n, used to approximate H(s) and theratio T/6, where 6 is the spacing of the windows. One of the aims of the presentresearch is to investigate the performances of window function approximations of H(s)for fixed n and varying 6 in removing echoes from lowpass signals characterized byspecific delays T, echo amplitude b, and bandwidth om . In particular, we wish todetermine the relationship between the limits of these signal parameters beyond whichsuccessful echo rejection cannot be achieved.The studies are being carried out using a computer simulation of the window-functionrealization of H(s), with test signals comprised of sums of sinusoids at arbitrarily chosenfrequencies and pseudo-randomly chosen amplitudes. As the work progresses, signalsmore typical of those found in echo-removal applications will be used. Evaluation ofthe performance of the filters is based on rms error calculations, as well as visualcomparison of desired, corrupted, and recovered waveforms. Future research will beconcerned with the problems of removal of multiple echoes with an attempt to determinewhat improvements in frequency response and phase-shift characteristics can beobtained by cascading the echo-removal filter with other filters.J. B. BourneReferences1. M. V. Cerrillo, Technical Report 269, Research Laboratory of Electronics, M. I. T.,Cambridge, Mass., May 3, 1950, pp. 122-139.QPR No. 100 242

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