Showing papers in "IEEE Transactions on Acoustics, Speech, and Signal Processing in 1985"
6,899 citations
TL;DR: Simulation results that illustrate the performance of the new method for the detection of the number of signals received by a sensor array are presented.
Abstract: A new approach is presented to the problem of detecting the number of signals in a multichannel time-series, based on the application of the information theoretic criteria for model selection introduced by Akaike (AIC) and by Schwartz and Rissanen (MDL). Unlike the conventional hypothesis testing based approach, the new approach does not requite any subjective threshold settings; the number of signals is obtained merely by minimizing the AIC or the MDL criteria. Simulation results that illustrate the performance of the new method for the detection of the number of signals received by a sensor array are presented.
3,341 citations
TL;DR: An analysis of a "spatial smoothing" preprocessing scheme, recently suggested by Evans et al., to circumvent problems encountered in direction-of-arrival estimation of fully correlated signals.
Abstract: We present an analysis of a "spatial smoothing" preprocessing scheme, recently suggested by Evans et al, to circumvent problems encountered in direction-of-arrival estimation of fully correlated signals Simulation results that illustrate the performance of this scheme in conjunction with the eigenstructure technique are described
1,791 citations
TL;DR: In this paper, a method of constructing a single signal subspace for high-resolution estimation of the angles of arrival of multiple wide-band plane waves is presented, which relies on an approximately coherent combination of the spatial signal spaces of the temporally narrow-band decomposition of the received signal vector from an array of sensors.
Abstract: This paper presents a method of constructing a single signal subspace for high-resolution estimation of the angles of arrival of multiple wide-band plane waves. The technique relies on an approximately coherent combination of the spatial signal spaces of the temporally narrow-band decomposition of the received signal vector from an array of sensors. The algorithm is presented, and followed by statistical simulation examples. The performance of the technique is contrasted with other suggested methods and statistical bounds in terms of the determination of the correct number of sources (detection), bias, and variance of estimates of the angles.
1,067 citations
TL;DR: A general class of spectral estimators of the Wigner-Ville spectrum is proposed: this class is based on arbitrarily weighted covariance estimators and its formal description corresponds to the generalclass of conjoint time-frequency representations of deterministic signals with finite energy.
Abstract: The Wigner-Ville spectrum has been recently introduced as the unique generalized spectrum for time-varying spectral analysis. Its properties are revised with emphasis on its central role in the analysis of second-order properties of nonstationary random signals. We propose here a general class of spectral estimators of the Wigner-Ville spectrum: this class is based on arbitrarily weighted covariance estimators and its formal description corresponds to the general class of conjoint time-frequency representations of deterministic signals with finite energy. Classical estimators like short-time periodograms and the recently introduced pseudo-Wigner estimators are shown to be special cases of the general class. The generalized framework allows the calculation of the moments of general spectral estimators and comparing the results emphasizes the versatility of the new pseudo-Wigner estimators. The effective numerical implementation, by an N-point FFT, of pseudo-Wigner estimators of 2N points is indicated and various examples are given.
573 citations
TL;DR: Two feature extraction methods for the classification of textures using two-dimensional Markov random field (MRF) models are presented and it is shown that the sample correlations over a symmetric window including the origin are optimal features for classification.
Abstract: The problem of texture classification arises in several disciplines such as remote sensing, computer vision, and image analysis. In this paper we present two feature extraction methods for the classification of textures using two-dimensional (2-D) Markov random field (MRF) models. It is assumed that the given M × M texture is generated by a Gaussian MRF model. In the first method, the least square (LS) estimates of model parameters are used as features. In the second method, using the notion of sufficient statistics, it is shown that the sample correlations over a symmetric window including the origin are optimal features for classification. Simple minimum distance classifiers using these two feature sets yield good classification accuracies for a seven class problem.
531 citations
TL;DR: A new algorithm is presented for adaptive notch filtering and parametric spectral estimation of multiple narrow-band or sine wave signals in an additive broad-band process and uses a special constrained model of infinite impulse response with a minimal number of parameters.
Abstract: A new algorithm is presented for adaptive notch filtering and parametric spectral estimation of multiple narrow-band or sine wave signals in an additive broad-band process. The algorithm is of recursive prediction error (RPE) form and uses a special constrained model of infinite impulse response (IIR) with a minimal number of parameters. The convergent filter is characterized by highly narrow bandwidth and uniform notches of desired shape. For sufficiently large data sets, the variances of the sine wave frequency estimates are of the same order of magnitude as the Cramer-Rao bound. Results from simulations illustrate the performance of the algorithm under a wide range of conditions.
472 citations
TL;DR: A new adaptive array beam-former able to work well even when the desired signal and the interference are coherent, and the results of simulations support the theoretical predictions.
Abstract: In this paper we introduce a new adaptive array beam-former able to work well even when the desired signal and the interference are coherent. The present adaptive beamformers fail to operate in these cases. The results of simulations support the theoretical predictions.
471 citations
TL;DR: It is shown that M filters can offer a more favorable combination of the running mean and median filters than can L filters, while MTM filters generally have better characteristics than M filters.
Abstract: We consider some generalizations of median filters which combine properties of both the linear and median filters. In particular, L filters and M filters are considered, motivated by robust estimators which are generalizations of the median as a location estimator. A related filter, which we call the modified trimmed mean (MTM) filter, is also described. The filters are evaluated for their performance on noisy signals containing sharp discontinuities or edges. It is shown that M filters can offer a more favorable combination of the running mean and median filters than can L filters, while MTM filters generally have better characteristics than M filters. We also show that an MTM filter is a data-dependent modification of L filters. The concept of double-window filtering is introduced as a refinement of MTM filtering. One representative set of filtered sequences of a test input using these filters are presented to illustrate the performance characterisics of these filters.
419 citations
TL;DR: It is found that the adaptive coefficient μ, which controls the rate of convergence of the algorithm, must be restricted to an interval significantly smaller than the domain commonly stated in the literature.
Abstract: Statistical analysis of the least mean-squares (LMS) adaptive algorithm with uncorrelated Gaussian data is presented. Exact analytical expressions for the steady-state mean-square error (mse) and the performance degradation due to weight vector misadjustment are derived. Necessary and sufficient conditions for the convergence of the algorithm to the optimal (Wiener) solution within a finite variance are derived. It is found that the adaptive coefficient μ, which controls the rate of convergence of the algorithm, must be restricted to an interval significantly smaller than the domain commonly stated in the literature. The outcome of this paper, therefore, places fundamental limitations on the mse performance and rate of convergence of the LMS adaptive scheme.
392 citations
TL;DR: The utility of the Volterra filter is demonstrated by utilizing it in studies of nonlinear drift oscillations of moored vessels subject to random sea waves.
Abstract: Some recent results on the design and implementation of second-order Volterra filters are presented. The (second-order) Volterra filter is a nonlinear filter with the filter structure of (second-order) Volterra series. A simple minimum mean-square error solution for the Volterra filter is derived, based on the assumption that the filter input is Gaussian. Also, we propose an iterative factorization technique to design a subclass of the Volterra filters, which can alleviate the complexity of the filtering operations considerably. Furthermore, an adaptive algorithm for the Volterra filter is investigated along with its mean convergence and asymptotic excess mean-square error. Finally, the utility of the Volterra filter is demonstrated by utilizing it in studies of nonlinear drift oscillations of moored vessels subject to random sea waves.
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TL;DR: The signal modeling methodology is discussed and experimental results on speaker independent recognition of isolated digits are given and the potential use of the modeling technique for other applications are discussed.
Abstract: In this paper a signal modeling technique based upon finite mixture autoregressive probabilistic functions of Markov chains is developed and applied to the problem of speech recognition, particularly speaker-independent recognition of isolated digits. Two types of mixture probability densities are investigated: finite mixtures of Gaussian autoregressive densities (GAM) and nearest-neighbor partitioned finite mixtures of Gaussian autoregressive densities (PGAM). In the former (GAM), the observation density in each Markov state is simply a (stochastically constrained) weighted sum of Gaussian autoregressive densities, while in the latter (PGAM) it involves nearest-neighbor decoding which in effect, defines a set of partitions on the observation space. In this paper we discuss the signal modeling methodology and give experimental results on speaker independent recognition of isolated digits. We also discuss the potential use of the modeling technique for other applications.
TL;DR: A real input, real coefficient version of the constant modulus algorithm is shown to perform arbitrarily close to the fully complex version, extended for the enhancement of signals having a nonconstant but known envelope, as might arise in data signals with pulse shaping.
Abstract: This paper presents three extensions of the constant modulus algorithm (CMA) introduced in an earlier paper as a means of correcting degradations in constant enyelope waveforms. As originally formulated, the CMA employs an FIR filter with complex coefficients and accepts complex (quadrature) input data. In this paper, first a real input, real coefficient version of the algorithm is shown to perform arbitrarily close to the fully complex version. Secondly, the algorithm is extended for the enhancement of signals having a nonconstant but known envelope, as might arise in data signals with pulse shaping. Lastly, a multichannel version of CMA, wherein several observations are linearly combined, is presented for joint adaptation of multiple filters. This approach can be used, for example, as a means of spatial or polarization "beamsteering" to reject additive interferers and compensate for channel-induced polarization rotation.
TL;DR: It is shown that the proposed parametric approach to bispectrum estimation based on a non-Gaussian white noise driven autoregressive (AR) model provides bispectral estimates that are far superior to the conventional estimates in terms of bispectrals fidelity and that in the case of detecting phase coupling among sinusoids, the method provides significantly better resolution.
Abstract: Higher order spectra contain information about random processes that is not contained in the ordinary power spectrum such as the degree of nonlinearity and deviations from normality. Estimation of the bispectrum, which is a third-order spectrum, has been applied in various fields to obtain information regarding quadratic phase coupling among harmonic components and non-Gaussianness of processes. Existing methods of bispectrum estimation are patterned after the conventional methods of power spectrum estimation which are known to possess certain limitations. The paper proposes a parametric approach to bispectrum estimation based on a non-Gaussian white noise driven autoregressive (AR) model. The AR parameter estimates are obtained by solving the third-order recursion equations which may be Toeplitz in form but not symmetric. It is shown that the method provides bispectral estimates that are far superior to the conventional estimates in terms of bispectral fidelity and that in the case of detecting phase coupling among sinusoids, the method provides significantly better resolution.
TL;DR: A complete set of fast algorithms for computing the discrete Hartley transform is developed, including decimation-in-frequency, radix-4, split radix, prime factor, and Winograd transform algorithms.
Abstract: The discrete Hartley transform (DHT) is a real-valued transform closely related to the DFT of a real-valued sequence. Bracewell has recently demonstrated a radix-2 decimation-in-time fast Hartley transform (FHT) algorithm. In this paper a complete set of fast algorithms for computing the DHT is developed, including decimation-in-frequency, radix-4, split radix, prime factor, and Winograd transform algorithms. The philosophies of all common FFT algorithms are shown to be equally applicable to the computation of the DHT, and the FHT algorithms closely resemble their FFT counterparts. The operation counts for the FHT algorithms are determined and compared to the counts for corresponding real-valued FFT algorithms. The FHT algorithms are shown to always require the same number of multiplications, the same storage, and a few more additions than the real-valued FFT algorithms. Even though computation of the FHT takes more operations, in some situations the inherently real-valued nature of the discrete Hartley transform may justify this extra cost.
TL;DR: A sampling theory which extends the uniform sampling theory of Whittaker et al. to include nonuniform sample distributions and shows that a more general result can be obtained by treating the sample sequence as the result of applying a coordinate transformation to the uniform sequence.
Abstract: The reconstruction of functions from their samples at nonuniformly distributed locations is an important task for many applications. This paper presents a sampling theory which extends the uniform sampling theory of Whittaker et al. [11] to include nonuniform sample distributions. This extension is similar to the analysis of Papoulis [15], who considered reconstructions of functions that had been sampled at positions deviating slightly from a uniform sequence. Instead of treating the sample sequence as deviating from a uniform sequence, we show that a more general result can be obtained by treating the sample sequence as the result of applying a coordinate transformation to the uniform sequence. It is shown that the class of functions reconstructible in this manner generally include nonband-limited functions. The two-dimensional uniform sampling theory of Petersen and Middle ton [16] can be similarly extended as is shown in this paper. A practical algorithm for performing reconstructions of two-dimensional functions from nonuniformly spaced samples is described, as well as examples illustrating the performance of the algorithm.
TL;DR: A clustering algorithm based on a standard K-means approach which requires no user parameter specification is presented and experimental data show that this new algorithm performs as well or better than the previously used clustering techniques when tested as part of a speaker-independent isolated word recognition system.
Abstract: Studies of isolated word recognition systems have shown that a set of carefully chosen templates can be used to bring the performance of speaker-independent systems up to that of systems trained to the individual speaker. The earliest work in this area used a sophisticated set of pattern recognition algorithms in a human-interactive mode to create the set of templates (multiple patterns) for each word in the vocabulary. Not only was this procedure time consuming but it was impossible to reproduce exactly because it was highly dependent on decisions made by the experimenter. Subsequent work led to an automatic clustering procedure which, given only a set of clustering parameters, clustered patterns with the same performance as the previously developed supervised algorithms. The one drawback of the automatic procedure was that the specification of the input parameter set was found to be somewhat dependent on the vocabulary type and size of population to be clustered. Since a naive user of such a statistical clustering algorithm could not be expected, in general, to know how to choose the word clustering parameters, even this automatic clustering algorithm was not appropriate for a completely general word recognition system. It is the purpose of this paper to present a clustering algorithm based on a standard K-means approach which requires no user parameter specification. Experimental data show that this new algorithm performs as well or better than the previously used clustering techniques when tested as part of a speaker-independent isolated word recognition system.
TL;DR: The purpose of this paper is to illustrate the usefulness of two dimensional noncausal autoregressive (NCAR) models for the synthesis of textures, and shows that the class of NCAR models is capable of generating a wide variety of image patterns posessing the local replication attribute, an essential ingredient of many natural textures.
Abstract: The purpose of this paper is to illustrate the usefulness of two dimensional noncausal autoregressive (NCAR) models for the synthesis of textures. These models characterize the gray level at a pixel as a linear combination of gray levels at nearby locations in all directions and an additive white noise variable. We first show that the class of NCAR models is capable of generating a wide variety of image patterns posessing the local replication attribute, an essential ingredient of many natural textures. It is also shown that the theoretical variograms of many NCAR models possess an oscillatory behavior, a characteristic of the variograms of many natural textures. Next, we give experimental results of synthesis of 64 × 64 textures resembling several real textures in the Brodatz album. The synthetic textures generated by 16 parameter NCAR models retain most the visual characteristics of the original textures. The variograms of the original and synthetic textures are also similar.
TL;DR: Preliminary results indicate that higher quality or lower bit rates may be achieved with enough computational resources, and an extension of the centroid computation used in vector quantization is presented.
Abstract: Rate-distortion theory provides the motivation for using data compression techniques on matrices of N LPC vectors. This leads to a simple extension of speech coding techniques using vector quantization. The effects of using the generalized Lloyd algorithm on such matrices using a summed Itakura-Saito distortion measure are studied, and an extension of the centroid computation used in vector quantization is presented. The matrix quantizers so obtained offer substantial reductions in bit rates relative to full-search vector quantizers. Bit rates as low as 150 bits/s for the LPC matrix information (inclusive of gain, but without pitch and voicing) have been achieved for a single speaker, having average test sequence and codebook distortions comparable to those in the equivalent full-search vector quantizer operating at 350 bits/s. Preliminary results indicate that higher quality or lower bit rates may be achieved with enough computational resources.
IBM1
TL;DR: It is shown that the class of quadrature mirror filters (QMF's) that satisfiesThese conditions is quite limited, and a class of filters which does satisfy these conditions is given, and an simple procedure for designing filters from this class is presented.
Abstract: In this paper, conditions are given for a two-band multi-rate filter bank to be alias free and to have a unity frequency response. It is shown that the class of quadrature mirror filters (QMF's) that satisfies these conditions is quite limited. A class of filters which does satisfy these conditions is given, and a simple procedure for designing filters from this class is presented with an example.
TL;DR: A key feature of this filter structure is that the number of multiplies, adds, and stored coefficients required for implementation is significantly less than those needed for the conventional QMF structure, given the same number of channels.
Abstract: The two-channel quadrature mirror filter structure of Croisier and Esteban may be extended to an arbitrary number of equal bandwidth channels, given certain restrictions on the bandpass filters. The most serious restriction is that the stopband attenuation of eacli band-pass filter must be high for all frequencies outside twice the nominal 3 dB bandwidth of the filter. This restriction is not really a limiting factor for speech subband waveform coding since high adjacent channel attenuation is a necessity for the confinement of quantization noise. A key feature of our filter structure is that the number of multiplies, adds, and stored coefficients required for implementation is significantly less than those needed for the conventional QMF structure, given the same number of channels. Fortran code for a 16-channel filter structure is listed as an example of efficient implementation.
TL;DR: It is demonstrated the existence of positive joint distributions of time and frequency for arbitrary signals and a method is given to readily generate an infinite number of them for any signal.
Abstract: We demonstrate the existence of positive joint distributions of time and frequency for arbitrary signals. A method is given to readily generate an infinite number of them for any signal. General properties of these distribution functions are derived and specific examples for some common signals are presented.
TL;DR: A new method for estimating the number and arrival times for overlapping signals with a priori known shape from noisy observations received by a sensor is presented, based on a recently developed eigenstructure technique for multitarget direction finding with passive antenna arrays and exploits the structure of the received signal covariance matrix.
Abstract: We present a new method for estimating the number and arrival times for overlapping signals with a priori known shape from noisy observations received by a sensor. The method is based on a recently developed eigenstructure technique for multitarget direction finding with passive antenna arrays and exploits the structure of the received signal covariance matrix. This problem is important in various applications such as radar and sonar data processing, geophysical/seismic exploration, and biomedical engineering. In many of these applications, a known signal is launched into a scattering medium and the returning response-in the form of delayed overlapping echos in noise-has to be processed to yield information on the nature and location of scatterers. The method presented also solves more general problems of signal detection and resolution.
TL;DR: A new scheme for decentralized processing in passive sensor arrays based on communicating the sample-covariance matrices of the subarrays with improved accuracy over the conventional triangulation scheme with only a modest increase in the communication load is presented.
Abstract: We present a new scheme for decentralized processing in passive sensor arrays based on communicating the sample-covariance matrices of the subarrays. The new scheme offers improved accuracy over the conventional triangulation scheme with only a modest increase in the communication load.
TL;DR: A two-dimensional fast cosine transform algorithm (2-D FCT) is developed for 2m× 2ndata points, an extended version of the 1- D FCT algorithm introduced in a recent paper, but with significantly reduced computations for a 2-D field.
Abstract: A two-dimensional fast cosine transform algorithm (2-D FCT) is developed for 2m× 2ndata points. This algorithm is an extended version of the 1-D FCT algorithm introduced in a recent paper, but with significantly reduced computations for a 2-D field. The rationale for this 2-D FCT is a 2-D decomposition of data sequences into 2- D subblocks with reduced dimension (halves), rather than serial, one-dimensional, separable treatment for the columns and rows of the data sets. Computer simulation for the 2-D FCT algorithms, using a smaller block of data and finite word precision, proves to be excellent in comparison with the direct 2-D discrete cosine transform (2-D DCT). An example of a 4 × 4 2-D inverse fast cosine transform (2-D IFCT) algorithm development is presented in this paper, together with a signal flow graph.
TL;DR: A fast algorithm to estimate the frequency of a sinusoid is presented, and it is shown that under easily met conditions, the root mean-square error of the estimator is practically equal to the Cramer-Rao bound after only two iterations of Newton's method for all signal-to-noise ratios above threshold.
Abstract: A fast algorithm to estimate the frequency of a sinusoid is presented here. It is based on Newton's method for finding the root of an equation, and it is shown that under easily met conditions, the root mean-square error (RMSE) of the estimator is practically equal to the Cramer-Rao bound after only two iterations of Newton's method for all signal-to-noise ratios (SNR's) above threshold. The estimator's probability density function is computed analytically, and the RMSE is calculated for one and two iterations of Newton's method. Its computational load is shown to be significantly less than other conventional algorithms.
TL;DR: The normalized FTF algorithms are introduced, at a modest increase in computational requirements, to significantly mitigate the numerical deficiencies inherent in all most-efficient RLS solutions, thus illustrating an interesting and important tradeoff between the growth rate of numerical errors and computational requirements for all fixed-order algorithms.
Abstract: New fixed-order fast transversal filter (FTF) algorithms are introduced for several common windowed recursive-least-squares (RLS) adaptive-filtering criteria. O(N) operations per data point, where N is the filter order, are required by the new algorithms. These algorithms are characterized by two different time-variant scaling techniques that are applied to the internal quantities, leading to normalized and over-normalized FTF algorithms. It is this scaling that distinguishes the new algorithms from the multitude of fast-RLS-Kalman or fast-RLS-Kalman-type algorithms that have appeared in the literature for these same windowed RLS criteria, and which use no normalization or scaling of the internal algorithmic quantities. The overnormalized fast transversal filters have the lowest possible computational requirements for any of the considered windows. The normalized FTF algorithms are then introduced, at a modest increase in computational requirements, to significantly mitigate the numerical deficiencies inherent in all most-efficient RLS solutions, thus illustrating an interesting and important tradeoff between the growth rate of numerical errors and computational requirements for all fixed-order algorithms. Performance of the algorithms, as well as some illustrative tracking comparisons for the various windows, is verified via simulation.