The Receiver Operating Characteristic (ROC) is a well-established representation of the tradeoff between detection and false alarm probabilities in binary hypothesis testing. In many practical contexts ROC's are generated by thresholding a measured score variable - applying score variable threshold tests (SVT's). In many cases the resulting curve is different from the likelihood ratio test (LRT) ROC and is therefore not Neyman-Pearson optimal. While it is well-understood that concavity is a necessary condition for an ROC to be Neyman-Pearson optimal, this paper establishes that it is also a sufficient condition in the case where the ROC was generated using SVT's. It further defines a constructive procedure by which the LRT ROC can be generated from a non-concave SVT ROC, without requiring explicit knowledge of the conditional PDF's of the score variable. If the conditional PDF's are known, the procedure implicitly provides a way of redesigning the test so that it is equivalent to an LRT.

Analog-to-digital (A/D) converters are the common interface between analog signals and the domain of digital discrete-time signal processing. In essence, this domain simultaneously incorporates quantization both in amplitude and time, i.e. amplitude quantization and uniform time sampling. Thus, we view A/D conversion as a sampling process in both the time and amplitude domains based on the observation that the underlying continuous-time signals representing digital sequences can be sampled in a lattice-i.e. at points restricted to lie on a uniform grid both in time and amplitude. We refer to them as lattice functions. This is in contrast with the traditional approach based on the classical sampling theorem and quantization error analysis. The latter has been mainly addressed with the help of probabilistic models, or deterministic ones either confined to very particular scenarios or considering worst-case assumptions. In this paper, we provide a deterministic theoretical analysis and framework for the functions involved in digital discrete-time processing. We show that lattice functions possess a rich analytic structure in the context of integral-valued entire functions of exponential type. We derive set and spectral properties of this class of functions. This allows us to prove in a deterministic way and for general bandlimited functions a fundamental lower bound on the maximum frequency component introduced by quantization that is independent of the resolution of the quantizer.

Traditional data acquisition systems rely on sampling of bandlimited signals at uniformly spaced time instants with high-precision amplitude representation. Amplitude sampling, as previously introduced by the authors, is based on uniform amplitude sampling with high precision timing information. This paper presents an iterative algorithm for signal recovery from amplitude samples and compares the results with the use of iterative recovery from the nonuniform time samples implied by the amplitude sampling process. The iterative amplitude sampling reconstruction algorithm (IASR) proposed and evaluated in this paper is based on the interpretation of amplitude sampling as uniform sampling of an associated function obtained from a reversible transformation of the bandlimited input signal. The IASR algorithm exploits uniform sampling and the frequency- and time-domain properties of the amplitude-time function. The IASR algorithm is compared with the use of iterative nonuniform sampling reconstruction as proposed by Voroni. While in numerical simulations the Voronoi algorithm converges to marginally better reconstruction than IASR, the convergence rate of IASR is significantly better.

This paper presents two novel regularization methods motivated in part by the geometric significance of biorthogonal bases in signal processing applications. These methods, in particular, draw upon the structural relevance of orthogonality and biorthogonality principles and are presented from the perspectives of signal processing, convex programming, continuation methods and nonlinear projection operators. Each method is specifically endowed with either a homotopy or tuning parameter to facilitate tradeoff analysis between accuracy and numerical stability. An example involving a basis comprised of real exponential signals illustrates the utility of the proposed methods on an ill-conditioned inverse problem and the results are compared to standard regularization techniques from the signal processing literature.

This paper presents a general framework for generating greedy algorithms for solving convex constraint satisfaction problems for sparse solutions by mapping the satisfaction problem into one of graph traversal on a rooted tree of unknown topology. For every pre-walk of the tree an initial set of generally dense feasible solutions is processed in such a way that the sparsity of each solution increases with each generation unveiled. The specific computation performed at any particular child node is shown to correspond to an embedding of a polytope into the polytope received from that nodes parent. Several issues related to pre-walk order selection, computational complexity and tractability, and the use of heuristic and/or side information is discussed. An example of a single-path, depth-first algorithm on a tree with randomized vertex reduction and a run-time path selection algorithm is presented in the context of sparse lowpass filter design.

Signal processing is a discipline in which functional composition and decomposition can potentially be utilized in a variety of creative ways. From an analysis point of view, further insight can be gained into existing signal processing systems and techniques by reinterpreting them in terms of functional composition. From a synthesis point of view, functional composition offers new algorithms and techniques with modular structure. Moreover, computations can be performed more efficiently and data can be represented more compactly in information systems represented in the context of a compositional structure. Polynomials are ubiquitous in signal processing in the form of z-transforms. In this paper, we summarize the fundamentals of functional composition and decomposition for polynomials from the perspective of exploiting them in signal processing. We compare exact polynomial decomposition algorithms for sequences that are exactly decomposable when expressed as a polynomial, and approximate decomposition algorithms for those that are not exactly decomposable. Furthermore, we identify efficiencies in using exact decomposition techniques in the context of signal processing and introduce a new approximate polynomial decomposition technique based on the use of Structured Total Least Norm (STLN) formulation.

This paper considers the environment of interleaved, multi-channel measurements as arises for example in time-interleaved A/D converters and in distributed sensor networks. Such systems take the form of either uniform or recurrent nonuniform sampling, depending on the timing offset between the channels. Quantization in each channel results in an effective overall signal to noise ratio in the reconstructed output which is dependent on the quantizer step sizes, the timing offsets between the channels and the oversampling ratio. Appropriate choice of these parameters together with the design of appropriate compensation filtering is discussed.

This paper considers two problems in sparse filter design, the first involving a least-squares constraint on the frequency response, and the second a constraint on signal-to-noise ratio relevant to signal detection. It is shown that both problems can be recast as the minimization of the number of non-zero elements in a vector subject to a quadratic constraint. A solution is obtained for the case in which the matrix in the quadratic constraint is diagonal. For the more difficult non-diagonal case, a relaxation based on the substitution of a diagonal matrix is developed. Numerical simulations show that this diagonal relaxation is tighter than a linear relaxation under a wide range of conditions. The diagonal relaxation is therefore a promising candidate for inclusion in branch-and-bound algorithms.

This paper explores the approximation properties of a unique basis expansion, which realizes a bilinear frequency warping between a continuous-time signal and its discrete-time representation. We investigate the role that certain parameters and signal characteristics have on these approximations, and we extend the analysis to a windowed representation, which increases the overall time resolution. Approximations derived from the bilinear representation and from Nyquist sampling are compared in the context of a binary detection problem. Simulation results indicate that, for many types of signals, the bilinear approximations achieve a better detection performance.

This paper explores the use of discrete-time randomized sampling as a method to mitigate the effects of aliasing. Two distinct sampling architectures are presented along with second-order characterizations of the resulting sampling error. In the first, denoted simple randomized sampling, non-white sampling processes are shown to frequency-shape the error spectrum, so that its power is minimized in the band of interest. The design of non-white binary processes for use in randomized sampling is considered. In the second model, denoted filtered randomized sampling, a pre-filter, post-filter, and the sampling process are used to achieve a similar effect. In both cases, optimal mean-squared-error solutions are derived. Results from simulation are shown.

Bacterial chemotaxis refers to the locomotory response of bacteria to chemical stimuli, where the general biological function is to increase exposure to some substances while reducing exposure to others. In this paper, we introduce an algorithm for surface mapping based on a model of the biological signaling network responsible for bacterial chemotaxis. The algorithm tracks the motion of a bacteria-like software agent, referred to as a bacterial agent, on an objective function. Results from simulations using one- and two-dimensional test functions show that the surface mapping algorithm produces an informative estimate of the surface, revealing some of its key characteristics. We also present a modification of the algorithm in which the software agent is given the ability to reduce the value of the surface at locations it visits (analogous to a bacterium consuming a substance as it moves in its environment) and show that it is more effective in reducing the surface integral within a certain period of time than a bacterial agent lacking the ability to sense surface information or respond to it.

This work explores low complexity systems to compensate for coefficient erasures in frame representations of signals. Assuming linear synthesis with a pre-specified frame it is demonstrated that erasures can be compensated for even if the origin of the representation coefficients is not known. If the transmitter is aware of the erasure occurrence, the compensation is performed by projecting the erasure error to the remaining coefficients. Furthermore, it is demonstrated that the same compensation can be executed using a transmitter/receiver combination in which the transmitter is not aware of the erasure occurrence. The transmitter compensates for all the coefficients using projections, assuming an erasure will occur. The receiver undoes the compensation for the coefficients that have not been erased, thus maintaining the compensation only of the erased coefficients

Quantization noise shaping is commonly used in oversampled A/D and D/A converters. This paper considers quantization noise shaping for arbitrary frame expansions of signals based on generalizing the view of first order noise shaping as a compensation of the quantization error through a projection. Two levels of generalization are developed, one a special case of the other, and two different cost models are proposed to evaluate the quantizer structures. Within our framework, the implementation of the quantizer and reconstruction are computationally straightforward. The computational complexity is in the initial determination of frame vector ordering, which is part of the quantizer design and carried out off-line. We show that in the case of frame representation corresponding to uniform oversampling, the natural ordering implied by sequential time sampling is optimal. Furthermore, for general finite frame expansions, the problem of optimal ordering corresponds to known problems in graph theory.

In some contexts, DACs fail in such a way that specific samples are dropped. For example, in flat-panel video displays, some of the pixel LEDs can malfunction and get permanently set to particular values. We refer to this as the "missing pixel" problem. Under certain conditions, it may be possible to compensate for the dropped samples by preprocessing the digital signal. The paper describes a number of such compensation strategies. Each strategy is analyzed and results from numerical simulations are presented. Of particular interest is the relationship between compensation and the class of discrete prolate spheroidal sequences.

Signal processing is an integral part of cell biology. The associated algorithms are implemented by signaling pathways that cell biologists are just beginning to understand and characterize. Our objective in the context of signal processing is to understand these algorithms and perhaps emulate them in other contexts such as communication and speech processing. Towards this end, the paper proposes a new framework for modeling cellular signal processing using interacting Markov chains. The model is presented and preliminary results that validate it are given. Specifically, the example of the mitogen activated protein kinase cascade is examined and model predictions are compared to experimental findings. The model is consistent with the key properties of the cascade, i.e. ultrasensitivity, adaptation, and bistability.

Performing robust detection with resource limitations such as low-power requirements or limited communication bandwidth is becoming increasingly important in contexts involving distributed signal processing. One way to address these constraints consists of reducing the amount of data used by the detection algorithms. Intelligent data selection in detection can be highly dependent on a priori information about the signal and noise. In this paper, we explore detection strategies based on randomized data selection and analyze the resulting algorithms' performance. Randomized data selection is a viable approach in the absence of reliable and detailed a priori information, and it provides a reasonable lower bound on signal processing performance as more a priori information is incorporated. The randomized selection procedure has the added benefits of simple implementation in a distributed environment and limited communication overhead. As an example of detection algorithms based upon randomized selection, we analyze a binary hypothesis testing problem, and determine several useful properties of detectors derived from the likelihood ratio test. Additionally, we suggest an adaptive detector that accounts for fluctuations in the selected data subset. The advantages and disadvantages of this approach in distributed sensor networks applications are also discussed.

This correspondence develops a linear whitening transformation that minimizes the mean-squared error (MSE) between the original and whitened data, i.e.,one that results in a white output that is as close as possible to the input, in an MSE sense. When the covariance matrix of the data is not invertible, the whitening transformation is designed to optimally whiten the data on a subspace in which it is contained. The optimal whitening transformation is developed both for the case of finite-length data vectors and infinite-length signals.

We consider the generic problem of detecting a transmitted signal when one of M known signals is transmitted. Instead of using a classical matched filter (MF) detector, matched to the transmitted signals, we propose using an orthogonal matched filter (OMF) detector, which is matched to a set of orthogonal signals that are closest in a least-squares sense to the transmitted signals. We show that this approach is equivalent to optimally whitening the output of the MF demodulator, and then basing the detection on the whitened output. We provide simulation results which suggest that, in many cases, the OMF detector outperforms the MF detector.

Signal estimation from a sequential encoding in the form of quantized noisy measurements is considered. As an example context, this problem arises in a number of remote sensing applications, where a central site estimates an information-bearing signal from low-bandwidth digitized information received from remote sensors, and may or may not broadcast feedback information to the sensors. We demonstrate that the use of an appropriately designed and often easily implemented additive control input before signal quantization at the sensor can significantly enhance overall system performance. In particular, we develop efficient estimators in conjunction with optimized random, deterministic, and feedback-based control inputs, resulting in a hierarchy of systems that trade performance for complexity.

This paper introduces a filter bank interpretation of various sampling strategies, which leads to efficient interpolation and reconstruction methods. An identity, referred to as the interpolation identity, is used to obtain particularly efficient discrete-time systems for interpolation to uniform Nyquist samples, either for further processing in that form or for conversion to continuous-time. The interpolation identity also leads to a new class of sampling theorems including an extension of Papoulis' (1997) generalized sampling expansion.

This paper proposes several methods for noise reduction using deterministic side information about the desired signal as a constraint on the reconstruction. Two forms of side information are considered separately: short-time linear predictive coefficients, and short-time zero-phase impulse response coefficients. We derive general expressions for the ML, MAP and MMSE estimators, and develop algorithms that yield the ML estimators with the above side information for speech corrupted by additive white Gaussian noise. We also explore the use of these methods in the traditional noise reduction problem with no side information.

This paper explores issues arising from designing digital signal processing algorithms for dynamically-varying computing environments such as an unreliable network of processors. We present a language for specifying signal processing algorithms which permits the execution path of the algorithm to be dynamically chosen. The language leads naturally to a graphical representation of the algorithm with interesting interpretations. Finally, we formulate and characterize the solution for the problem of dynamically and optimally choosing the execution path of algorithms to minimize a system-wide cost function such as expected congestion.

Low-complexity schemes for digital encoding of a noise-corrupted signal and associated signal estimators are presented. This problem arises in wireless distributed sensor networks where an environmental signal of interest is to be estimated at a central site from low-bandwidth digitized information received from collections of remote sensors. We show that the use of a properly designed and often easily implemented additive control input before signal quantization can significantly enhance overall system performance. In particular, efficient estimators can be constructed and used with optimized pseudo-noise, deterministic, and feedback-based control inputs, resulting in a hierarchy of practical systems with very attractive performance-complexity characteristics.

It has been observed empirically that each coefficient in a Parks-McClellan filter converges to a steady state value as the filter length increases. This suggests the possibility of obtaining filters that are near optimal while "re-using" filter coefficients from shorter filters in the design of longer filters. In the context of approximate processing this then allows a filtering operation to be done in stages. This paper demonstrates this observation and examines some of its implications.

The problem of estimating parameters of discrete-time non-Gaussian autoregressive (AR) processes is addressed. The subclass of such processes considered is restricted to those whose driving noise samples are statistically independent and identically distributed according to a Gaussian-mixture probability density function (PDF). Because the likelihood function for this problem is typically unbounded in the vicinity of undesirable, degenerate parameter estimates, a global maximum likelihood approach is not appropriate. Hence, an alternative approach is taken whereby a finite local maximum of the likelihood surface is sought. This approach, which is termed the quasi-maximum likelihood (QML) approach, is used to obtain estimates of the AR parameters as well as the means, variances, and weighting coefficients that define the Gaussian-mixture PDF. A technique for generating solutions to the QML problem is derived using a generalized version of the expectation-maximization principle.

Most strategies proposed for utilizing chaotic signals for communications exploit the self-synchronization property of a class of chaotic systems. Any realistic communication channel will introduce distortion including time-dependent fading, dispersion, and modification of the frequency content due to channel filtering and multipath effects. All of these distortions will affect the ability of the chaotic receiver to properly synchronize. This paper develops and illustrates some specific approaches to channel equalization to compensate for these distortions for self-synchronizing chaotic systems. The approaches specifically exploit the properties of chaotic drive signals and the self-synchronization properties of the receiver.

In the context of FFT-based maximum-likelihood (ML) detection of a complex sinusoid in noise, we consider the result of terminating the FFT at an intermediate stage of computation and applying the ML detection strategy to its unfinished results. We show that detection performance increases monotonically with the number of FFT stages completed, converging ultimately to that of the exact ML detector. The receiver operating characteristic associated with the completion of each FFT stage is derived. This enables the calculation of the minimum number of FFT stages that must be completed in order for desired detection and false alarm probabilities to be obtained.

Active noise cancellation is an approach to noise reduction in which a secondary noise source that destructively interferes with the unwanted noise is introduced. In general, active noise cancellation systems rely on multiple sensors to measure the unwanted noise field and the effect of the cancellation. This paper develops an approach that utilizes a single sensor. The noise field is modeled as a stochastic process, and a time-adaptive algorithm is used to adaptively estimate the parameters of the process. Based on these parameter estimates, a canceling signal is generated. In general, the transfer function characteristics from the canceling source to the error sensor need to be accounted for. If these can be accurately measured in advance and are invertible except for the propagation delay between the source and sensor, then the essential problem becomes one of predicting future values of the noise field. The algorithm developed is evaluated with both artificially generated noise and with recordings of aircraft noise.>

Identification of an unknown system and recovery of the input signals from observations of the outputs of an unknown multiple-input, multiple-output linear system are considered. Attention is focused on the two-channel case, in which the outputs of a 2*2 linear time invariant system are observed. The approach consists of reconstructing the input signals by assuming that they are statistically uncorrelated and imposing this constraint on the signal estimates. In order to restrict the set of solutions, additional information on the true signal generation and/or on the form of the coupling systems is incorporated. Specific algorithms are developed and tested. As a special case, these algorithms suggest a potentially interesting modification of Widrow's (1975) least-squares method for noise cancellation, where the reference signal contains a component of the desired signal.>

Because chaotic signals are potentially useful both in describing physical phenomena and in engineering applications, signal processing algorithms exploiting their unique characteristics are of interest. The authors consider issues pertaining to processing signals in convolutional distortion. Specifically, they discuss the effects of convolutional distortion on two parameters commonly used in the description of chaotic signals-the Lyapunov exponents and the fractal dimension of the attractor. In addition, a blind deconvolution technique based on minimizing a nonlinear prediction error for data generated by one-dimensional chaotic maps is presented.>

Signals generated by chaotic systems represent a potentially rich class of signals both for detecting and characterizing physical phenomena and in synthesizing new classes of signals for communications, remote sensing, and a variety of other signal processing applications. Since classical techniques for signal analysis do not exploit the particular structure of chaotic signals there is both a significant challenge and an opportunity in exploring new classes of algorithms matched to chaotic signals. The authors outline a variety of signal processing issues associated with the analysis and synthesis of chaotic signals. In addition two examples are described in detail, illustrating some possible ways in which the characteristics of chaotic signals and systems can be exploited. One example is a binary signaling scheme using chaotic signals. The second example is the use of synchronized chaotic systems for signal masking and recovery.>

The authors develop an approach to active noise cancellation using a single microphone. The noise field is modelled as a stochastic process, and a time-adaptive algorithm based on a modification of the block-estimate-maximize (EM) algorithm is used to adaptively estimate the parameters of this process. Based on these parameter estimates a canceling signal is generated. The algorithm developed is evaluated with recordings of aircraft noise, and has been implemented in real time with a single AT&T DSP32C chip.>

A nonlinear generalization of the family of autoregressive signal models is introduced. This generalization can be viewed as an autoregressive model with state-varying parameters. For such signals, minimum mean-square error prediction can be reformulated as an interpolation problem. A novel interpretation of the signal as a codebook for its own prediction leads to an interpolation strategy resembling a predictive counterpart to vector quantization. The applicability of this model is then demonstrated empirically for a variety of signals.>

A potentially important family of self-similar signals based upon a deterministic scale-invariance characterization is introduced. These signals, which are referred to as 'dy-homogeneous' signals because they generalize the well-known homogeneous functions, have highly convenient representations in terms of orthonormal wavelet bases. In particular, wavelet representations can be exploited to construct orthonormal self-similar bases for these signals. The spectral and fractal characteristics of dy-homogeneous signals make them appealing candidates for use in a number of applications. As one potential example, their use in a communications-based context is considered. Specifically, a strategy for embedding information into a dy-homogeneous waveform on multiple time-scales is developed. This multirate modulation strategy, called fractal modulation, is potentially well-suited for use with noisy channels of simultaneously unknown duration and bandwidth.>

Recent results indicate that reconstruction of two-dimensional signals from crossings of one level requires, in theory and practice, extreme accuracy in positions of the samples. The representation of signals with one-level crossings can be viewed as a tradeoff between bandwidth and dynamic range, in the sense that if the available bandwidth is sufficient to preserve the level crossings accurately, then the dynamic range requirements are significantly reduced. On the other hand, representation of signals by their samples at the Nyquist rate can be considered as requiring relatively small bandwidth and large dynamic range, because, at least in theory, amplitude information at prespecified points is needed, to infinite precision. An overview of existing results in zero crossing representation is presented, and a number of new results on sampling schemes for reconstruction from multiple-level threshold crossing are developed. The quantization characteristics of these sampling schemes appear to lie between those of Nyquist sampling and one-level crossing representations, thus bridging the gap between explicit Nyquist sampling and implicit one-level crossing sampling strategies.>

A class of sequential and adaptive algorithms for parameter estimation are presented that are based on the iterative estimate-maximize (EM) algorithm. In some cases sequential algorithms are derived that perform an exact EM step in each recursion; an example for these cases is given for the linear least-squares problem. In general, however, it is necessary to approximate the EM iteration in order to develop sequential algorithms. The application of this class of algorithms to the two-microphone noise cancellation problem is described.>

A signal corrupted by a ghosting channel can be deghosted by the appropriate inverse system. If the channel is nonminimum-phase, the inverse system has a noncausal impulse response. It is pointed out that the inverse system can be implemented with recursive digital filters, provided there are system elements to time-flip the signal. Such noncausal recursive filtering has advantages over strictly causal recursive filtering in its ability to equalize the phase as well as the magnitude response of the channel. It also has advantages over nonrecursive nonminimum-phase deghosting in that it requires much lower filter order.>

Detection of a sinusoid of unknown frequency in wideband noise is performed efficiently by the FFT (fast Fourier transform). The detector performs a hypothesis test on the magnitude of the FFT output. When the FFT is implemented, error due to arithmetic roundoff coefficient quantization limits the accuracy of the transform and degrades the detection performance. When the FFT is used as a detector of an unknown sinusoidal signal, the coefficient quantization error is significant and increases with the FFT length. The decimation is analyzed in time for a radix-2 FFT. The FFT output error is defined to be the maximum magnitude of the difference between the true FFT and FFT computed with the quantized coefficients. An upper bound on the error is derived by a deterministic analysis and is verified to be close to the actually measured error. Using the functional form of the bound and scaling it to fit the measured error, an empirical formula for the error is derived. The probability of detection of the quantized-coefficient FFT is computed using the empirical error formula. The probability of detection curves is presented as a function of the FFT length. Simulations indicate that when a sufficient number of bits is used to quantize the coefficients, the probability of detection does not significantly degrade.>

Two intermediate sampling schemes are developed which bridge the gap between Nyquist sampling and one-level crossing representation by enabling signals to be recovered from multiple-level threshold crossings. To this end, semi-implicit and implicit sampling strategies and their corresponding reconstruction algorithms are derived. A preliminary investigation of the quantization characteristics of some of the proposed sampling and reconstruction schemes, is included.>

Single microphone speech enhancement systems have typically shown limited performance, while multiple microphone systems based on a least-squares error criterion have shown encouraging results in some contexts. In this paper we formulate a new approach to multiple microphone speech enhancement. Specifically, we formulate a maximum likelihood (ML) problem for estimating the parameters needed for canceling the noise in a two microphone speech enhancement system. This ML problem is solved via the iterative EM (Estimate-Maximize) technique. The resulting algorithm shows encouraging results when applied to the speech enhancement problem.

In this paper, an approximate real-part sufficiency condition is developed for complex-valued one-dimensional even signals and two-dimensional circularly symmetric signals. The two-dimensional result is used in a reconstruction algorithm which is applied to synthetic and experimental underwater acoustic fields.

In this paper, we present new results on the reconstruction of two-dimensional signals from zero crossing or threshold crossing information. These results follow from our previous work on the reconstruction of two-dimensional signals from one bit of Fourier transform phase. Experimental results illustrating image reconstruction from threshold crossings are included.

In this paper, we present new results on the reconstruction of signals from one bit of Fourier transform phase, defined as the sign of the real part of the Fourier transform. Specifically, we develop a new theoretical result which shows that most two-dimensional signals can in fact be reconstructed to within a scale factor from only one bit of FF phase. Experimental results showing images reconstructed from one bit of FT phase are also presented.

This paper describes a system for speech analysis and enhancement which combines signal processing and symbolic processing in a closely coupled manner. The system takes as input both a noisy speech signal and a symbolic description of the speech signal. The system attempts to reconstruct the original speech waveform using symbolic processing to help model the signal and to guide reconstruction. The system uses various signal processing algorithms for parameter estimation and reconstruction.

Knowledge-based signal processing combines the symbolic manipulation facilities of artificial intelligence with the numerical methods of signal processing. This paper considers pitch detection as a problem for developing techniques for signal/symbol interaction. Specifically an overview of the design of the Pitch Detector's Assistant program is discussed, along with some strategies followed in the program. for the use of information derived from both signals and symbols.

Recent work has demonstrated the perceptual importance of the long-time phase of speech. In this paper, the possibility of using the long-time phase of the LPC residual signal in speech synthesis is investigated. The perceptual importance of the various parts of the long-time spectrum of the residual is also suggested.

Major artifacts of the spectral subtraction signal restoration technique are the presence of harmonic patterns and blurring effects for images, and the presence of short tone bursts of varying frequency for speech signals. In this paper, we discuss several techniques developed to reduce these artifacts. Examples are shown to illustrate the performance of these techniques.

The problem of locating the position of individual pulses within a group of overlapping pulses can be simplified by preprocessing the data to reduce the overlap. This paper proposes the use of Recursive Least Squares (RLS) prediction for this purpose. The pulse compression performance of two signals derived from the RLS algorithm is compared using all-pole data with different noise levels, and the effects of zeroes in the data and prefiltering are discussed.

In this paper, we develop a set of conditions under which a sequence is uniquely specified by the phase or samples of the phase of its Fourier transform. These conditions are applicable to mixed-phase one-dimensional and multi-dimensional sequences. Under the specified conditions, we also present several algorithms which may be used to reconstruct a sequence from its phase.

It is generally known that preservation of phase information in images is important as evidenced by the fact that modifying an image such that phase is preserved but the magnitude of all the spectral components is set to unity generally preserves many of the features of the original image. A similar experiment has been carried out with speech, showing that preservation of only the long-time phase retains many important features of the original speech. An interpretation of these results, and their potential application to blind deconvolution, is suggested.

In a variety of situations the problem of enhancing speech degraded by the presence of a competing speaker or background noise arises. A possible key to such enhancement