Contains research objectives and reports on work completed and one research project.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.

Bruce, J. D.

Bruce-Lockhart, M. P.

Nelsen, D. E.

Oppenheim, Alan V.

Searle, Campbell L.

Zimmermann, Henry J.

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XXIX. SIGNAL PROCESSINGAcademic and Research StaffProf. A. G. Bose Prof. A. V. Oppenheim Prof. H. J. ZimmermannProf. J. D. Bruce Prof. C. L. Searle Dr. M. V. CerrilloProf. D. E. Nelsen Dr. V. N. KuleshovGraduate StudentsS. A. Hendryx R. M. Mersereau R. K. StockwellM. Bruce-Lockhart S. G. Peltan J. L. VeranthM. R. SamburRESEARCH OBJECTIVESThis research encompasses a variety of studies pertaining to the recording, pro-cessing and reproduction of acoustic and visual signals. Examples include nonlinearand time-variant filters, signal-to-noise ratio improvement in tape recording, inputand output transducers, and the effects of signal variations on perceptual responses.Included in these research activities are several projects that are stimulated by theideas and work of Dr. Manuel V. Cerrillo, and several that were formerly reportedunder the heading of "Statistical Communication Theory."1. Signals and PerceptionFor many years, Dr. M. V. Cerrillo has conducted numerous existential experi-ments with acoustic and visual signals. In each case, he was able to show that smallchanges in physical signals can produce relatively large changes in perceptual response.He also showed that certain types of distortion or the addition of certain kinds of noisein either the acoustic or visual case can yield a subjectively more pleasing result thanhigh-fidelity linear transmission or reproduction. He also initiated work on the relationof symmetries to the recognition process and to the esthetic aspects of the perceptualresponse.The insights gained by Dr. Cerrillo in his experiments on perceptual responses tovarious signal processes have stimulated an interest in related studies, many of whichwould have been difficult to perform a decade or more ago. For example, recentimprovements in circuit technology in the form of high-performance, low-cost, inte-grated circuits ease the design, construction, and operation of the audio signal-processing systems needed for more detailed study of perceptual responses. For visualsignals, modern computer display techniques offer opportunities for rapid variation ofparameters compared with the laborious and time-consuming methods used byDr. Cerrillo. Preliminary work with a multichannel sound system is under way, andexperiments with a computer display system are being initiated.2. Noise in Switching CircuitsMechanisms contributing to switching-time jitter in regenerative bistable devices andcircuits have been the subject of intensive study for several years. Models relating timejitter to more basic I/f, shot, and thermal noise processes in the circuit components havebeen found for the tunnel diode switch I and for a class of bipolar transistor circuits. 2This 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. 96 255(XXIX. SIGNAL PROCESSING)We plan to continue this work. There are classes of nonlinear differential equationsthat relate dynamic variables in a given regenerative circuit to noise present at theswitch input or generated within components of the circuit. We shall investigate theseequations. The solutions of these equations are related, in some regions of operation,to first-passage time problems. Consequently, we are also trying to solve some basicfirst-passage time problems for low-order Markov processes by using a combination ofFokker-Planck equation and Monte Carlo simulation methods.A. G. Bose, J. D. Bruce, D. E. Nelsen, A. V. Oppenheim,C. L. Searle, H. J. ZimmermannReferences.1. D. E. Nelsen, "Statistics of Switching-Time Jitter for a Tunnel Diode Threshold-Crossing Detector," Technical Report 456, Research Laboratory of Electronic's,M.I.T., Cambridge, Mass., August 31, 1967.2. B. W. Stuck, "Switching-Time Jitter Statistics for Bipolar Transistor Threshold-Crossing Detectors," S. M. Thesis, Department of Electrical Engineering, M. I. T.,June 1969.A. WORK COMPLETED1. FIRST-PASSAGE TIME STATISTICS OFA RAMP PLUS NOISEA Master's thesis with this title was presented to the Department of Electrical Engi-neering, M. I. T., by Marvin R. Sambur, in August 1969.D. E. NelsenB. TIME-DOMAIN SYNTHESISIn 1956, M. V. Cerrillo reported on a method of time-domain linear synthesiswherein he considered systems whose impulse responses were of the type shown inFig. XXIX-la. By approximating them with a string of m pulses (as in Fig. XXIX-lb)he was able to show that any of the following operations could be realized: pure trans-mission, delayed transmission, advanced transmission, any derivative up to order (m-1),any linear combination of these.Two such systems have been built for mmax = 4, one of which is reported here. Theheart of this realization is an analog shift register (see Fig. XXIX-2). This is essen-tially a string of sample-and-hold circuits, clocked by a digital timing network in sucha way as to operate like a shift register with analog sampled levels in place of ones andzeros. The contents of each sample-hold are tapped and multiplied by some ak, thensummed together so thaty(t) = alx(t-6) + a 2 x(t-26) + a 3 x(t-36) + a 4 x(t-46)= x(t)* [alUo(t-)+a 2 uo(t-26)+a 3 uo(t-36)+a 4 uo(t-46)].QPR No. 96 256'48 58 68 78 88 98h (t)h (t)hsr (t)(b)38 48 a5a2 a 4(c)Fig. XXIX-1. (a)(b)(c)f(t)Fig. XXIX-2.Type of impulse response under consideration.Pulse approximation of h(t). AShift-register realization of h(t).I - y(t)ADiagram of the system for synthesizing h(t).QPR No. 96(a)257(XXIX. SIGNAL PROCESSING)If all of the frequencies of interest in x(t) are sufficiently below 1/6, it makes littledifference if impulses or pulses are used as long as correct areas and spacings aremaintained. Thus we have a valid approximation of the type of response under consid-eration.By setting the coefficients properly and in the manner that Dr. Cerrillo had stated,quite good results were obtained. Within the bandwidth restrictions set out above, thesystem was able to produce all of the predicted operators very satisfactorily. Furtherresearch into the behavior of such systems in the frequency domain is being carried outby R. Kent Stockwell.M. Bruce-LockhartQPR No. 96 258

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