Showing papers in "IEEE Transactions on Acoustics, Speech, and Signal Processing in 1982"
TL;DR: In this paper, the estimation procedure presented here makes use of "backward prediction" in addition to singular value decomposition (SVD) for accurate estimation of closely spaced frequencies of sinusoidal signals in noise.
Abstract: We have presented techniques [1] - [6] based on linear prediction (LP) and singular value decomposition (SVD) for accurate estimation of closely spaced frequencies of sinusoidal signals in noise. In this note we extend these techniques to estimate the parameters of exponentially damped sinusoidal signals in noise. The estimation procedure presented here makes use of "backward prediction" in addition to SVD. First, the method is applied to data consisting of one and two exponentially damped sinusoids. The choice of one and two signal components facilitates the comparison of estimation error in pole damping factors and pole frequencies to the appropriate Cramer-Rao (CR) bounds and to traditional methods of linear prediction. Second, our method is applied to an example due to Steiglitz [8] in which the data consists of noisy values of the impulse response samples (composed of many exponentially damped sinusoids) of a linear system having both poles and zeros. The poles of the system are accurately determined by our method and the zeros are obtained subsequently, using Shanks' method.
881 citations
TL;DR: It is proved that the output of a recursive median filter is invariant to subsequent passes by the same filter and that for nonmedian nth ranked-order operations, repeated application of the operation will reduce any signal to a constant.
Abstract: Some modifications of the median filter are given and their properties are derived. In addition, some results for standard median filters are given. It is shown that for nonmedian nth ranked-order operations, repeated application of the operation will reduce any signal to a constant. Also, it is proved that the output of a recursive median filter is invariant to subsequent passes by the same filter.
505 citations
TL;DR: In this article, the phase or magnitude information alone is not sufficient, in general, to uniquely specify a sequence, however, a large class of sequences are shown to be recoverable from their phases or magnitudes.
Abstract: This paper addresses two fundamental issues involved in the reconstruction of a multidimensional sequence from either the phase or magnitude of its Fourier transform The first issue relates to the uniqueness of a multidimensional sequence in terms of its phase or magnitude Although phase or magnitude information alone is not sufficient, in general, to uniquely specify a sequence, a large class of sequences are shown to be recoverable from their phase or magnitude The second issue which is addressed in this paper concerns the actual reconstruction of a multidimensional sequence from its phase or magnitude For those sequences which are uniquely specified by their phase, several practical algorithms are described which may be used to reconstruct a sequence from its phase Several examples of phase-only reconstruction are also presented Unfortunately, however, even for those sequences which are uniquely defined by their magnitude, it appears that a practical algorithm is yet to be developed for reconstructing a sequence from only its magnitude Nevertheless, an iterative procedure which has been proposed is briefly discussed and evaluated
472 citations
TL;DR: In this article, the importance of Fourier transform phase in speech enhancement is considered and it is shown that a more accurate estimation of phase is unwarranted in the S/N ratios where the intelligibility scores of unprocessed speech range from 5 to 95 percent.
Abstract: The importance of Fourier transform phase in speech enhancement is considered. Results indicate that a more accurate estimation of phase is unwarranted in speech enhancement at the S/N ratios where the intelligibility scores of unprocessed speech range from 5 to 95 percent, if the phase estimate is used to reconstruct speech by combining it with an independently estimated magnitude or to reconstruct speech using the phase-only signal reconstruction algorithm.
378 citations
TL;DR: In this article, the variance of the time delay estimate for both a gated mode and an ungated mode is examined for both the correlation peak closest to the true time delay, and the observed variance for both modes is compared with the theoretical variance based on a small error analysis.
Abstract: The estimate of the difference in time of arrival of a common random signal received at two sensors, each of which also receives uncorrelated noise, is examined for both small and large estimation errors. It is shown that as the post-integration signal-to-noise ratio decreases, the correlator exhibits a thresholding effect; that is, the probability of a large error (an anomalous estimate) increases rapidly. Approximate theoretical results for the probability of an anomaly are presented and are verified experimentally. The variance of the time delay estimate is examined for both a gated mode, in which the time delay corresponding to the correlation peak closest to the true time delay is used as the estimate of time delay, and an ungated mode, in which the time delay corresponding to the largest peak over the full range of the correlator delay times is used as the estimate. The observed variance for both modes is compared with the theoretical variance based on a small error analysis. For the gated modes, the signal-to-noise ratio below which the observed variance begins to differ significantly from the small error theory can be reliably predicted from a linearity criterion. It is shown, however, that the expected variance for the ungated mode can depart from the small error theory at a higher signal-to-noise ratio than for the gated modes; thus the variance due to anomalies can be the most important factor in determining the region of applicability of the small error analysis.
272 citations
TL;DR: In this article, an adaptive beamforming method is proposed to improve the bearing resolution of a passive array, having many similarities to the minimum energy approach, where the evaluation of energy in each steered beam is preceded by an eigenvalue-eigenvector analysis of the empirical correlation matrix.
Abstract: A method of improving the bearing-resolving capabilities of a passive array is discussed. This method is an adaptive beamforming method, having many similarities to the minimum energy approach. The evaluation of energy in each steered beam is preceded by an eigenvalue-eigenvector analysis of the empirical correlation matrix. Modification of the computations according to the eigenvalue structure results in improved resolution of the bearing of acoustic sources. The increase in resolution is related to the time-bandwidth product of the computation of the correlation matrix. However, this increased resolution is obtained at the expense of array gain.
264 citations
TL;DR: In this paper, an unconstrained frequency-domain least mean square (UFLMS) algorithm is presented, which converges to the Wiener solution without the time-domain constraint on the impulse response as proposed by Ferrara.
Abstract: An unconstrained frequency-domain least mean-squares (UFLMS) algorithm is presented. The algorithm is based on the "overlap-save" technique used in frequency-domain filtering. The proposed algorithm converges to the Wiener solution without the time-domain constraint on the impulse response as proposed by Ferrara. For a large number of taps ( \geq32 ), the UFLMS algorithm offers a significant reduction in computation. Another advantage is its fast convergence for highly correlated input signals. The performance of the algorithm is illustrated by a simulation.
257 citations
TL;DR: A method is presented for computing an orthonormal set of eigenvectors for the discrete Fourier transform (DFT) based on a detailed analysis of the eigenstructure of a special matrix which commutes with the DFT.
Abstract: A method is presented for computing an orthonormal set of eigenvectors for the discrete Fourier transform (DFT). The technique is based on a detailed analysis of the eigenstructure of a special matrix which commutes with the DFT. It is also shown how fractional powers of the DFT can be efficiently computed, and possible applications to multiplexing and transform coding are suggested.
243 citations
TL;DR: LP estimation of frequencies can be greatly improved at low SNR by singular value decomposition (SVD) of the LP data matrix, as is done in Pisarenko's method and its variants.
Abstract: Linear-prediction-based (LP) methods for fitting multiple-sinusoid signal models to observed data, such as the forward-backward (FBLP) method of Nuttall [5] and Ulrych and Clayton [6], are very ill-conditioned. The locations of estimated spectral peaks can be greatly affected by a small amount of noise because of the appearance of outliers. LP estimation of frequencies can be greatly improved at low SNR by singular value decomposition (SVD) of the LP data matrix. The improved performance at low SNR is also better than that obtained by using the eigenvector corresponding to the minimum eigenvalue of the correlation matrix, as is done in Pisarenko's method and its variants.
238 citations
TL;DR: In this paper, the singular value decomposition (SVD) of a 3 × 3 matrix containing the eight so-called pure parameters is used to determine the 3D motion parameters of a rigid planar patch.
Abstract: We show that the three-dimensional (3-D) motion parameters of a rigid planar patch can be determined by computing the singular value decomposition (SVD) of a 3 × 3 matrix containing the eight so called "pure parameters." Furthermore, aside from a scale factor for the translation parameters, the number of solutions is either one or two, depending on the multiplicity of the singular values of the matrix.
238 citations
TL;DR: A comparison of the results for the real speech and the simulated speech provides a quantitative measure of the accuracy of such models and, hence, of the applicability of information theory bounds and code designs based on probabilistic models.
Abstract: An algorithm for the design of vector quantizers that are locally optimum in the sense of minimizing an average quantitative distortion measure is used to design 1 and 2 bit/sample vector quantizers for both real sampled speech and a simulated speech-like auto-regressive random process. Both weighted and unweighted squared-error distortion measures are considered. Several comparisons are made and discussed based on the average distortions of the vector quantization schemes. The results for the simulated speech are compared to mathematical performance bounds from information theory to provide an indication of how nearly globally optimal vector quantization is for such highly correlated sources. A comparison of the results for the real speech and the simulated speech provides a quantitative measure of the accuracy of such models and, hence, of the applicability of information theory bounds and code designs based on probabilistic models. The signal-to-quantization-noise ratios of vector quantizers designed to minimize squared-error distortion are compared to those of several popular speech waveform coding systems of similar rates.
TL;DR: An 800 bit/s vector quantization linear predictive coding (LPC) vocoder has been developed that preserves most of the intelligibility of an LPC system and compatibility with any LPC-10 vocoder is guaranteed.
Abstract: An 800 bit/s vector quantization linear predictive coding (LPC) vocoder has been developed. The recently developed LPC vector quantization theory is applied to reduce the bit rate for LPC coefficients coding by a factor of four. Branch search techniques and separation of voiced and unvoiced codebooks are applied for better algorithm efficiency. Differential coding is applied to reduce the bit rate for the pitch and gain parameters by one third. Formal subjective evaluation shows that the 800 bit/s vocoder preserves most of the intelligibility of an LPC system. It is also robust under different transmission error and acoustic conditions. Informal listening comparisons show the quality to be acceptable and sometimes very close to 2400 bit/s LPC speech. The computational cost of the 800 bit/s vocoder is equivalent to or even lower than the 2400 bit/s LPC-10. Compatibility with any LPC-10 vocoder is guaranteed because the 800 bit/s design only differs in the quantization and encoding algorithms. Further bit rate reduction can be achieved by removing frame to frame redundancy in the code.
IBM1
TL;DR: It is shown that for certain filter requirements, common to decimation and interpolation, an Nth-band filter exists with passband and stopband ripples only slightly larger than those of the optimal FIR filter.
Abstract: Half-band FIR digital filters are known to be important due to their reduced computational requirements. They are especially valuable when used to decimate or interpolate by a factor of 2 [1], where their characteristics well match the filtering requirements. Computational savings can also be achieved by extending the concept of half-band filters to Nth-band filters for use in decimation or interpolation by a factor of N. In this paper, it is shown that for certain filter requirements, common to decimation and interpolation, an Nth-band filter exists with passband and stopband ripples only slightly larger than those of the optimal FIR filter. It is demonstrated that optimal half-band filters can be designed by using the computer program of McClellan, Parks, and Rabiner [2]. It is also shown that useful Nth-band filters can be designed by using this program, which is perhaps the most widely available filter design program.
TL;DR: In this paper, the convergence rate and misalignment noise of adaptive transversal filters with arbitrary correlation multiplier nonlinearities are derived and a power-of-two multiplier is suggested as a better alternative.
Abstract: It is well known that the correlation multiplier used to form the update signal in adaptive transversal filters need not be a true multiplier. By using an approximate multiplier such as a sign-bit-only multiplier, implementation can be made less costly. In this paper we derive expressions for the convergence rate and misalignment noise of adaptive transversal filters with arbitrary correlation-multiplier non-linearities. The analysis shows any such nonlinearities to always harm performance and quantifies the penalty suffered. Sign-bit-only multiplication suffers a significant penalty, and power-of-two multiplication is suggested as a better alternative. Its performance is almost equal to that of a true multiplier, and in a digital implementation, at least, it is only slightly more difficult to realize than a sign-bit-only multiplier. The theory is developed in a way emphasizing physical understanding and has been verified to be in good agreement with simulation.
TL;DR: By using spatial interaction models, this paper develops restoration algorithms that do not require the availability of the original image or its prototype, and the specific structure of the underlying lattice enables the implementation of the filters using fast Fourier transform (FFT) computations.
Abstract: This paper is concerned with developing fast nonrecursive algorithms for the minimum mean-squared error restoration of degraded images. The degradation is assumed to be due to a space invariant, periodic, nonseparable known point-spread function, and additive white noise. Our basic approach is to represent the images by a class of spatial interaction models, namely the simultaneous autoregressve models and the conditional Markov models defined on toroidal lattices, and develop minimum mean-squared error restoration algorithms using these models. The restoration algorithms are optimal, if the parameters characterizing the interaction models are exactly known. However, in practice, the parameters are estimated from the images. By using spatial interaction models, we develop restoration algorithms that do not require the availability of the original image or its prototype. The specific structure of the underlying lattice enables the implementation of the filters using fast Fourier transform (FFT) computations, Several restoration examples are given.
TL;DR: The proposed scheme for generating a random sequence with a specified marginal distribution and autocovariance consists of a white Gaussian noise source input to a linear digital filter followed by a zero-memory nonlinearity (ZMNL).
Abstract: We consider the problem of generating a random sequence with a specified marginal distribution and autocovariance. The proposed scheme for generating such a sequence consists of a white Gaussian noise source input to a linear digital filter followed by a zero-memory nonlinearity (ZMNL). The ZMNL is chosen so that the desired distribution is exactly realized and the digital filter is designed so that the desired autocovariance is closely approximated. Both analytic results and examples are included. The proposed scheme should prove useful in simulations involving non-Gaussian processes.
TL;DR: A new spectral estimator is developed from the high-order Yule-Walker equations and pseudoinverse solutions to the equations that provides high resolution spectral estimates as substantiated by simulation results and produces a constant false alarm rate detector for a single sinusoid in noise.
Abstract: A new spectral estimator is developed from the high-order Yule-Walker equations and pseudoinverse solutions to the equations. The approach circumvents the usual difficulties associated with inverting ill-conditioned matrices and allows the choice of high model order. It also provides high resolution spectral estimates as substantiated by simulation results. A byproduct of this spectral estimator is a constant false alarm rate detector for a single sinusoid in noise. The detector's receiver operating characteristics curves are constructed from histograms, based on 1000 runs, of the detection statistics.
TL;DR: An alternative Gauss-Newton type recursive algorithm, which also used the second derivative matrix (or Hessian), which may be viewed as an approximate least squares algorithm and has faster convergence in the beginning, while its convergence rate close to the true parameters depends on the signal-to-noise ratio of the input signal.
Abstract: Pisarenko's harmonic retrieval method involves determining the minimum eigenvalue and the corresponding eigenvector of the covariance matrix of the observed random process. Recently, Thompson [9] suggested a constrained gradient search procedure for obtaining an adaptive version of Pisarenko's method, and his simulations have verified that the frequency estimates provided by his procedure were unbiased. However, the main cost of this technique was that the initial convergence rate could be very slow for certain poor initial conditions. Restating the constrained minimization as an unconstrained nonlinear problem, we derived an alternative Gauss-Newton type recursive algorithm, which also used the second derivative matrix (or Hessian); this algorithm may also be viewed as an approximate least squares algorithm. Simulations have been performed to compare this algorithm to (a slight variant of) Thompson's original algorithm. The most important conclusions are that the least squares type algorithm has faster convergence in the beginning, while its convergence rate close to the true parameters depends on the signal-to-noise ratio of the input signal. The approximate least squares algorithm resolves the sinusoids much faster than the gradient version.
TL;DR: The distortion performance of the vector quantization approach for LPC voice coding is examined both analytically and experimentally to show its relationship with the residual minimization process in LPC analysis.
Abstract: The distortion performance of the vector quantization approach for LPC voice coding is examined both analytically and experimentally. Analytically, interpretations of the interparameter coupling effects of a distortion measure and the clustering nature of the algorithm for LPC vector quantization are obtained to show its relationship with the residual minimization process in LPC analysis. Experimentally, a large database of speech is used to compare its performance and properties to scalar quantization. The results lend further insight into the superior performance of vector quantization.
TL;DR: In this paper, the optimal source localization and tracking by utilizing differential delay and Doppler observations at a linear array of receivers is investigated. But the authors focus on source ranges large compared with array baseline and with the distance traversed by the source during the observation interval.
Abstract: If the signal of a moving source is observed at several spatially separated locations during a common time interval, the received signals exhibit differential delays and Doppler shifts which provide information about source location and velocity. This paper deals with the optimal (in the minimum mean-square error sense) source localization and tracking by utilizing differential delay and Doppler observations at a linear array of receivers. We shall be concerned with source ranges large compared with array baseline and with the distance traversed by the source during the observation interval. It is shown that the optimal estimation procedure can be carried out in two sequential steps without any loss in performance. In the first step source location is estimated from the differential delay group of measurements. In the second step source velocity is estimated from the differential Doppler group of measurements and the outcome of the first step. Furthermore, by employing an intermediate track-dependent parameter set, the two-step algorithm yields a closed form solution of the estimation problem.
TL;DR: This paper concerns the use of Widrow's least-mean-square (LMS) algorithm for implementing a time delay estimation algorithm for fixed and moving passive sonar sources.
Abstract: This paper concerns the use of Widrow's least-mean-square (LMS) algorithm for implementing a time delay estimation algorithm for fixed and moving passive sonar sources. Digital simulation results are included for evaluating the related performance of the LMS algorithm.
TL;DR: The most salient feature of the algorithm is that it consists of calculations of scalar quantities, thus completely avoiding matrix manipulations accompanying usual multivariate processing methods.
Abstract: Recently, Pagano has found a one-to-one relationship between multivariate autoregression and scalar periodic autoregressions, and derived a set of fundamental Yule-Walker (YW) type equations for estimating the parameters of the periodic autoregressions. In this paper, we first obtain a Levinson-type recursive algorithm for solving the above mentioned YW equations. Then using this recursion we show a circular lattice structure of the process. This enables us to obtain a Burg-type algorithm which guarantees the filter stability. Lastly, we modify it to an adaptive form for on-line computation. This circular lattice filter simultaneously performs whitening and orthogonalization of the components of multivariate input samples. The most salient feature of the algorithm is that it consists of calculations of scalar quantities, thus completely avoiding matrix manipulations accompanying usual multivariate processing methods.
TL;DR: In this article, the authors extend the Levinson recursion for inversion of a Toeplitz matrix to problems involving the sum of Toe-plitz and Hankel matrices.
Abstract: There are well-known fast algorithms, such as the Levinson recursion, for solving linear equations with a Toeplitz (or Hankel) coefficient matrix. This paper extends the saving obtained by the Levinson recursion for inversion of a Toeplitz matrix to problems involving the inversion of matrices which are the sum of Toeplitz and Hankel matrices.
TL;DR: A tree structure for the root signal set of median filters, where signals invariant to median filters are called roots of the signal, is obtained for binary signals.
Abstract: Median filtering is a simple digital technique for smoothing signals. One main characteristic of the filter is that it maps the input signal space into a root signal space, where signals invariant to median filters are called roots of the signal. In this paper, we develop the theory for the root signal set of median filters. A tree structure for the root signal set is obtained for binary signals. The number of roots R (n) for a signal of length "n" and window size filter "2s- 1" is exactly represented by the difference equation R(n) = R(n - 1) + R(n - s). A general solution is obtained in a Z domain approach. Finally, a method for faster one dimensional median filter operation is introduced.
TL;DR: An algorithm for the numerical factorization of very high degree but well-conditioned polynomials is developed and is used to factor the z-transform of finite-length signals, and the zeros are used to calculate the unwrapped phase.
Abstract: An algorithm for the numerical factorization of very high degree but well-conditioned polynomials is developed. This is used to factor the z-transform of finite-length signals, and the zeros are used to calculate the unwrapped phase. The method has been tested on signals up to 512 points in length. A complete Fortran 77 program is given for the case of a real-valued signal. Two related analytical issues are treated. First, the interpretation of phase unwrapping as an interpolation problem is discussed. Second, an explanation is given for the observed numerical difficulties in the method of phase unwrapping using adaptive integration of the phase derivative. The trouble is due to the clustering of the zeros of high degree polynomials near the unit circle.
TL;DR: Fast methods for the determination of the autoregressive (AR) portion of the ARMA model are presented and the definition of two broad classes of matrices, called diagonal innovation matrices (DIM) and peripheral innovation Matrices (PIM), for which fast schemes can be developed are introduced.
Abstract: In many signal processing applications, one often seeks the solution of a linear system of equations by means of fast algorithms. The special form of the matrix associated with the linear system may permit the development of algorithms requiring 0 (p2) or fewer operations. Hankel and Toeplitz matrices provide well known examples and various fast schemes have been developed in the literature to cover these cases. These techniques have common characteristics so that they may be generalized to cover a wider class of linear systems. The purpose of this paper is to develop fast algorithms that cover this wider set of systems. An important feature of the general scheme introduced here is that it leads to the definition of two broad classes of matrices, called diagonal innovation matrices (DIM) and peripheral innovation matrices (PIM), for which fast schemes can be developed. The class of PIM matrices includes many structures appearing in signal processing applications. Most of them are extensively studied in this paper and Fortran coding is provided. Finally, ARMA modeling is considered and within the general framework already introduced, fast methods for the determination of the autoregressive (AR) portion of the ARMA model are presented.
TL;DR: In this article, the improvement achieved by using integer programming over simple coefficient rounding in the design of finite impulse response (FIR) filters with discrete coefficients is most significant when the discrete coefficient space is the powers-of-two space or when a specification is to be met with a given coefficient word length by increasing the filter length.
Abstract: It is demonstrated that the improvement achieved by using integer programming over simple coefficient rounding in the design of finite impulse response (FIR) filters with discrete coefficients is most significant when the discrete coefficient space is the powers-of-two space or when a specification is to be met with a given coefficient word length by increasing the filter length. Both minimax and least square error criteria are considered.
TL;DR: The noise reduction performance of error spectrum shaping (ESS) structures and of the optimal linear state-space (LSS) structure are compared for second-order digital filter sections and it is shown that some of the simple ESS structures can outperform the optimal LSS structure.
Abstract: The noise reduction performance of error spectrum shaping (ESS) structures and of the optimal linear state-space (LSS) structure are compared for second-order digital filter sections. It is shown that optimal direct form 1 and direct form 2 ESS realizations have a higher signal-to-noise ratio than the optimal LSS structure. In practice, suboptimal ESS structures with simple hardware implementations are of greater interest. Several of these implementations are considered and optimal values for the ESS coefficients in these structures are derived. For filters with zeros at z = -1, it is shown that some of the simple ESS structures can outperform the optimal LSS structure. For elliptic filters, it is shown that several of the suboptimal ESS structures perform poorly, but that others still perform well.
TL;DR: In this article, the problem of multidimensional maximum entropy method (MEM) spectral estimation from nonuniformly spaced correlation measurements is investigated and a necessary and sufficient condition is derived for the existence and uniqueness of the MEM spectral estimate in its usual form.
Abstract: The problem of multidimensional maximum entropy method (MEM) spectral estimation from nonuniformly spaced correlation measurements is investigated. A necessary and sufficient condition is derived for the existence and uniqueness of the MEM spectral estimate in its usual form. It is shown that this condition is not satisfied in many multidimensional problems of interest, although it is satisfied in the important practical case of spectral supports composed of a finite number of points. When the existence condition is satisfied, calculation of the MEM estimate reduces to the solution of a finite-dimensional convex optimization problem. The application of standard optimization techniques to this problem results in iterative computational algorithms which are guaranteed to converge. The algorithms so obtained are compared to those previously proposed and a spectral estimation example is presented.
TL;DR: Methods for performing voiced/unvoiced/mixed excitation classification of speech are explored, and three aspects of the task are examined: classifier type, decision structure, and feature selection.
Abstract: Methods for performing voiced/unvoiced/mixed excitation classification of speech are explored. The decision-making process is viewed as a pattern recognition problem. Three aspects of the task are examined: classifier type, decision structure, and feature selection. A variety of different approaches are compared. A classifier is obtained which, in limited tests, achieves 95 percent classification accuracy on speaker dependent tests (with 82.7 percent correct identification of mixed excitation frames), and 94 percent accuracy on speaker independent tests (with 77.6 percent correct identification of mixed excitation frames). The classifier uses a binary decision tree structure, in which a speech segment is first classified as predominantly voiced or predominantly unvoiced, then tested to determine if the excitation for the segment is mixed or not. Each decision is made using a Bayes classifier. The feature selection procedure identified a set of 14 features to make the voiced/unvoiced/mixed excitation classification.