After years of experimentation, online teaching has gone through a phase transition with the appearance of massive open online courses (MOOCs), following the model pioneered by Salman Khan with short videos and the use of tablets. Dozens of university-level courses are now available, and followed by hundreds of thousands of online students. We report on early experiences with teaching “Fundamentals of Electrical Engineering” and “Digital Signal Processing” on an open online platform (Coursera). We address in particular: (i) suitability of online platforms for signal processing oriented topics; (ii) structuring of material for the online format; (iii) quizzes and exercises for large classes; (iv) grading methods and possible certification issues; (v) learning from teaching, forums, and data mining of students feedback.

Weave analysis of artist canvas examines x-ray images taken of the paintings. Algorithms assume an underlying regularity of the canvas weave over short distances and exploits short-space spectral analysis to determine the fundamental frequency of the horizontal and vertical thread regularity. However, many paintings are too large to be covered by a single x-ray. Feature point analysis exploits brushstrokes and composition to merge several x-ray images into a single one, taking into account and removing both spatial and amplitude distortions. Certain master artists used low-quality canvas that is more irregular than the norm. A theoretical study of quasi-periodic signals shows that while the expected spectrum is a peak that broadens as period irregularity increases, sample function spectra have distinct peaks having an envelope equal to the expected spectrum.

Thread counting algorithms seek to determine from x-ray images the vertical and horizontal thread counts (frequencies) of the canvas weave comprising a painting's support. Our spectral-based algorithm employs a variant of short-time Fourier analysis to the image domain that reveals isolated peaks at the proper vertical and horizontal frequencies. Paintings made on canvas sections cut from the same canvas roll have been hypothesized to have similar, distinctive weave characteristics, allowing art historians to more accurately date paintings. Spatial variation of weave frequency measurements across a painting were cross-correlated using a new measure to determine possible common weave patterns between pairs of x-rays. By analyzing a database of x-rays made from 180 paintings by van Gogh, our algorithms confirmed situations where paintings were known to have been made on canvases cut from the same roll and found new ones.

Neuroscientists want to quantify how well neurons, individually and collectively, process information and encode the result in their outputs. We demonstrate that while classic information theory demarcates optimal performance boundaries, it does not provide results that would be useful in analyzing an existing system about which little is known (such as the brain). In the classical vein, non-Poisson channels, which describe the communication medium for neural signals, are shown to have individually a capacity strictly smaller than the Poisson ideal. We describe recent capacity results for Poisson neural populations, showing that connections among neurons can increase capacity. We then present an alternative theory more amenable to data analysis and to situations wherein systems actively extract and represent information. Using this theory, we show that the ability of a neural population to jointly represent information depends nature of its input signal, not on the encoded information.

We compute the capacity of neural prostheses using a vector Poisson process model for the neural population channel. For single-electrode stimulation prostheses, the capacity is proportional to the size of the population being stimulated, the same value that results when each neuron is stimulated individually. In contrast, when gross recordings are used in control prostheses, the capacity is much less than it is when each neuron's output is treated separately. Consequently, spike sorting, whereby gross recordings are sorted into their constituent spike trains, is crucial to the performance of neural control devices. By computing the capacity of the neural population channel with spike sorting, we find that false positives cause a far greater reduction in capacity than either missed spikes or mislabeled spikes. Thus, a good spike sorting algorithm for neural prostheses should be biased against committing false positives, even at the expense of altering the spike train statistics.

Information theory sprung from Shannonpsilas desire to determine the performance limits of communication systems. Neuroscience seeks to determine how an existing system the brain encodes and processes information. Information theory has made few inroads into neuroscience and when it has, the theory has occasionally been applied incorrectly in both obvious and subtle ways. We review both successes and failures of classic information theory in neural coding studies. We present a non-classical approach to the analysis motivated by neuroscience problems that relies heavily on the data processing theorem and properties of the Kullback-Leibler distance.

While evidence indicates that neural systems may be employing sparse approximations to represent sensed stimuli, the mechanisms underlying this ability are not understood. We describe a locally competitive algorithm (LCA) that solves a collection of sparse coding principles minimizing a weighted combination of mean-squared error and a coefficient cost function. LCAs are designed to be implemented in a dynamical system composed of many neuron-like elements operating in parallel. These algorithms use thresholding functions to induce local (usually one-way) inhibitory competitions between nodes to produce sparse representations. LCAs produce coefficients with sparsity levels comparable to the most popular centralized sparse coding algorithms while being readily suited for neural implementation. Additionally, LCA coefficients for video sequences demonstrate inertial properties that are both qualitatively and quantitatively more regular (i.e., smoother and more predictable) than the coefficients produced by greedy algorithms.

We develop a simulated annealing technique to jointly optimize a distributed quantization structure meant to maximize the asymptotic error exponent of a downstream classifier or detector. This distributed structure sequentially processes an input vector and exploits broadcasts to improve the best possible error exponents. The annealing approach is a robust technique that avoids local maxima and is easily tailored to a broadcast quantizer's structural constraints

Spike sorting refers to the detection and classification of electric potentials (spikes) from multi-neuron recordings, a difficult but essential pre-processing step before neural data can be analyzed for information content. While several spike sorting algorithms have been proposed, our goal is to determine the ultimate limits of spike classification and to characterize this error, regardless of spike sorting algorithm. We account for the major factors influencing the sorting procedure: SNR, relative amplitude ratio and inter-spike correlation in time and waveform morphology. Using an ideal detection/estimation system we calculate detection probabilities and time delay estimation errors as they vary with these parameters, establishing upper bounds on spike classification in terms of these metrics.

Practical sparse approximation algorithms (particularly greedy algorithms) suffer two significant drawbacks: they are difficult to implement in hardware, and they are inefficient for time-varying stimuli (e.g., video) because they produce erratic temporal coefficient sequences. We present a class of locally competitive algorithms (LCAs) that correspond to a collection of sparse approximation principles minimizing a weighted combination of reconstruction MSE and a coefficient cost function. These systems use thresholding functions to induce local nonlinear competitions in a dynamical system. Simple analog hardware can implement the required nonlinearities and competitions. We show that our LCAs are stable under normal operating conditions and can produce sparsity levels comparable to existing methods. Additionally, these LCAs can produce coefficients for video sequences that are more regular (i.e., smoother and more predictable) than the coefficients produced by greedy algorithms.

We previously presented a model for some wireless sensor and actuator network (WSAN) applications based on the vector space tools of frame theory. In this WSAN model there is a weight associated to each sensor-actuator link denoting the importance of that communication link to the actuation fidelity. These weights were shown to be useful in pruning away communication links to reduce the number of active channels. Inspired by recent work in power scheduling for decentralized estimation, we investigate the optimal allocation of system resources for achieving a desired actuation fidelity. In this scheme, each sensor acquires a noisy observation and sends a message to a subset of actuators using an MQAM transmission strategy. The message sent on each sensor-actuator communication link is quantized with a variable number of bits, with the number of bits optimized to minimize the total network power consumption subject to a constraint on the actuation distortion. We show analytically and verify through simulation that performing this optimal power scheduling can yield significant power savings over communication strategies that use a fixed number of bits on each communication link.

We present a simple but general model for feature-based information processing with selective attention. We model feature extraction as projections onto frames of subspaces, which accounts for redundancies in the representations of individual features as well as between features. To manage limited resources, we use feedback attentional signals to dynamically allocate system resources according to the observed events. In our model, attention maximizes the average information retained about all events weighted by their relative priorities. We illustrate the model with a simple system under a total bit constraint and discuss how the organization of the feature extraction affects the optimal bit allocation

A new telemetry method in oil well services uses compressional acoustic waves to transmit data along the drill string to the surface. Normal drilling operations produce in-band acoustic noise at intensities comparable to the transducer output while lossy propagation through the drill string and surface noise further degrade the signal. A single receiver system has a capacity of several hundreds bits per second. A two-receiver scheme exploits the fact that the surface noise source and the signal propagate in opposite directions to remove the downward propagating surface noise, which produces substantial increases in channel capacity. We use training with easily obtained data to determine how the signals need to be processed in a way that does not rely on knowing sensor placement or the acoustic model.

We considered signal reconstruction with redundant expansions under distributed processing in noisy environments. Redundant expansions have the ability to reduce noise corrupting the coefficients, but distributed processing schemes are not able to take full advantage of the redundancy present. We apply frame theory and a generalization called "frames of subspaces" to find conditions when distributed reconstruction suffers no loss in noise reduction ability, and we bound performance loss in more general cases.

We describe two multivariate statistical dependence measures which can be orthogonally decomposed to separate the effects of pairwise, triplewise, and higher order interactions between the random variables. These decompositions provide a convenient method of analyzing statistical dependencies between large groups of random variables, within which smaller "sub-groups" may exhibit dependencies separately from the rest of the variables. The first dependence measure is a generalization of Pearson's /spl phi//sup 2/, and we decompose it using an orthonormal series expansion of joint probability density functions. The second measure is based on the Kullback-Leibler distance, and we decompose it using information geometry. Applications of these techniques include analysis of neural population recordings and multimodal sensor fusion. We discuss in detail the simple example of three jointly defined binary random variables.

This paper is an initial investigation into the following question: can cooperation among sensors in a sensor network improve detection performance in a simple hypothesis test? We analyze a simple cooperative system using the Kullback-Leibler (KL) discrimination distance and a quantity known as the information transfer ratio which is a ratio of KL distances. We discover that, asymptotically, gain over a non-cooperative system depends on the conditional KL distance. We conclude with an illustrative example which demonstrates that cooperation not only significantly improves performance but can also degrade it.

A new method of wireless data telemetry in oil well services uses compressional acoustic waves to transmit data along the drill string. Coded wave trains are produced by an acoustic transducer, travel through the drill string and are subsequently decoded to recover the data. Normal drilling operations produce in-band acoustic noise at multiple sources at intensities comparable to the transducer output, while propagation through the long drill string further degrades the signal. We describe a theoretical channel model, and, based on this model, demonstrate that a single receiver system has a capacity of several hundred bits per second in such noisy drilling conditions. We analyze a two-receiver scheme that exploits the fact that the dominant noise source and the signal propagate in opposite directions. We show that with two receivers this dominant noise can be cancelled, which results in a significant improvement in capacity over the single receiver.

When transmitting a sampled signal digitally, data and error correction bits must be transmitted at least as fast as the sampling rate. Typically, each bit is allocated the same transmission time interval, which means the optimal detector yields the same error probability for each bit. An alternative is to vary the bit interval duration according to the bit's contribution to the reconstructed sample. The optimal solution yields significant gains in mean-squared error (several dB) over that provided by equal-duration bit intervals. These gains occurred over a wide range of signal-to-noise ratios. When block error correction is performed, we derive the optimal decoder from a Bayesian viewpoint and show that gains obtain here as well.

The paper develops a new systematic method of studying the benefits of 2 bit soft decisions by applying the concepts of information processing theory. We quantify performance in terms of the information transfer ratio and demonstrate the performance gain over hard decision detectors in several noise environments. In addition, we show that likelihood ratio tests maximize the information transfer ratio, and we propose a method of optimizing threshold values for the 2 bit soft decision detector.

This paper describes the development of the voltage-source equivalent circuit. A subsequent paper concerns the current-source equivalent and summarizes the story. The formal roots of equivalent circuits are Ohm's Law, Kirchoff's Laws, and the Principle of Superposition.

The voltage-source equivalent was first derived by Hermann von Helmholtz (1821-1894) in an 1853 paper. Exactly thirty years later in 1883, Leon Charles Thevenin (1857-1926) published the same result, apparently unaware of Helmholtz's work. The generality of the equivalent source network was not appreciated until forty-three years later. Then, in 1926, Edward Lawry Norton (1898-1983) wrote an internal Bell Laboratory technical report that described in passing the usefulness in some applications of using the current-source form of the equivalent circuit. In that same year, Hans Ferdinand Mayer (1895-1980) published the same result and detailed it fully. As detailed subsequently, these people intertwine in interesting ways.

Connexions is a new approach to authoring, teaching, and learning that aims to fully exploit modern information technology. Available free of charge to anyone under open-content and open-source licenses, Connexions offers custom-tailored, current course material, is adaptable to a wide range of learning styles, and encourages students to explore the links among courses and disciplines. In contrast to the traditional process of textbook writing and publishing, Connexions fosters world-wide, cross-institution communities of authors, instructors, and students, who collaboratively and dynamically fashion “modules” from which courses are constructed. We believe the ideas and philosophy embodied by Connexions have the potential to change the very nature of textbook writing and publishing, producing a dynamic, interconnected educational environment that is pedagogically sound, both time and cost efficient, and fun. This paper overviews the philosophy and technology behind Connexions and describes a nascent community developing material for DSP education.

Information processing is performed when a system preserves aspects of the input related to what the input represents while it removes other aspects. To describe a system's information processing capability, input and output need to be compared in a way invariant to the way signals represent information, Kullback-Leibler distance, information-theoretic measure that reflects the data processing theorem, is calculated on the input and output separately and compared to obtain information transfer ratio. We consider the special case where input serves several parallel systems and show that this configuration has the capability to represent the input information without loss. We also derive bounds for asymptotic rates at which the loss decreases as more parallel systems are added and show that the rate depends on the input distribution.

We have developed a method for quantifying neural response changes in terms of the Kullback-Leibler distance between the intensity functions for each stimulus condition. We use empirical histogram estimates to characterize the intensity function of the neural response. A critical factor in determining the histogram estimates is selection of bin-width. We analytically derive the Kullback-Leibler distance between two Poisson processes and two dead time modified Poisson processes in terms of the bin-width selected. Our results show that, for constant intensity processes having the same number of expected counts, the distance between the dead time modified processes is larger than between the Poisson processes.

Symbolic signals are, in discrete-time, sequences of quantities that do not assume numeric values. In the most general case, these quantities have no mathematical structure other than that they are members of some set, but they can have a sequential structure. The authors show that processing such signals does not entail mapping them directly to the integers, which would impose more structure-ordering and arithmetic-than present in the data. The authors describe how linear estimation and prediction can be performed on symbolic sequences. They show how spectrograms can be computed from neural population responses and from DNA sequences.

We describe a family of new techniques for analyzing single- and multi-unit discharge patterns. These techniques are based on information theoretic distance measures and on empirical theories derived from work on universal signal processing. They are capable of determining transneuron statistical dependencies even when time-varying responses occur. The response portion contributing most to information coding can be identified and the coding fidelity can be quantified regardless of the neural coding mechanisms-be it timing, rate or transneural correlations.

Traditional introductory courses in electrical engineering are typically circuit theory courses, which may include both analog and digital hardware and possibly software. The alternatives have focused on how to teach (using discrete-time signals rather than analog) than on what to teach. We developed a top-down course sequence that uses as its underlying principle the transmission and manipulation of information. Students are given a broad perspective of both analog and digital approaches, with the goals of helping students appreciate electrical and computer engineering and framing a context for advanced courses. Laboratories stress construction of analog systems and analysis with signal processing tools.

The channel characteristics of practical code division multiple access (CDMA) systems are usually unknown and difficult to model accurately. Type-based receivers, without assuming any a priori model, extract signals successfully from background noise. In this paper, we develop type-based receivers that address two major issues in CDMA signal reception: multiple access interference and multipath fading. We first present the type-based receiver with interference suppression capability, assuming the knowledge of the code and timing of the intended user only. We then show that equal-gain combining (EGC) of type-based statistics is the asymptotically optimal technique for diversity empirical detection. Compared with maximal ratio combining of matched filter outputs, the diversity receiver with EGC of type-based statistics assumes less channel knowledge and yields competitive detection performance in Gaussian noise and better performance in Laplacian noise.

Universal classification refers to the empirical detection problem based on training sequences without assuming any a priori models, and the theory finds important applications in signal detection in the presence of uncertainties. Because the channel characteristics of a code division multiple access wireless system are difficult to model, we develop type-based receivers that operate in a data-driven fashion based on universal classification theory. On the downlink, we focus on the type-based single-user receiver that is capable of multiple access interference suppression with a reasonable amount of training data. We extend universal classification theory to interleaved stationary Markov sources, and propose the type-based multi-user receiver for the uplink. The error probability of type-based receivers decay exponentially asymptotically regardless of the nature of the channel noise.

When applied to continuous-time observations, type-based detection strategies are limited by the necessity to crudely quantize each sample. To alleviate this problem, we smooth the types for both the training and observation data with a linear filter. This post-processing improves the detector performance significantly (error probabilities decrease by over a factor of three) without incurring a significant computational penalty. However this improvement depends on the amplitude distribution and on the quantizer's characteristics.

The maximum likelihood sequence estimator is the optimal receiver for the intersymbol interference (ISI) channel with additive white noise. A receiver is demonstrated that estimates sequence likelihood using a variable order Markov model constructed from a crudely quantized training sequence. Receiver performance is relatively unaffected by heavy-tailed noise that can undermine the performance of Gaussian based algorithms such as decision feedback equalization with gradient based (LMS) adaptation.

Type-based receivers assume no a priori channel model, and were previously shown to be effective in direct-sequence spread spectrum communications. In this paper, we investigate the macro-diversity combining of multiple type-based receivers in single-mobile-user reception (BPSK). We present a method for the exact calculation of the bit error rate of type-based receivers in this scenario. Maximal ratio combining of type-based receivers gives near optimal performance in Gaussian noise and better performance than combining matched filter outputs in Laplacian noise. The performance gain achieved by diversity reception is significant regardless of noise statistics, especially in the presence of frequency non-selective Rayleigh fading.

The universal classifier using empirically observed statistics, developed by Gutman (1989), is applied to the spread-spectrum communications problem. We call the resulting classifier a type-based detector and show that it has close to optimal performance over a wide range of unknown channel environments, including static and multipath fading channels in additive Gaussian and non-Gaussian noise. In a multiple-access system, the type-based detector is capable of rejecting high levels of multiple-access interference. The type-based detector uses a training sequence to form its knowledge about the bit hypotheses, and in a communications system, the training sequence corresponds to a periodically transmitted preamble or "sync" sequence.

In two-hypothesis detection problems with i.i.d. observations, the minimum error probability decays exponentially with the amount of data, with the constant in the exponent equal to the Chernoff distance between the probability distributions characterizing the hypotheses. We extend this result to the general M-hypothesis Bayesian detection problem where zero cost is assigned to correct decisions, and find that the Bayesian cost function's exponential decay constant equals the minimum Chernoff distance among all distinct pairs of hypothesized probability distributions.

This paper describes the ongoing efforts of the participants of the Signal Processing Education consortium (SPEC) in bringing the most up-to-date technologies to the teaching of undergraduate digital signal processing. In particular, we describe herein the use of new multimedia technologies for distributed teaming of undergraduates and faculty to both take advantage of the diverse faculty expertise and to mimic the increasingly common practice of distributed teaming in industry.

Traditional change detection strategies are limited in cases where the data are nonstationary and the distributions are unknown. We present an algorithm for change detection problems in which we do not know the form of the distribution. Our algorithm uses distributed detection with a bank of type-based front end detectors that achieve asymptotically optimal type I error performance. Our simulations indicate that this algorithm performs much better than traditional methods.

A type is the histogram estimate of a stationary sequence's amplitude distribution. From training data, types are computed and use to determine which training data best describe subsequently obtained observations. Such type-based detectors are asymptotically optimal in the sense that the maximal exponential error rate is achieved. For digital communication systems using direct-sequence signaling, type-based detectors are shown to be effective. Training data are obtained from preambles, and then used to make individual bit decisions. Simulations show that in this communications scenario, type-based detectors yield nearly optimal performance without any a priori channel information.

Competitive pressures in the global marketplace have forced companies to form teams from the best talent available irrespective of their geographical location. As it comes online, the National information Infrastructure will be increasingly used to support such interactions. American companies are far ahead of the universities in realizing systems to support such geographically distributed interactions. Universities must catch up by exposing their students to such design environments. In addition, universities should help define and evaluate network-based information dissemination systems by serving as testbeds for new interactive strategies. The paper presents initial results in a distance teaming experiment at the University of Colorado, George Mason University, and Rice University.

The Signal Processing Information Base (SPIB) represents an attempt by the Signal Processing Society to make generally available information-data, papers, software, and bibliographies-necessary for state-of-the-art research and development. Access to the repository relies on the Internet, which makes SPIB available to students, researchers, and developers around the world. The variety of information, changing information transfer techniques, and persistent changes in user computational platforms cause difficulties in creating uniform accessibility for the information base's user population. As SPIB evolves, in concert with similar projects in a wide variety of disciplines, into a seamless, cross-linked, indexed, computer network that makes information available rapidly, these difficulties will intensify unless software environments are created that can support high-speed networks and platforms, and publication policies change to facilitate rapid dissemination.>

The optimal procedure for detecting the presence of discrete-time signals in additive noise can be derived from the likelihood ratio test. When the noise has statistically independent, identically distributed components, the dependence of the detector's performance on signal characteristics can be related to the Kullback-Leibler (KL) distance between the distributions governing the hypotheses. Performance predictions based on the central limit theorem are shown to be poor approximations to the true performance. Performance of the optimal detector has long been known to increase exponentially with increasing KL distance. Symmetric noise amplitude distributions yield a symmetric dependence on the difference between the signals' amplitudes at each time index. Small-signal (locally optimal) detection performance is shown to depend on signal energy, whereas large-signal performance depends on the signal waveform. When a distance measure can be defined, performance depends on a different measure than that used in the detector with one exception (the Gaussian).>

The establishment of a unique infrastructure for distributed robotics and remote operations research within an educational environment is reported. The distributed laboratory consists of sites at four universities and NASA's Johnson Space Center. The distributed laboratory configuration provides the opportunity to quantitatively study the effects of various system components and technologies on overall telerobotic task performance. The ability to execute representative inspection and manipulation tasks with multiple control, robot, and performance/workload monitoring sites simultaneously connected has been demonstrated. Operations are carried out on a routine basis. During the process, needs for hardware and software standards development have been identified. The current implementation provides a basis for linking government, industrial, and university facilities to realize a truly collaborative research and development environment, enabling graduate students to experience educational opportunities that would otherwise not be possible.>

It is noted that the dependence structure and the amplitude distribution of stationary random sequences are linked, with specification of one placing constraints on the other. Time-reversible processes can be Gaussian or non-Gaussian, but all Gaussian processes must be time reversible. The authors examine the thermodynamics of measurements, showing that while information can be extracted from a system without altering system entropy, most measurement techniques irreversibly alter the thermodynamic state with a consequent entropy increase. Because of the second law of thermodynamics, such entropy changes cannot be undone and measurements reflecting thermodynamic state cannot be time reversible. It is concluded that physical measurements are not time reversible, implying that only non-time-reversible processes model physically relevant signals. Consequently, Gaussian processes would seem to be imprecise representations of physical measurements.>

Fractal point processes are modeled as doubly stochastic point processes for which the intensity is a fractal stochastic waveform process. With this model, the fractal point process is shown to be self-similar only over long time scales, with short time scales exhibiting little fractal effects. Parameters of the fractal process are measured with the Fano factor: the ratio of the variance to the mean of the number of events occurring in a time interval. The application of the analysis techniques is illustrated by an example taken from single auditory neuron recordings.>

Array processing algorithms generally assume that the received signal, composed of both narrowband signals and noise, is Gaussian. This is not true in general. In the context of the narrowband array processing problem, the authors develop robust methods to estimate accurately the spatial correlation matrix. This estimate is robust against amplitude distribution of the noise, be it Gaussian or not, and takes into account sensor placement. Given this estimate, existing array processing algorithms designed for Gaussian circumstances can be used on non-Gaussian problems. The resulting algorithms can be used in the presence of any type of second-order noise process and perform nearly as well as existing algorithms do with Gaussian noise.>

Doppler-time images (DTIs) of a rotating object were formed from the returns of high resolution radars by expressing the Doppler values as a function of time over a span of ranges. Returns from scatterers on the object yielded a characteristic signature of the object's rotation: a section of a sinusoid centered about the negatively sloped zero-crossing. As several scatterers are usually present, these signatures may overlap. The return from each scatterer is noisy and, more importantly, may be missing (falling below the detection threshold) or may be multi-valued (yielding several values exceeding the detection threshold). The Hough transform-the extraction of parametrically expressible features-was used to extract straight line approximations to the return signatures. This algorithm is shown to be insensitive to missing or extraneous values. Quantization in Hough transform computation is shown to determine the sensitivity of the calculation to noisy values. Parameters of the signatures were extracted using a data-dependent clustering algorithm designed to be insensitive to quantization and feature parameterization.>

Averaging of the spatial correlation function over the spatial variable-spatial averaging- is performed on the estimated spatial correlation matrix prior to beamforming calculations. Generally speaking, this preprocessing operation reduces the intersignal coherence in the spatial correlation matrix and the variance of the spatial correlation function estimate. Two types of spatial averaging are considered: subaperture averaging and redundancy averaging. Subaperture averaging is shown to significantly reduce coherence only when the source propagation directions are widely spaced while variance reduction is accompanied by a reduction in apparent aperture. In contrast, the reduction of coherence resulting from redundancy averaging is relatively insensitive to source bearing separations. While the aperture is not affected, redundancy averaging may induce bias in the estimated source bearings.>

A simple first-order autoregressive model for the generation of non-Gaussian time series is described. It is defined by X/sub n/= rho X/sub n-1/+W/sub n/ and has a hyperbolic secant marginal distribution. This hyperbolic secant model can be used to generate random non-Gaussian sequences which are free of the degeneracy that afflicts the sequences generated using the Laplace model. The generation formula and the bivariate distributions of this model are derived. It is shown that the mean-square (MS) backward prediction error is strictly less than the MS forward prediction error for all first-order autoregressive non-Gaussian models.>

In many situations some information about the structure of the covariance matrix of a random process is known beyond the fact that it is symmetric and positive definite; for instance, the matrix is frequently Toeplitz. Many people have considered the structured covariance matrix estimation problem for Gaussian processes. However, in actual practice, random signals are seldom, if ever, Gaussian. By using a generalization to processes with known non-Gaussian densities, the authors demonstrate how to find the maximum-likelihood estimate of complex Toeplitz covariance matrices and then evaluate the use of this estimate in some passive array beamforming algorithms. There is substantial improvement in the performance of these bearing estimation algorithms when the authors' estimate is used, especially when non-Gaussian noise is present. >

It is shown that non-Gaussian time series require new analysis methods to extract their structure. Spectral analysis does not seem to provide the precise information required to analyze important aspects of a time series. The conditional expected value can, in simple cases, be related to Components of the Barrett-Lampard expansion, which provides a mathematical tool for determining the system which can generate the time series.

The fundamental signal model for narrowband direction finding - the propagation of several sinusoidal planar wavefronts in a medium containing an array of sensors with additive Gaussian noise present - is assumed implicitly in most high resolution beamforming algorithms. The "natural" parameters for this problem - angles of arrival, signal strengths, inter-signal coherences, and noise strength - specify entirely the statistic used by many algorithms, the spatial correlation matrixR. Combining the relevant parameters for a given situation in a parameter vector p, an estimate of the true parameter vector can be obtained as the solution of an optimization problem:\min{\hat{p}}\max{\min}\parallel\hat{R} - R(\hat{p})\parallelwhere\hat{R}is an estimate ofR. The minimizing\hat{p}yields direct estimates of the relevant parameters rather than extracting them from an intermediate quantity such as a beampattern. This parametric method is an unbiased estimator which is capable of resolving closely spaced, completely coherent sources at low signal to noise ratios and low time-bandwidth product.

Knowing the number of sources in the acoustic field of a narrowband passive array can be very useful when determining the bearing of these sources relative to the array; many of the "high resolution" bearing estimation algorithms assume that the number of sources is known. The sphericity test is a well-known algorithm for estimating the number of sources from the eigenvalues of the spatial correlation matrix of the array. A new sphericity test statistic is proposed whose distribution approaches the asymptotic chi-squared distribution much faster than previously proposed statistics and, consequently, weaker sources are more readily detected. The capability of this algorithm to detect closely spaced sources is examined and compared to the resolution capabilities of well-known bearing estimation algorithms.

A Block Diagram Compiler (BOC) has been designed and implemented for converting graphic block diagram descriptions of signal processing tasks into source code to be executed on a Multiple Instruction Stream - Multiple Data Stream (MIMD) array computer. The compiler takes as input a block diagram of a real-time DSP application, entered on a graphics CAE workstation, and translates it into efficient real-time assembly language code for the target multiprocessor array. The current implementation produces code for a rectangular grid of Texas Instruments TMS32010 signal processors built at Lincoln Laboratory, but the concept could be extended to other processors or other geometries in the same way that a good assembly language programmer would write it. This report begins by examining the current implementation of the BOC including relevant aspects of the target hardware. Next, we describe the task-assignment module, which uses a simulated annealing algorithm to assign the processing tasks of the DSP application to individual processors in the array. Finally, our experiences with the current version of the BOC software and hardware are reported.

The use of eigenanalysis to aid in the determination of bearing in passive sonar systems is shown to fall into two classes, each of which has been applied to minimum energy and linear prediction algorithms. The application of eigenanalysis is extended to non-white ambient noise environments in a particular class. The performances of these various methods is compared to some extent in this situation.

The exact equations governing the narrow-band resolution and detection capabilities of conventional (CONV) and minimum energy (ME) adaptive beamforming [1], are the basis for a class of linear arrays which offers simultaneously optimum resolution and detection capacities. Signal processing considerations indicate that, in this class, linear minimum redundancy (LMR) arrays [2] are best suited to CONV beamforming, and linear minimum hole (LMH) arrays [3] are best suited to minimum energy (ME) beamforming. The effect of coarray redundancies and holes on sidelobe level is examined analytically, and lower bounds are established on the number of coarray redundancies and holes. A simple recursive algorithm for the design of LMH arrays is presented.

A signal processing software system is described which allows the simulation of systems described by block diagrams or signal-flow graphs. Component systems are allowed to be multi-input, multi-output, and to be programmed in any language. A high level dataflow language describes the interconnection of the components. Special display software was written to allow any signal in the system to be displayed on any graphics device.

A signal-processing model for the generation of point processes is derived. In the context of this model, the interval between successive events is treated as a time series. The input-output relationship of a system generating inter-event intervals is shown to be derivable from the intensity of the desired point process. Both stationary and non-stationary processes can be generated with this technique. The input-output characteristic of this system is shown to be nonlinear for most interesting cases.

The effect of source coherence on the capabilities of classical, minimum energy (ME), and linear predictive (LP) array processing algorithms to estimate the bearings of two equal-energy sources is examined. Source coherence is shown to adversely affect the resolution and detection capabilities, as well as the bias characteristics, of all three algorithms. For linear arrays of equally-spaced sensors (LES arrays), the superior resolution capability of the LP algorithm is demonstrated. However, the LP algorithm is least capable of detecting highly coherent sources. The estimates of source bearing produced by each algorithm are shown to be asymptotically biased.

Conventional all-pole parameter estimators applied to noise corrupted all-pole sequences result in biased estimates. This paper describes a procedure by which reduction of this bias is accomplished by applying pole-preserving, signal to noise ratio improving functions to the sequence. Correlation like pole-preserving functions are investigated and pole dependent signal to noise ratio improvement is described. An all-pole parameter estimator using successive application of a pole-preserving function (successive autocorrelation) is given. Comparison is made with the least squares combination of the higher order Yule-Walker equations, an approach to bias reduction reported by Cadzow. Successive autocorrelation is found to result in improved performance, with estimates of higher Q poles being most effectively enhanced.

A technique for local-area communication among a large number of digital speech terminals is presented. The terminals communicate over a common wide-band broadcast transmission medium using packets. Access to the medium is controlled by a carrier-sense multiple-access protocol with collision detection. Analytic results indicate that many speech terminals having different characteristics can be supported without the necessity of buffering more than one packet. Several distributed access control algorithms are described, and a technique for predicting the performance of these algorithms is presented. Computer simulations were performed to verify the feasibility of these ideas. The simulation results agree with the prediction of the analysis.