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Signal Processing, IEEE Transactions on

Issue 8 • Date Aug 1992

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Displaying Results 1 - 25 of 32
  • Multiscale autoregressive processes. II. Lattice structures for whitening and modeling

    Page(s): 1935 - 1954
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    For pt.I see ibid., vol.40, no.8, p.1915-34 (1992). Lattice structures for the whitening and modeling of isotropic processes on trees are developed, and a result relating the stability properties of these models to the reflection coefficient sequence introduced in pt.I is presented. This framework allows one to obtain a detailed analysis of the Wold decomposition of processes on trees. One interesting aspect of this is that there is a significantly larger class of singular processes on dyadic trees than on the integers View full abstract»

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  • Estimation of the directions of arrival of signals in unknown correlated noise. I. The MAP approach and its implementation

    Page(s): 2007 - 2017
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    The authors propose a method of direction of arrival (DOA) estimation of signals in the presence of noise whose covariance matrix is unknown and arbitrary, other than being positive definite. They examine the projection of the data onto the noise subspace. The conditional probability density function (PDF) of the projected data given the signal parameters and the unknown projected noise covariance matrix is first formed. The a posteriori PDF of the signal parameters alone is then obtained by assigning a noninformative a priori PDF to the unknown noise covariance matrix and integrating out this quantity. A simple criterion for the maximum a posteriori (MAP) estimate of the DOAs of the signals is established. Some properties of this criterion are discussed, and an efficient numerical algorithm for the implementation of this criterion is developed. The advantage of this method is that the noise covariance matrix does not have to be known, nor must it be estimated View full abstract»

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  • Transform domain filtering based on pipelining structure

    Page(s): 2061 - 2064
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    The concept of transform domain filtering (TDF) is defined, and a pipelining structure is proposed as a means to implement it. TDF refers to filtering applied directly to transform domain data. The proposed structure consists of product blocks and an array of M adders, where M is the transform block length. The TDF output data can be obtained by summing the outputs of each product block. The product block in the proposed structure performs the product operation between an M×M matrix and an M-vector, which can be effectively implemented by using a distributed arithmetic structure of a systolic array structure. The proposed structure is simple, with localized interconnections, and is therefore suitable for VLSI implementations View full abstract»

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  • Can one evaluate the Gabor expansion using Gabor's iterative algorithm?

    Page(s): 1852 - 1861
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    D. Gabor's original (1946) approach for calculation of expansion coefficients was examined and it was found that convergence of the suggested algorithm is conditional on the window function chosen. The method of analysis enables a process of synthesis, whereby eligible windows can be defined, ensuring convergence of the algorithm for every represented signal. For windows having a finite support of width D , the coefficients calculated according to the algorithm are obtained after a single iteration. It is proved that in the special case of a Gaussian window the algorithm converges only for specific signals. On the basis of the conclusions drawn, conditions are formulated which ensure convergence of the Gabor algorithm, permitting examination of alternative windows View full abstract»

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  • Robust maximum likelihood bearing estimation in contaminated Gaussian noise

    Page(s): 1983 - 1986
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    A robust maximum likelihood (ML) direction-of-arrival (DOA) estimation method that is insensitive to outliers and distributional uncertainties in Gaussian noise is presented. The algorithm has been shown to perform much better than the Gaussian ML algorithm when the underlying noise distribution deviates even slightly from Gaussian while still performing almost as well in pure Gaussian noise. As with the Gaussian ML estimation, it is still capable of handling correlated signals as well as single snapshot cases. Performance of the algorithm is analyzed using the unique resolution test procedure which determines whether a DOA estimation algorithm, at a given confidence level, can resolve two dominant sources with very close DOAs View full abstract»

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  • Estimating a covariance matrix from incomplete realizations of a random vector

    Page(s): 2097 - 2100
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    It is desired to estimate the mean and the covariance matrix of a Gaussian random vector from a set of independent realizations, with the complication that not every component of each realization of the random vector is observed. Subject to some restrictions, the authors obtained an exact, noniterative solution for the maximum likelihood (ML) estimates of the mean and the covariance matrix. The ML estimate of the covariance matrix that is obtained from the set of incomplete realizations is guaranteed to be positive definite, in contrast to ad hoc approaches based on averaging products of components from the same realization. The key to obtaining the ML estimates is a tractable expression for the likelihood function in terms of the Cholesky factors of the inverse covariance matrix. With this formulation, the ML estimates are found by fitting regression operators to appropriate subsets of the data. The Cholesky formulation also leads to a simple calculation by Cramer-Rao bounds View full abstract»

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  • A bit-level systolic array for median filter

    Page(s): 2079 - 2083
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    A bit-level systolic array for median filters based on the majority of the bit strings of input samples is presented. The majority function can be implemented by a 1-b odd/even transposition network, which is regular and can be designed easily. If each input sample is represented by r bits, the systolic array contains r processor elements and requires time complexity O(N+ n+r-1) for a stream of N samples with window size n in a one-dimensional median filter View full abstract»

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  • Adaptive filtering in subbands with critical sampling: analysis, experiments, and application to acoustic echo cancellation

    Page(s): 1862 - 1875
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    An exact analysis of the critically subsampled two-band modelization scheme is given, and it is demonstrated that adaptive cross-filters between the subbands are necessary for modelization with small output errors. It is shown that perfect reconstruction filter banks can yield exact modelization. These results are extended to the critically subsampled multiband schemes, and important computational savings are seen to be achieved by using good quality filter banks. The problem of adaptive identification in critically subsampled subbands is considered and an appropriate adaptation algorithm is derived. The authors give a detailed analysis of the computational complexity of all the discussed schemes, and experimentally verify the theoretical results that are obtained. The adaptive behavior of the subband schemes that were tested is discussed View full abstract»

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  • Negacyclic convolution using polynomial transforms on hypercubes

    Page(s): 1845 - 1851
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    A polynomial-transform-based algorithm for calculating products modulo Zn+1 on a hypercube is presented. All interprocessor communication in this algorithm occurs over a Hamming distance of one; that is processors communicate only with their immediate neighbors. This algorithm has been implemented on a Connection Machine, and the performance results are discussed. Current figures show a time of 358 ms for negacyclic convolution of 1 K 16 bit samples, up to about 8 s for a 64 K data set. The authors discuss the use of this algorithm in the calculation of convolution, compare communication costs with the FFT, and discuss directions for future work View full abstract»

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  • A unified approach to the STFT, TFDs, and instantaneous frequency

    Page(s): 1971 - 1982
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    Cohen's class of time-frequency representations (TFRs) is reformulated into a discrete-time, discrete-frequency, computer-implementable form. It is shown how, in this form, many of the properties of the continuous-time, continuous-frequency formulation are either lost or altered. Intuitions applicable in the continuous-time case do not necessarily carry over to the discrete-time case examined. The properties of the discrete variable formulation examined are the presence and form of cross-terms, instantaneous frequency estimation, and relationships between Cohen's class of TFRs. A parameterized class of distributions which is a blending between the short-time Fourier transform (STFT) and the Wigner-Ville distribution. The two main conclusions are that all TFRs of Cohen's class implementable in the given form (which includes all commonly used TFRs) possess cross-terms and that instantaneous frequency estimation using periodic moments of these TFRs is purposeless, since simpler methods obtain the same result View full abstract»

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  • Wigner-space synthesis of discrete-time periodic signals

    Page(s): 1997 - 2006
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    A procedure that facilitates at least-squares synthesis of periodic, discrete-time signals from Wigner quasi-distributions is proposed. The scheme is based on expanding the desired time sequence on a generally nonorthogonal, Gabor-type basis whose associated biorthogonal function presumably exists. The specific basis selection may crucially affect the efficiency and quality of the ensuing synthesis procedure. The cited basis type constitutes a considerable generalization over the standardly used orthogonal variety, thus creating previously unavailable degrees of freedom. Of primary significance is the acquired capability of generating time-frequency basis functions that are well localized. Localization is a highly desirable property that can advantageously serve in various applications. It is shown and numerically demonstrated that benefits of localization as well as the fact that achieving effective time-frequency basis localization renders a certain degree of oversampling unavoidable View full abstract»

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  • New square wave transform for digital signal processing

    Page(s): 2095 - 2097
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    A novel transform for spectral decomposition that uses regular square waves as the basis functions is presented. The digital transform requires order N operations. The transform possesses unusually symmetry properties which may prove useful in many applications. In particular, it can act as a generalized frequency filter that only depends on the periodicity of the data View full abstract»

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  • METEOR: a constraint-based FIR filter design program

    Page(s): 1901 - 1909
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    It is proposed to specify a filter only in terms of upper and lower limits on the response, find the shortest filter length which allows these constraints to be met, and then find a filter of that order which is farthest from the upper and lower constraint boundaries in a minimax sense. The simplex algorithm for linear programming is used to find a best linear-phase FIR filter of minimum length, as well as to find the minimum feasible length itself. The simplex algorithm, while much slower than exchange algorithms, also allows the incorporation of more general kinds of constraints, such as concavity constraints (which can be used to achieve very flat magnitude characteristics). Examples are given to illustrate how the proposed and common approaches differ, and how the proposed approach can be used to design filters with flat passbands, filters which meet point constraints, minimum phase filters, and bandpass filters with controlled transition band behavior View full abstract»

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  • Estimation of the directions of arrival of signals in unknown correlated noise. II. Asymptotic behavior and performance of the MAP approach

    Page(s): 2018 - 2028
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    For pt.I see ibid., vol.40, no.8, p.2007-17 (1992). The asymptotic behavior and the statistical performance of the maximum a posteriori (MAP) estimate of the directions of arrival (DOAs) of signals applicable in an environment where the sensor noise is unknown and correlated. Computer simulations were performed to confirm the correctness of the performance analysis, and a comparison of the performance of the MAP estimate with other methods is also presented View full abstract»

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  • Fast iterative algorithm for real-time array processing

    Page(s): 2087 - 2089
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    An online iterative conjugate gradient algorithm for array processing is presented. The basic idea is to recast the array processing problem into a form so that the iterative method can be applied to compute the array weights vector recursively. To speed up the rate of convergence of the iterative process, the conjugate gradient method is used. Under moderate signal-to-noise ratios the algorithm converges to the minimum Euclidean norm least-squares solution in p iterations for p number of signals. It does not require eigendecomposition of the covariance matrix and prior information regarding the number of signals. It is capable of handling fully coherent sources and is effective for a small number of snapshots. Numerical examples are presented to illustrate the performance achievable View full abstract»

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  • New fast recursive algorithms for the computation of discrete cosine and sine transforms

    Page(s): 2083 - 2086
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    Fast recursive algorithms for the computation of the discrete cosine and sine transforms are developed. An N-point discrete cosine transform (DCT) or discrete sine transform (DST) can be computed from two N/2-point DCTs or DSTs. Compared to the existing algorithms the algorithms have less multiplications by two, and add operations are better positioned, giving rise to faster computation and easier VLSI implementation View full abstract»

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  • Online and offline computational reduction techniques using backward filtering in CELP speech coders

    Page(s): 2090 - 2093
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    The authors review the backward filtering algorithm and give a compact proof of its validity using matrix notation. They review the relation between backward filtering and offline perceptual weighting in sparse codebook CELP and show how a combination online/offline parallel weighting algorithm can be used to reduce the search complexity of an overlapped sparse codebook by 30% to 50% View full abstract»

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  • The Nehari shuffle: FIR(q) filter design with guaranteed error bounds

    Page(s): 1876 - 1883
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    An approach to the problem of designing a finite impulse response filter of specified length q which approximates in uniform frequency (L) norm a given desired (possibly infinite impulse response) causal, stable filter transfer function is presented. An algorithm-independent lower bound on the achievable approximation error is derived, and an approximation method that involves the solution of a fixed number of all-pass (Nehari) extension problems (and is therefore called the Nehari shuffle) is presented. Upper and lower bounds on the approximation error are derived for the algorithm. Examples indicate that the method closely approaches the derived global lower bound. The method is compared with the Preuss (complex Remez exchange) algorithm in some examples View full abstract»

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  • A Schur algorithm and linearly connected processor array for Toeplitz-plus-Hankel matrices

    Page(s): 2065 - 2078
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    A Levinson-Durbin type algorithm for solving Toeplitz-plus-Hankel (T+H) linear systems of equations is used to induce a Schur-type algorithm for such systems. A Schur-type algorithm is defined as one which efficiently computes the LDU-decomposition of the matrix. On the other hand, Levinson-Durbin type algorithms are defined as those algorithms which efficiently compute the UDL-decomposition of the inverse of a matrix. It is shown that the Schur algorithm so obtained is amenable to efficient implementation on a linearly connected array of processors in a manner which generalizes the results of S.-Y. Kung and Y.H. Ku (1983) for symmetric Toeplitz matrices. Specifically, if T+H is of order n, then the Schur algorithm runs on O(n ) processors in O(n) time View full abstract»

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  • A reverse formulation of the RISE algorithm

    Page(s): 2105 - 2108
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    The recently developed recursive/iterative self-adjoint eigenspace (RISE) decomposition algorithm recursively computes the complete eigenspace decomposition of successively larger Hermitian matrices. However, some practical applications also require that the decomposition of successively smaller matrices be computed. A modification to the RISE algorithm is presented that makes it possible to run this algorithm backward on successively smaller Hermitian matrices. This important modification increases the number of practical applications of this algorithm View full abstract»

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  • Construction of a Hermitian Toeplitz matrix from an arbitrary set of eigenvalues

    Page(s): 2093 - 2094
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    A solution to the inverse eigenvalue problem for Hermitian Toeplitz matrices is presented. The approach taken is to first construct a real symmetric negacyclic matrix of order 2n and to then relate the negacyclic matrix to a Hermitian Toeplitz matrix of order n with the desired eigenspectrum View full abstract»

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  • Strongly consistent identification algorithms and noise insensitive MSE criteria

    Page(s): 1955 - 1970
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    Windowed cumulant projections of nonGaussian linear processes yield autocorrelation estimators which are immune to additive Gaussian noise of unknown covariance. By establishing strong consistency of these estimators, strongly consistent and noise insensitive recursive algorithms are developed for parameter estimation. These computationally attractive schemes are shown to be optimal with respect to a modified mean-square-error (MSE) criterion which implicitly exploits the high signal-to-noise ratio domain of cumulant statistics. The novel MSE objective function is expressed in terms of the noisy process, but it is shown to be a scalar multiple of the standard MSE criterion as if the latter was computed in the absence of noise. Simulations illustrate the performance of the proposed algorithms and compare them with the conventional algorithms View full abstract»

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  • Multiscale autoregressive processes. I. Schur-Levinson parametrizations

    Page(s): 1915 - 1934
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    In many applications it is of interest to analyze and recognize phenomena occurring at different scales. The recently introduced wavelet transforms provide a time-and-scale decomposition of signals that offers the possibility of such analysis. A corresponding statistical framework to support the development of optimal, multiscale statistical signal processing algorithms is described. The theory of multiscale signal representation leads naturally to models of signals on trees, and this provides the framework for investigation. In particular, the class of isotropic processes on homogeneous trees is described, and a theory of autoregressive models is developed in this context. This leads to generalizations of Schur and Levinson recursions, associated properties of the resulting reflection coefficients, and the initial pieces in a system theory for multiscale modeling View full abstract»

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  • An optimal recovery approach to interpolation

    Page(s): 1987 - 1996
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    A filter class is defined as a ball in an inner product space, and some standard results on inner product spaces are applied to filter classes. The filter design problem is addressed. The theory of optimal recovery is reviewed, and the interpolation problem is examined within an optimal recovery context. It is shown that the interpolation problem can be reduced to studying a hypercircle in an inner product space. The notion of the Chebyshev center of a set is introduced, and it is noted that the solution to the interpolation problem, from the optimal recovery viewpoint, is to find the Chebyshev center of the hypercircle. The interpolation filter is then the operator that transforms the vector of known samples into the center of the hypercircle. Some auxiliary results such as the linearity and time invariance of the interpolation filter are deduced. It is then shown that the estimation of an unknown sample is the same as the problem of approximating the representer of the unknown sample by a linear combination of the representers of the known samples. Hence the interpolation problem is equivalent to minimizing the L2 norm of the error frequency response, from the filter design point of view View full abstract»

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  • A generalized sidelobe canceller with soft constraints

    Page(s): 2112 - 2116
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    An efficient beamforming structure similar to a generalized sidelobe canceller is derived from the soft constrained minimum variance (SCMV) method of B. Van Veen (see ibid., vol.39, no.9, p.1964-72, 1991). The structure greatly reduces the computational load of the SCMV method and provides insight into the nature of SCMV beamforming View full abstract»

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Aims & Scope

IEEE Transactions on Signal Processing covers novel theory, algorithms, performance analyses and applications of techniques for the processing, understanding, learning, retrieval, mining, and extraction of information from signals

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Editor-in-Chief
Zhi-Quan (Tom) Luo
University of Minnesota