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Signal Processing, IEEE Transactions on

Issue 9 • Date Sep 1992

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Displaying Results 1 - 25 of 32
  • A fast 4×4 DCT algorithm for the recursive 2-D DCT

    Page(s): 2166 - 2173
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (460 KB)  

    The authors present an efficient algorithm for the computation of the 4×4 discrete cosine transform (DCT). The algorithm is based on the decomposition of the 4×4 DCT into four 4-point 1-D DCTs. Thus, only 1-D transformations and some additions are required. It is shown that the proposed algorithm requires only 16 multiplications, which is half the number needed for the conventional row-column method. Since the 2m×2m DCT can be computed using the 4×4 DCT recursively for any m, the proposed algorithm leads to a fast algorithm for the computation of the 2-D DCT View full abstract»

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  • Glottal impedance based on a finite element analysis of two-dimensional unsteady viscous flow in a static glottis

    Page(s): 2125 - 2135
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (944 KB)  

    Unsteady viscous flows in various static models of the glottis are numerically simulated using a finite-element method, and parameters of the electrically equivalent impedances in the models are determined. Different shapes of the static models, which are obtained by varying the angle and diameter of the glottis, produce flow patterns quite different from each other. Really complicated flow patterns have been obtained with the help of appropriate preprocessing/postprocessing software. The equivalent glottal impedance parameters are evaluated. The equivalent resistance values are compared with those derived by previously proposed formulas, and the equivalent inductance values are compared with the analytic solution derived from the Navier-Stokes equations. The present results closely approximate real flow measurements already reported, thus indicating that the numerical method approximates the real phenomena and is therefore useful for the analysis of vocal sources View full abstract»

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  • Fast algorithms for the discrete cosine transform

    Page(s): 2174 - 2193
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1124 KB)  

    Several fast algorithms for computing discrete cosine transforms (DCTs) and their inverses on multidimensional inputs of sizes which are powers of 2 are introduced. Because the 1-D 8-point DCT and the 2-D 8×8-point DCT are so widely used, they are discussed in detail. Algorithms for computing scaled DCTs and their inverses are also presented. These have applications in compression of continuous tone image data, where the DCT is generally followed by scaling and quantization View full abstract»

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  • On implementing the arithmetic Fourier transform

    Page(s): 2233 - 2242
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (656 KB)  

    The arithmetic Fourier transform (AFT), a method for computing the Fourier coefficients of a complex-valued periodic function, is based on a formula which has the advantage of eliminating many of the multiplications usually associated with computing discrete Fourier coefficients, but has the disadvantage of requiring samples of the signal at nonuniformly spaced time values. A method for computing the Fourier coefficients which allows uniform sampling at arbitrarily chosen sampling rates is developed. The technique still requires few multiplications, albeit at the expense of a limited amount of linear interpolation of the sample values. Efficient hardware implementations of this algorithm are presented View full abstract»

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  • Hidden Markov models with first-order equalization for noisy speech recognition

    Page(s): 2136 - 2143
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    A particularly effective distortion measure that takes into account the norm shrinkage bias in the noisy cepstrum is considered. A first-order equalization mechanism, specifically aiming at avoiding the norm shrinkage problem, is incorporated in a hidden Markov model (HMM) framework to model the speech cepstral sequence. Such a modeling technique requires special care, as the formulation inevitably involves parameter estimation from a set of data with singular dispersion. Solutions to this HMM stochastic modeling problem are provided, and algorithms for estimating the necessary model parameters are given. It is experimentally shown that incorporation of the first-order mean equalization model makes the HMM-based speech recognizer robust to noise. With respect to a conventional HMM recognizer, this leads to an improvement in recognition performance which is equivalent to a gain of about 15-20 dB in signal-to-noise ratio View full abstract»

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  • On the reduction in multiplicative complexity achieved by the polynomial residue number system

    Page(s): 2318 - 2320
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    The polynomial residue number system is known to reduce the complexity of polynomial multiplication from O(N2 ) to O(N). A new interpretation of this complexity reduction is given in the context of associative algebras over a finite field. The new point of view provides a clearer understanding of the Chinese remainder theorem View full abstract»

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  • A comment on the finite memory of stochastic processes

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    It is shown that a proposed concept of finite memory for a zero-mean strictly stationary stochastic process results in a stochastic process of random variables each of which is almost surely equal to zero View full abstract»

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  • An algorithm for computing the inverse Z transform

    Page(s): 2194 - 2198
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    The authors determine an infinite impulse response of a causal system via a sampling algorithm applied to the transform on the unit circle View full abstract»

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  • An extrapolation for general analytic signals

    Page(s): 2243 - 2249
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    An extrapolation scheme for general analytic signals is presented, which extends a result in bandlimited signal extrapolations suggested by J.L.C. Sanz and T.S. Huang (ibid., vol.ASSP-31, no.6, Dec. 1983). Some properties of this scheme are discussed View full abstract»

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  • Block 2-D interpolation, efficient matrix factorization and application to signal processing

    Page(s): 2321 - 2323
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    A block 2-D decomposition and a new block LU matrix factorization based on a Newton approach are presented for solving quickly and efficiently polynomial or exponential 2-D interpolation problems. The sample grids under consideration are described by the product representation {x0, x1, . . ., xn} x{y0, y 1, . . ., ym}, where the x grid and the y-grid are not necessarily uniformly spaced. The attractive features of the method are the inherent efficient parallelism, the reduced computational requirements needed for the LU decomposition, and the capability of implementation of 1-D fast and accurate algorithms. The proposed method can be used for modeling 2-D discrete signals, designing 2-D FIR filters, 2-D Fourier matrix factorization, 2-D DFT, etc View full abstract»

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  • Two-dimensional digital filters without overflow oscillations and instability due to finite word length

    Page(s): 2311 - 2317
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (464 KB)  

    New criteria for the absence of finite word-length effects, such as overflow oscillations and instability, in two-dimensional digital filters are presented. The criteria are formulated using the state-space representations and are based on results concerning the 2D Lyapunov equation. Several examples illustrate the theoretical results View full abstract»

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  • A new adaptive algorithm to reduce weight fluctuations caused by high variance data

    Page(s): 2324 - 2327
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (296 KB)  

    A nongradient iterative algorithm that has reduced adaptive filter weight fluctuations caused by high variance input data is presented. The algorithm adapts a single weight at each time step and has approximately the same computational requirements as the LMS algorithm View full abstract»

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  • Some representation properties of stack filters

    Page(s): 2261 - 2266
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (468 KB)  

    Stack filters, a class of nonlinear filters which are based on positive Boolean functions as the window operators, are considered. The representations of these window operations are presented via the structures of on-set and off-set of the positive Boolean functions, which can be expressed as a Boolean expression containing no complements of the input variables. A fast algorithm for finding the representation of stack filters is designed. This algorithm can be easily extended to find the representation of morphological filters mentioned by P. Maragos (1989) View full abstract»

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  • A control theory approach to the stability and transient analysis of the filtered-x LMS adaptive notch filter

    Page(s): 2341 - 2346
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (436 KB)  

    A method is presented for analyzing the stability and transient response of the filtered-x LMS adaptive notch filter by formulating the problem in the complex weight domain and applying standard control theory. Examples are given for pure delay and second-order low-pass cancellation path transfer functions. The method is also extended to the multichannel case, where the eigenvalues of the equivalent open-loop transfer function matrix characterize the behavior View full abstract»

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  • On Kharitonov-type results for complex-coefficient interval Schur polynomials

    Page(s): 2304 - 2310
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (492 KB)  

    A Kharitonov-type result for the stability analysis of real Schur polynomials that have been transformed by a new transformation technique has been proposed, and the necessary and sufficient conditions for the stability of the transformed polynomials were developed by P.P. Vaidyanathan (see IEEE Trans. Acoust. Speech Signal Process, vol.38, no.2, p.277-85, 1990). These results are generalized to the case of the complex coefficient, and the stability of the whole transformed family of interval polynomials is proved. The sufficiency conditions of this test for the stability of the original interval polynomial family is commented on, and checking the stability of the required polynomials for low-order cases is addressed. Some illustrative examples are given. The results may be found useful to testing the interval stability of two-dimensional digital filters View full abstract»

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  • Adaptive algorithms with nonlinear data and error functions

    Page(s): 2199 - 2206
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (700 KB)  

    The tools of nonlinear system theory are used to examine several common nonlinear variants of the LMS algorithm and derive a persistence of excitation criterion for local exponential stability. The condition is tight when the inputs are periodic, and a generic counterexample is demonstrated which gives (local) instability for a large class of such nonlinear versions of LMS, specifically, those which utilize a nonlinear data function. The presence of a nonlinear error function is found to be relatively benign in that it does not affect the stability of the error system. Rather, it defines the cost function the algorithm tends to minimize. Specific examples include the dead zone modification, the cubed data nonlinearity, the cubed error nonlinearity, the signed regressor algorithm, and a single-layer version of the backpropagation algorithm View full abstract»

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  • Statistic-based MAP image-reconstruction from Poisson data using Gibbs priors

    Page(s): 2290 - 2303
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1604 KB)  

    A statistical method for selecting the Gibbs parameter in MAP image restoration from Poisson data using Gibbs priors is presented. The Gibbs parameter determines the degree to which the prior influences the restoration. The presented method yields a MAP restored image, minimally influenced by the prior, for which a statistic falls within an appropriate confidence interval. The method assumes that a close approximation to the blurring function is known. A simple iterative feedback algorithm is presented to statistically select the parameter as the MAP image restoration is being performed. This algorithm is heuristically based on a model reference control formulation, but it requires only a minimal number of iterations for the parameter to settle to its statistically specified value. The performance of the statistical method for selecting the prior parameter and that of the iterative feedback algorithm are demonstrated using both 2-D and 3-D images View full abstract»

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  • A prime factor fast W transform algorithm

    Page(s): 2361 - 2368
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (568 KB)  

    A method for converting any nesting DFT algorithm to the type-I discrete W transform (DWT-I) is introduced. A nesting algorithm that differs from either the Windograd Fourier transform algorithm (WFTA) or the prime factor FFT algorithm (PFA) is presented. New small- N DETs, which are suitable for this nesting algorithm, are developed based on using sparse matrix decomposition. The proposed algorithm is more efficient that either WFTA or PFA for large N, and it is more flexible for the choice of transform length, because 32 points are used. For 2D processing, the proposed algorithm is more efficient than the polynomial transform View full abstract»

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  • On the cascade realization of 2-D FIR filters designed by McClellan transformation

    Page(s): 2338 - 2340
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    Multidimensional finite impulse response (FIR) filters designed by the McClellan transform can be implemented efficiently by the direct transformed structure, transpose direct transformed structure, cascade structure, Chebyshev structure, and reversed Chebyshev structure. Peak scaling and section reconfiguration are provided here to modify the cascade structure realization. The modifications result in a reduction in the output roundoff noise power and the number of operations required View full abstract»

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  • On the design of FIR digital differentiators which are maximally linear at the frequency π/p, p ∈ {positive integers}

    Page(s): 2334 - 2338
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (348 KB)  

    Digital differentiators (DDs) which are maximally linear at the spot frequency ω=π/p, p ∈ {positive integers} are proposed for operation over a narrow band of frequencies. The suggested DDs, besides giving zero phase error over the entire band of frequencies (-π⩽ω⩽π), can achieve very high accuracy in the magnitude response, over a given frequency range, with attractively low order of structure. For example, for p=3, magnitude accuracy better than 99.999% can be achieved over the passband 0.26π⩽ω⩽0.41π with an order of structure of 21. Mathematical formulas for the weighting coefficients required in the design have also been given View full abstract»

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  • A new unwindowed lattice filter for RLS estimation

    Page(s): 2158 - 2165
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    Adaptive lattice algorithms are derived for the solution of unwindowed least squares estimation problems for AR and FIR models. The basic approach is to embed the unwindowed problem in a larger prewindowed problem and then eliminate superfluous terms in the lattice. Initializations are given to allow the lattice to use no initial parameter estimates or to include initial parameter estimates with desired weightings in the quadratic criterion for parameter estimation. A numerical example is given View full abstract»

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  • Estimating two-dimensional frequencies by matrix enhancement and matrix pencil

    Page(s): 2267 - 2280
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (900 KB)  

    A new method, called the matrix enhancement and matrix pencil (MEMP) method, is presented for estimating two-dimensional (2-D) frequencies. In the MEMP method, an enhanced matrix is constructed from the data samples, and then the matrix pencil approach is used to extract out the 2-D sinusoids from the principal eigenvectors of the enhanced matrix. The MEMP method yields the estimates of the 2-D frequencies efficiently, without solving the roots of a 2-D polynomial or searching in a 2-D space. It is shown that the MEMP method can be faster than a 2-D FFT method if the number of the 2-D sinusoids is much smaller than the data set. Simulation results are provided to show that the accuracy of the MEMP method can be very close to the Cramer-Rao lower bound View full abstract»

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  • An analysis of ESPRIT under random sensor uncertainties

    Page(s): 2353 - 2358
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (456 KB)  

    A general expression for the mean-square error (MSE) of the ESPRIT direction-of-arrival (DOA) estimation of narrowband far-field sources under random sensor perturbations is derived. Explicit solutions for the case of an arbitrary ESPRIT array geometry with one and two sources are given. Solutions for the case of a uniform linear array and arbitrary number of sources are found provided that the number of sensors is large. For this case, it is found that the MSE of ESPRIT with maximum aperture (i.e., maximum-overlapping subarrays) is lower than that of ESPRIT with nonoverlapping subarrays. A comparison with MUSIC suggests that the MSE for MUSIC is lower than that for ESPRIT. Furthermore, for the cases studied, it is shown that the MSE of ESPRIT depends only on sensor phase errors while that of MUSIC is dependent on both sensor grain and phase errors View full abstract»

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  • Wavelets and filter banks: theory and design

    Page(s): 2207 - 2232
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1948 KB)  

    The wavelet transform is compared with the more classical short-time Fourier transform approach to signal analysis. Then the relations between wavelets, filter banks, and multiresolution signal processing are explored. A brief review is given of perfect reconstruction filter banks, which can be used both for computing the discrete wavelet transform, and for deriving continuous wavelet bases, provided that the filters meet a constraint known as regularity. Given a low-pass filter, necessary and sufficient conditions for the existence of a complementary high-pass filter that will permit perfect reconstruction are derived. The perfect reconstruction condition is posed as a Bezout identity, and it is shown how it is possible to find all higher-degree complementary filters based on an analogy with the theory of Diophantine equations. An alternative approach based on the theory of continued fractions is also given. These results are used to design highly regular filter banks, which generate biorthogonal continuous wavelet bases with symmetries View full abstract»

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  • An optimal design for a homomorphic deconvolution system

    Page(s): 2250 - 2260
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    A precise expression for the deconvolved signal is derived by introducing the transmission factor, which is defined as the factor of the ratio of the deconvolved signal to the desired signal. An optimal deconvolution system is then defined as the system which minimizes the energy of the maximum distortion factor (=1-transmission factor). It is shown by numerical examples that the proposed system gives superior performance compared to the conventional 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