XXIV. SIGNAL PROCESSING Academic and Research Staff Prof. A. G. Bose Prof. A. V. Oppenheim Prof. H. J. Zimmermann Prof. J. D. Bruce Prof. C. L. Searle Dr. M. V. Cerillo Graduate Students J. B. Bourne D. A. Feldman J. R. Samson, Jr. M. F. Davis J. M. Kates R. M. Stern, Jr. RESEARCH OBJECTIVES AND SUMMARY OF RESEARCH Projects related to recording, processing and reproducing acoustic signals are included in our research on signal processing. Both digital and analog techniques are being used to implement linear, time-variant, and nonlinear filters. Similar tech- niques are being applied to various forms of visual signals. An important aspect of this work is the attempt to establish quantitative relationships between physical signals and perceptual response. Numerous experiments conducted over the years have indicated qualitatively that small changes in physical signals can cause large perceptual changes. Accordingly, the consideration of sensory mechanisms and perceptual phenomena have important implications for the performance of communi- cation systems. 1. Signal Separation Our work on time-variant linear systems has recently been focused on the problem of signal separation. More specifically, we are designing systems which can separate two signals according to both spectral and temporal differences of the two waveforms. Our first experiments will be done with trumpet and clarinet notes because these appear to have quite different spectral and temporal properties. The methods will then be extended to other more complicated signals such as speech. It is hoped that this study will lead to a better understanding of how humans perform this signal-separation task. A second facet of our work also involves human auditory perception. We are studying the perceptual phenomenon of ambience: What constitutes ambience in a sound field and what auditory mechanisms are involved in its detection? This study will involve, among other things, simulating ambient information in an anechoic environ- ment. 2. Signals, Noise and Systems Atmospheric radio noise in the VLF and LF ranges is caused principally by elec- trical disturbances in the Earth' s atmosphere. This noise has long been recognized as having a distinctly non-Gaussian character because of its impulsive or bursty char- acter. A simple impulse model (e. g., a wave of random height impulses with a Poisson time distribution) will not, in general, account for the complex nature of this process, especially at frequencies above 30 kHz. Current research has been directed toward exploring the suitability of a multiplicative noise model,1 defined as Observed noise = a(t) . n(t). In this model a(t) represents a slowly varying envelope process of the noise process This work is supported by the Joint Services Electronics Programs (U. S. Army, U. S. Navy, and U. S. Air Force) under Contract DAAB07-71-C-0300, and by the U. S. Coast Guard (Contract DOT-CG-13446-A). QPR No. 104 349 (XXIV. SIGNAL PROCESSING) n(t). The latter is a Gaussian process whose power density spectrum is determined by the RF bandwidth of the observation receiver. Based upon the preliminary investigation of this model, D. A. Feldman has sug- gested that the envelope function a(t) of noise waveforms observed in disjoint RF chan- nels may be statistically related. To explore this specific concept and determine the general applicability of the multiplicative noise model to low-frequency atmospheric noise, a multiple-channel digital data system has been constructed to sample and record noise waveforms. Data have been collected at various frequencies and bandwidths from 10 kHz to 150 kHz. Among the preliminary results of the analysis of these data is a verification of the statistical dependence of a(t) between disjoint RF channels. A linear relationship has been observed between the noise envelope in a l-kHz channel at 83 kHz and the rms level of the RF noise in an empty "signal" channel located at 65 kHz or 100 kHz with bandwidth 1, 10 or 20 kHz. This relationship has been observed to span three decades of the noise-envelope value in some cases. This result has possible significance in the design of digital communication receivers or navigation receivers (analog estimation receivers), since it reduces a difficult non- Gaussian problem to a time-variant Gaussian problem. Solutions to the latter, in many cases, are known. A receiver using this co-channel information is by definition infinitely adaptable to the nonstationary character of a(t) caused by weather, time of day, and time of year. We are continuing to apply this noise concept to the design of low-frequency navigation receivers. We shall verify performance predictions by simu- lating various receivers and random physical motions of the receiver on a computer and adding the sampled atmospheric noise records as an additive disturbance. This will allow evaluation of various receiver designs for the same atmospheric noise and signal stimulus. 3. Sound Reproduction The problems associated with the reproduction of sound can be roughly categorized into the three areas: spectral, spatial, and temporal. In connection with music, the spectral and spatial aspects of sound reproduction have received considerable attention. There is much to learn, however, about the tem- poral aspects which hold promise of realizing a far higher degree of realism; for example, when music from a concert hall is reproduced in a relatively small room. A study of the temporal aspects of sound reproduction will begin by developing techniques to measure impulse responses in large auditoriums. At present, practical techniques do not simultaneously overcome ambient noise and provide sufficient time definition in the impulse response. 4. Digital Spectral Analysis of Two-Dimensional Signals in Polar Coordinates The computation of the Fourier transform of two-dimensional digital signals has been greatly simplified by the fast Fourier transform algorithm. This algorithm applies to the transform of data sampled on a rectangular grid and provides spec- tral samples on a rectangular grid. In many applications, however, the data are avail- able on polar grid; for example, in weather radar, in electron microscopy, and so forth. In these cases the data must either be interpolated from a polar grid to a rec- tangular grid or a direct computation of the transform or of a polar grid must be imple- mented. The proposed research is directed toward comparison and development of techniques for spectral analysis of data in polar coordinates. A. G. Bose, J. D. Bruce, A. V. Oppenheim, C. L. Searle, H. J. Zimmermann References 1. Originally suggested by H. Hall, Jr., "A New Approach to 'Impulsive' Phenomena," AP-648-650, 1966. QPR No. 104 350 (XXIV. SIGNAL PROCESSING) A. MODEL FOR LOW-FREQUENCY ATMOSPHERIC NOISE 1. Introduction The low-frequency electromagnetic spectrum from 10 kHz to 200 kHz is used exten- sively for digital radio communication and radio navigation. When the performance of radio systems in this frequency region is limited by noise, it is generally by atmo- spheric radio noise, as opposed to thermal circuit noise of the receiver. The dominant source of this radio noise is lightning, and the resulting noise is both nonstationary and non-Gaussian. While the physical mechanism of the lightning-discharge process and some statistics of the resulting noise process have been extensively studied during the past 20 years, there is no noise model that has proved suitable for improvement in low-frequency receivers. Such improvement in receiver performance is very desir- able because other improvement, which can be achieved through increased signal power, is very expensive because of transmitter limitations and the cost of the large antenna structures that are required at these frequencies. The general goal of our research was to develop a low-frequency atmospheric noise model, useful in engineering design, buttressed with experimental data, and tested with design applications. This report describes the selection of a conceptual basis for our model and some of the noise sta- tistics that were measured to characterize the noise. Subsequent reports will present a mathematical model for the noise and describe the results of applying the model to a particular problem in the design of a radio navigation receiver. 2. Noise Source The lightning-discharge process is extremely complex, involving charge movement within clouds, cloud-to-cloud movements and the familiar cloud-to-ground movement. Low-frequency radiations caused by these movements are dominated by two essential features; a low-level current pulse of approximately 1-ms duration, termed the leader, and a main current pulse, lasting approximately 50-100 ps, termed the return stroke. The leader pulse is caused by the initial ionization of the air dielectric along the dis- charge path and is actually composed of very short current pulses as the ionization path advances. The return stroke is caused by the transfer of the charge which had created the ionization potential between discharge points. This basic process is further com- plicated by the phenomena of multiple discharges that occur in large cloud structures. These multiple discharges follow the initial stroke and have been reported to exhibit a nearly continuous leader structure and upwards of 10 to 20 main strokes, the entire pro- cess spanning tenths of seconds. Examples of the noise fields created by these discharge processes are shown in Fig. XXIV-la, - b, and - c. These photographs were made at the amplified output of a broadband loop antenna with -3 dB points of 15 kHz and 85 kHz. Figure XXIV-la shows QPR No. 104 351 Ill I I I I (XXIV. SIGNAL PROCESSING) a single discharge, Fig. XXIV-lb a multiple discharge, and Fig. XXIV-lc a longer mul- tiple discharge. Experiments 2 have shown that the noise pulse created by the return stroke has an energy density spectrum centered at 6 kHz with a 1/ 2 dependence above 60 kHz.