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Showing papers in "IEEE Transactions on Acoustics, Speech, and Signal Processing in 1983"


Journal ArticleDOI
J. Treichler1, B. Agee
Abstract: An adaptive digital filtering algorithm that can compensate for both frequency-selective multipath and interference on constant envelope modulated signals is presented. The method exploits the fact that multipath reception and various interference sources generate incidental amplitude modulation on the received signal. A class of so-called constant modulus performance functions is developed which sense this AM term but are insensitive to the angle modulation. Simple adaptive algorithms for finite-impulse-response (FIR) digital filters are developed which employ a gradient search of the performance function. One of the resulting algorithms is simulated for the example of an FM signal degraded by specular multipath propagation. Substantial improvements in noise power ratio (NPR) are observed (e.g., 25 dB) with moderately rapid convergence time. These results are then extended to include tonal interference on a FM signal and intersymbol interference on a QPSK data signal.

1,327 citations


Journal ArticleDOI
Abstract: We consider a class of nonlinear filters whose output is given by a linear combination of the order statistics of the input sequence. Assuming a constant signal in white noise, the coefficients in the linear combination are chosen to minimize the output MSE for several noise distributions. It is shown that the optimal order statistic filter (OSF) tends toward the median filter as the noise becomes more impulsive. The optimal OSF is applied to an actual noisy image and is shown to perform well, combining properties of both the averaging and median filters. A more general design scheme for applications involving nonconstant signals is also given.

598 citations


Journal ArticleDOI
TL;DR: The Prony-Pisarenko estimator is adapted to this nonstationary context, the signal considered in this case being the output of a zero-input time-varying system corrupted by an additive white noise.
Abstract: Modeling of nonstationary signals can be achieved through time-dependent autoregressive moving-average models and lattices, by the use of a limited series expansion of the time-varying coefficients in the models. This method leads to an extension of several well-known techniques of stationary spectral estimation to the nonstationary case. Time-varying AR models are identified by means of a fast (Levinson) algorithm which is also suitable for the AR part of a mixed ARMA model. An alternative to this method is given by the extension of Cadzow's method. Lattices with time-dependent reflection coefficients are identified through an algorithm which is similar to Burg's. Finally, the Prony-Pisarenko estimator is adapted to this nonstationary context, the signal considered in this case being the output of a zero-input time-varying system corrupted by an additive white noise. In all these methods the estimation is global in the sense that the parameters are estimated over a time interval [0, T], given the observations [y 0 ... y T ]. The maximum likelihood method which falls within the same framework is also briefly studied in this paper. Simulations of these algorithms on chirp signals and on transitions between phonemes in speech conclude the paper.

446 citations


Journal ArticleDOI
Abstract: FIR digital filters with discrete coefficient values selected from the powers-of-two coefficient space are designed using the methods of integer programming. The frequency responses obtained are shown to be superior to those obtained by simply rounding the coefficients. Both the weighted minimax and the weighted least square error criteria are considered. Using a weighted least square error criterion, it is shown that it is possible to predict the improvement that can be expected when integer quadratic programming is used instead of simple coefficient rounding.

443 citations


Journal ArticleDOI
Abstract: The concept of transform domain adaptive filtering is introduced. In certain applications, filtering in the transform domain results in great improvements in convergence rate over the conventional time-domain adaptive filtering. The relationship between several existing frequency domain adaptive filtering algorithms is established. Applications of the discrete Fourier transform (DFT) and the discrete cosine transform (DCT) domain adaptive filtering algorithms in the areas of speech processing and adaptive line enhancers are discussed.

439 citations


Journal ArticleDOI
G. Bienvenu1, L. Kopp1
Abstract: In the classical approach to underwater passive listening, the medium is sampled in a convenient number of "look-directions" from which the signals are estimated in order to build an image of the noise field. In contrast, a modern trend is to consider the noise field as a global entity depending on few parameters to be estimated simultaneously. In a Gaussian context, it is worthwhile to consider the application of likelihood methods in order to derive a detection test for the number of sources and estimators for their locations and spectral levels. This paper aims to compute such estimators when the wavefront shapes are not assumed known a priori. This justifies results previously found using the asymptotical properties of the eigenvalue-eigenvector decomposition of the estimated spectral density matrix of the sensor signals: they have led to a variety of "high resolution" array processing methods. More specifically, a covariance matrix test for equality of the smallest eigenvalues is presented for source detection. For source localization, a "best fit" method and a test of orthogonality between the "smallest" eigenvectors and the "source" vectors are discussed.

357 citations


Journal ArticleDOI
TL;DR: A new method is presented to analyze the mean-square error performance of delay estimation schemes based on a modified (improved) version of the Ziv-Zakai lower bound (ZZLB) to yield the tightest results on the attainable system performance for a wide range of signal-to-noise ratio (SNR) conditions.
Abstract: Time delay estimation of a noise-like random signal observed at two or more spatially separated receivers is a problem of considerable practical interest in passive radar/sonar applications. A new method is presented to analyze the mean-square error performance of delay estimation schemes based on a modified (improved) version of the Ziv-Zakai lower bound (ZZLB). This technique is shown to yield the tightest results on the attainable system performance for a wide range of signal-to-noise ratio (SNR) conditions. For delay estimation using narrow-band (ambiguity-prone) signals, the fundamental result of this study is illustrated in Fig. 3. The entire domain of SNR is divided into several disjoint segments indicating several distinct modes of operation. If the available SNR does not exceed SNR 1 , signal observations from the receiver outputs are completely dominated by noise thus essentially useless for the delay estimation. As a result, the attainable mean-square error \bar{\epsilon}^{2} is bounded only by the a priori parameter domain. If SNR 1 2 , the modified ZZLB coincides with the Barankin bound. In this regime differential delay observations are subject to ambiguities. If SNR > SNR 3 the modified ZZLB coincides with the Cramer-Rao lower bound indicating that the ambiguity in the differential delay estimation can essentially be resolved. The transition from the ambiguity-dominated mode of operation to the ambiguity-free mode of operation starts at SNR 2 and ends at SNR 3 . This is the threshold phenomenon in time delay estimation. The various deflection points SNR i and the various segments of the bound (Fig. 3) are given as functions of such important system parameters as time-bandwidth product (WT), signal bandwidth to center frequency ratio (W/ω 0 ) and the number of half wavelengths of the signal center frequency contained in the spacing between receivers. With this information the composite bound illustrated in Fig. 3 provides the most complete characterization of the attainable system performance under any prespecified SNR conditions.

353 citations


Journal ArticleDOI
Abstract: From the standpoint of reporting a new contribution, this paper shows that by using bilinear interpolation followed by direct two-dimensional Fourier inversion, one can obtain reconstructions of quality which is comparable to that produced by the filtered-backpropagation algorithm proposed recently by Devaney. For an N × N image reconstructed from N diffracted projections, the former approach requires approximately 4N FFT's, whereas the backpropagation technique requires approximately N2FFT's. We have also taken this opportunity to present the reader with a tutorial introduction to diffraction tomography, an area that is becoming increasingly important not only in medical imaging, but also in underwater and seismic mapping with microwaves and sound. The main feature of the tutorial part is the statement of the Fourier diffraction projection theorem, which is an extension of the traditional Fourier slice theorem to the case of image formation with diffracting illumination.

340 citations


Journal ArticleDOI
TL;DR: A class of linear constraints, also termed as derivative constraints, which is applicable to broad-band element space antenna array processors, is presented and can be made as broad as desired and the beam spacings can be selected without fear of substantial signal suppression in the event of signal arrivals between beams.
Abstract: In this paper a class of linear constraints, also termed as derivative constraints, which is applicable to broad-band element space antenna array processors, is presented. The performance characteristics of the optimum processor with derivative constraints are demonstrated by computer studies involving two types of array geometries, namely linear and circular arrays. As a consequence of derivative constraints, the beam width in the look direction can be made as broad as desired and the beam spacings can be selected without fear of substantial signal suppression in the event of signal arrivals between beams. However, this increased beam width is achieved at the price of reducing array gain.

293 citations


Journal ArticleDOI
TL;DR: The increased computational speed of the introduced algorithm stems from an alternative definition of the so-called Kalman gain vector, which takes better advantage of the relationships between forward and backward linear prediction.
Abstract: A new computationally efficient algorithm for sequential least-squares (LS) estimation is presented in this paper. This fast a posteriori error sequential technique (FAEST) requires 5p MADPR (multiplications and divisions per recursion) for AR modeling and 7p MADPR for LS FIR filtering, where p is the number of estimated parameters. In contrast the well-known fast Kalman algorithm requires 8p MADPR for AR modeling and 10p MADPR for FIR filtering. The increased computational speed of the introduced algorithm stems from an alternative definition of the so-called Kalman gain vector, which takes better advantage of the relationships between forward and backward linear prediction.

275 citations


Journal ArticleDOI
TL;DR: A signal is shown to be uniquely represented by the magnitude of its short-time Fourier transform (STFT) under mild restrictions on the signal and the analysis window of the STFT.
Abstract: In this paper, a signal is shown to be uniquely represented by the magnitude of its short-time Fourier transform (STFT) under mild restrictions on the signal and the analysis window of the STFT. Furthermore, various algorithms are developed which reconstruct signal from appropriate samples of the STFT magnitude. Several of the algorithms can also be used to obtain signal estimates from the processed STFT magnitude, which generally does not have a valid short-time structure. These algorithms are successfully applied to the time-scale modification and noise reduction problems in speech processing. Finally, the results presented here have similar potential for other application areas, including those with multidimensional signals.

Journal ArticleDOI
TL;DR: The maximum likelihood (ML) estimator of the location of multiple sources and the corresponding Cramer-Rao lower bound on the error covariance matrix are derived and Iterative algorithms for the actual computation of the ML estimator are presented.
Abstract: The maximum likelihood (ML) estimator of the location of multiple sources and the corresponding Cramer-Rao lower bound on the error covariance matrix are derived. The derivation is carried out for the general case of correlated sources so that multipath propagation is included as a special case. It is shown that the ML processor consists of a bank of beam-formers, each focused to a different source, followed by a variable matrix-filter that is controlled by the assumed location of the sources. In the special case of uncorrelated sources and very low signal-to-noise ratio this processor reduces to an aggregate of ML processors for a single source with each processor matched to a different source. Iterative algorithms for the actual computation of the ML estimator are also presented.

Journal ArticleDOI
Abstract: Specific implementations of the finite impulse response (FIR) block adaptive filter in the frequency domain are presented and some of their important properties are discussed. The time-domain block adaptive filter implemented in the frequency domain is shown to be equivalent to the frequency-domain adaptive filter (derived in the frequency domain), provided data sectioning is done properly. All of the known time- and frequency-domain adaptive filters [1]-[12], [16]-[18] are contained in the set of possible block adaptive filter structures. Thus, the block adaptive filter is generic and its formulation unifies the current theory of time- and frequency-domain FIR adaptive filter structures. A detailed analysis of overlap-save and overlap-add implementations shows that the former is to be preferred for adaptive applications because it requires less computation, a fact that is not true for fixed coefficient filters.

Journal ArticleDOI
TL;DR: The purpose of this paper is to analyze the behavior of several jump detection algorithms when applied to the same real data (geophysical signals) and to compare these algorithms from different points of view: complexity, efficiency, robustness, and ability to characterize the detected jumps.
Abstract: The purpose of this paper is to analyze the behavior of several jump detection algorithms when applied to the same real data (geophysical signals) and to compare these algorithms from different points of view: complexity, efficiency, robustness, and ability to characterize the detected jumps. Three types of algorithms are investigated: "filtered derivatives" detectors, cumulative sum (cusum) tests, and Willsky's generalized likelihood ratio (GLR) algorithm. A modified version of this last test is elaborated, and a new detector, mixing GLR and cusum tests, is presented.

Journal ArticleDOI
TL;DR: The rational vector space generalization of the signal subspace approach is presented and applied to the estimation of multiple wide-band emitter locations from the signals received at multiple sensors.
Abstract: The rational vector space generalization of the signal subspace approach is presented and applied to the estimation of multiple wide-band emitter locations from the signals received at multiple sensors. The signal subspace and array manifold concepts first introduced by Schmidt are generalized to rational vector space. These concepts are used to develop the rational signal subspace theory and prove the signal subspace theorem, on which signal subspace algorithms are based. The theory is applied in discrete time to derive a class of rational signal subspace algorithms for source location and spectral estimation using unit circle eigendecomposition of multivariate rational models of sensor outputs. Simulation results are presented for an algorithm in this class, including sample statistics from Monte Carlo trials and comparisons with the Cramer-Rao bound.

Journal ArticleDOI
TL;DR: The design and implementation of a VLSI chip for the one-dimensional median filtering operation is presented, designed to operate on 8-bit sample sequences with a window size of five samples and able to filter at rates up to ten megasamples per second.
Abstract: The design and implementation of a VLSI chip for the one-dimensional median filtering operation is presented. The device is designed to operate on 8-bit sample sequences with a window size of five samples. Extensive pipelining and employment of systolic data-flow concepts at the bit level enable the chip to filter at rates up to ten megasamples per second. A configuration for using the chip for approximate two-dimensional median filtering operation is also presented.

Journal ArticleDOI
TL;DR: A highly concurrent Toeplitz system solver, featuring maximum parallelism and localized communication, and a pipelined processor architecture is proposed which uses only localized interconnections and yet retains themaximum parallelism attainable.
Abstract: The design of VLSI parallel processors requires a fundamental understanding of the parallel computing algorithm and an appreciation of the implementational constraint on communications. Based on such consideration, this paper develops a highly concurrent Toeplitz system solver, featuring maximum parallelism and localized communication. More precisely, a highly parallel algorithm is proposed which achieves O(N) computing time with a linear array of O(N) processors. This compares very favorably to the O(N \log_{2} N) computing time attainable with the traditional Levinson algorithm implemented in parallel. Furthermore, to comply with the communication constraint, a pipelined processor architecture is proposed which uses only localized interconnections and yet retains the maximum parallelism attainable.

Journal ArticleDOI
Abstract: The zeros of a linear prediction-error filter polynomial for a class of deterministic signals, that are a sum of samples of M exponentially damped/undamped sinusoids, is studied. It is assumed that N samples are available for processing and that they are uncorrupted by noise. It is shown that the exponent parameters of the M signals can be determined from M zeros (called "signal zeros") of an Lth degree prediction-error filter polynomial (L>M) if L lies in between M and N - M (N - M/2 in a special case). The rest of the L - M zeros of the filter polynomial switch are called extraneous zeros, are shown to be approximately uniformly distributed with in the unit circle, regardless of the type of exponentials in the signal, if the prediction filter coefficients are chosen to have minimum Euclidean length. The results obtained provide insight into the estimation problem with noisy data.


Journal ArticleDOI
Abstract: An attempt is made to analyze the fixed point error performance of the normalized ladder algorithm, for autoregressive system identification, assuming rounding arithmetic. A preliminary simulation study of this algorithm has shown that the bias in the estimated reflection coefficients is much more predominant than the variance of the error in the estimate. The study, therefore, is directed to find a model for predicting the bias in the estimated reflection coefficients. The analysis shows that the roundoff errors associated with the square root operations in one of the algorithm equations are mainly responsible for the bias in the estimated reflection coefficients. These errors arise because of the normalization procedure that makes the quantities under the square root operations very close to one. Two main results are presented in the paper. 1) A simplified theoretical expression for predicting the average bias in the estimated reflection coefficients at any stage is derived. 2) A recursive relation for the average error, arising from the finite precision arithmetic in the squared residuals, is derived. This relation illustrates how the errors made in one stage affect the errors in the succeeding stages. Simulations are performed to check the theoretical models. The experimental results agree very closely with the theoretical predictions.

Journal ArticleDOI
A. Nadas1
TL;DR: The currently used method of maximum likelihood, while heuristic, is shown to be superior under certain assumptions to another heuristic: the method of conditional maximum likelihood.
Abstract: The choice of method for training a speech recognizer is posed as an optimization problem. The currently used method of maximum likelihood, while heuristic, is shown to be superior under certain assumptions to another heuristic: the method of conditional maximum likelihood.

Journal ArticleDOI
TL;DR: A fast Kalman filter is derived for the nearly optimal recursive restoration of images degraded in a deterministic way by blur and in a stochastic way by additive white noise.
Abstract: In this paper a fast Kalman filter is derived for the nearly optimal recursive restoration of images degraded in a deterministic way by blur and in a stochastic way by additive white noise. Straightforwardly implemented optimal restoration schemes for two-dimensional images degraded by both blur and noise create dimensionality problems which, in turn, lead to large storage and computational requirements. When the band-Toeplitz structure of the model matrices and of the distortion matrices in the matrix-vector formulations of the original image and of the noisy blurred observation are approximated by circulant matrices, these matrices can be diagonalized by means of the FFT. Consequently, a parallel set of N dynamical models suitable for the derivation of N low-order vector Kalman filters in the transform domain is obtained. In this way, the number of computations is reduced from the order of O(N4) to that of O(N^{2} \log_{2} N) for N × N images.

Journal ArticleDOI
TL;DR: Results of performance evaluation of several types of filter bank analyzers in a speaker trained isolated word recognition test using dialed-up telephone line recordings indicate that the best performance is obtained by both a 15-channel uniform filter bank and a 13-channel nonuniform filter bank.
Abstract: The vast majority of commercially available isolated word recognizers use a filter bank analysis as the front end processing for recognition. It is not well understood how the parameters of different filter banks (e.g., number of filters, types of filters, filter spacing, etc.) affect recognizer performance. In this paper we present results of performance evaluation of several types of filter bank analyzers in a speaker trained isolated word recognition test using dialed-up telephone line recordings. We have studied both DFT (discrete Fourier transform) and direct form implementations of the filter banks. We have also considered uniform and nonuniform filter spacings. The results indicate that the best performance (highest word accuracy) is obtained by both a 15-channel uniform filter bank and a 13-channel nonuniform filter bank (with channels spacing along a critical band scale). The performance of a 7-channel critical band filter bank is almost as good as that of the two best filter banks. In comparison to a conventional linear predictive coding (LPC) word recognizer, the performance of the best filter bank recognizers was, on average, several percent worse than that of an eighth-order LPC-based recognizer. A discussion as to why some filter banks performed better than others, and why the LPC-based system did the best, is given in this paper.

Journal ArticleDOI
TL;DR: Algorithms for processing multidimensional signals which are sampled on regular, but nonrectangular sampiing lattices, and how generalized decimators and interpolators can be used to convert from one sampling lattice to another are discussed.
Abstract: This paper discusses algorithms for processing multidimensional signals which are sampled on regular, but nonrectangular sampiing lattices. Such sampling lattices are dictated by some applications and may be chosen for others because of their resulting symmetric responses or computational efficiencies. We show that any operation which can be performed on a rectangular lattice can be performed on any regular periodic lattice, including FIR and IIR filtering, DFT calculation, and decimation and interpolation. This paper also discusses how generalized decimators and interpolators can be used to convert from one sampling lattice to another.

Journal ArticleDOI
TL;DR: An iterative algorithm for the inversion of a Toeplitz-block ToePlitz matrix consisting of m × m blocks of size p × p and outperforms Akaike's algorithm by a factor of \max {2(p/m), 2} .
Abstract: An iterative algorithm for the inversion of a Toeplitz-block Toeplitz matrix consisting of m × m blocks of size p × p is described. The algorithm presented exploits the structure of the Toeplitz-block Toeplitz matrix and outperforms Akaike's algorithm by a factor of \max {2(p/m), 2} . The use of this algorithm for an iterative solution of a Toeplitz-block Toeplitz set of linear equations is also presented.

Journal ArticleDOI
Abstract: There is no straightforward way to proceed from the continuous-time Wigner distribution to a discrete-time version of this time-frequency signal representation. A previously given definition of such a function turned out to yield a distribution that was periodic with period π instead of 2π and this caused aliasing to occur. Various alternative definitions are considered and compared with respect to aliasing and computational complexity. From this comparison it appears that no definition leads to a function that is optimum in all respects. This is illustrated by an example.

Journal ArticleDOI
Abstract: The array processing problem is briefly discussed and an abstract spectral estimation problem is formulated. This problem involves the estimation of a multidimensional frequency-wave vector power spectrum from measurements of the correlation function and knowledge of the spectral support. The investigation of correlation-matching spectral estimates leads to the extendibility question: does there exist any positive spectrum on the spectral support that exactly matches a given set of correlation samples? In answering this question, a mathematical framework is developed in which to analyze and design spectral estimation algorithms. Pisarenko's method of spectral estimation, which models the spectrum as a sum of impulses plus a noise component, is extended from the time series case to the more general array processing case. Pisarenko's estimate is obtained as the solution of a linear optimization problem, which can be solved using a linear programming algorithm such as the simplex method.

Journal ArticleDOI
TL;DR: The use of the residual signal in defining a practical criterion to indicate when the numerical algorithm has converged is investigated and the advantage of this criterion over the criterion of examining successive iterations is demonstrated.
Abstract: While many iterative signal restoration methods have been shown to converge in the mathematical sense, a practical criterion is needed to indicate when the numerical algorithm has converged. The use of the residual signal in defining such a criterion is investigated. The advantage of this criterion over the criterion of examining successive iterations is demonstrated.

Journal ArticleDOI
Abstract: The transient and steady-state mean and covariance of the complex-valued LMS adaptive element weights are investigated when the inputs are samples from circularly normal processes. It is shown that the data covariance diagonalizing matrix also diagonalizes the weight covariance matrix. This result permits describing the complete transient behavior of the adaptive line enhancer (ALE) weight covariance matrix in closed form for the case of multiple, equal power, narrow-band, statistically independent, orthogonal, Rayleigh fading sinusoids in broad-band noise. Based on these transient covariance results, it is shown that for any stage of adaptation, there exists an optimum ALE gain constant that minimizes the excess mean squared prediction error. This result is of particular significance when processing time-limited data.

Journal ArticleDOI
TL;DR: A novel model for voiced speech that allows for local non-stationarities not only in terms of pitch perturbations, but in Terms of vocal tract variations as well, and supports new forms of spectral prediction, which can be put to advantage in speech coding applications.
Abstract: The main purpose of this paper is to present a novel model for voiced speech. The classical model, which is being used in many applications, assumes local stationarity, and consequently imposes a simple and well known line structure to the short-time spectrum of voiced speech. The model derived in this paper allows for local non-stationarities not only in terms of pitch perturbations, but in terms of vocal tract variations as well. The resulting structure of the short-time spectrum becomes more complex, but can still be interpreted in terms of generalized lines. The proposed model supports new forms of spectral prediction, which can be put to advantage in speech coding applications. Experimental results are presented supporting the validity of both the model itself and the prediction relationships. Finally, a new class of speech coders, denoted harmonic coders, based on the presented model, is proposed, and a specific implementation is presented.