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Signal Processing, IEEE Transactions on

Issue 10 • Date Oct 1993

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Displaying Results 1 - 12 of 12
  • Detection in incompletely characterized colored non-Gaussian noise via parametric modeling

    Page(s): 3066 - 3070
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    The problem of detecting a weak signal known except for amplitude in incompletely characterized colored non-Gaussian noise is addressed. The problem is formulated as a test of composite hypotheses, using parameteric models for the statistical behavior of the noise. A generalized likelihood ratio test (GLRT) is employed. It is shown that for a symmetric noise probability density function the detection performance is asymptotically equivalent to that obtained for a similar detector designed with a priori knowledge of the noise parameters. Non-Gaussian distributions are found to be more favorable for the purpose of detection than the Gaussian distribution. The computational burden of the GLRT may be partially reduced by employing a Rao efficient score test which shares all the nice asymptotic properties of the GLRT for small signal amplitudes. Computer simulations of the performance of the Rao detector support the theoretical results View full abstract»

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  • Energy separation in signal modulations with application to speech analysis

    Page(s): 3024 - 3051
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    An efficient solution to the fundamental problem of estimating the time-varying amplitude envelope and instantaneous frequency of a real-valued signal that has both an AM and FM structure is provided. Nonlinear combinations of instantaneous signal outputs from the energy operator are used to separate its output energy product into its AM and FM components. The theoretical analysis is done first for continuous-time signals. Then several efficient algorithms are developed and compared for estimating the amplitude envelope and instantaneous frequency of discrete-time AM-FM signals. These energy separation algorithms are used to search for modulations in speech resonances, which are modeled using AM-FM signals to account for time-varying amplitude envelopes and instantaneous frequencies. The experimental results provide evidence that bandpass-filtered speech signals around speech formants contain amplitude and frequency modulations within a pitch period View full abstract»

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  • Frequency tracking using hidden Markov models with amplitude and phase information

    Page(s): 2965 - 2976
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    It is demonstrated how the hidden Markov model (HMM) frequency tracker can be extended by the addition of amplitude and phase information. The HMM tracker as originally formulated uses a gate of spectral bins from fast Fourier transform (FFT) processing, and associates each cell with a state of the hidden Markov chain. A measurement sequence based on the output of a simple threshold detector forms the input to the HMM tracker. Two extensions to the original tracker are proposed. The first, the HMM/A tracker, incorporates the FFT amplitudes in the cells of the measurement sequence. The second, the HMM/AP tracker, does not use a measurement sequence, but uses instead the FFT amplitude and phase values in all cells within the gate. A comparison of the results obtained in using the three HMM-based trackers with simulated data reveals that the extended trackers outperform the original. An analysis of the effect of parameter mismatch for the three trackers is presented. Their use as detectors is also discussed View full abstract»

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  • Three different criteria for the design of two-dimensional zero phase FIR digital filters

    Page(s): 3070 - 3074
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    An error criterion for the design of FIR filters is proposed. Filters with relatively many free filter coefficients are designed using the Chebyshev, the weighted-least-squares (WLS), and a new partitioned minimax error criterion, and the performance of the filters is compared. A general and fast technique for the WLS design is also presented View full abstract»

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  • Schur type algorithms for spatial LS estimation with highly pipelined architectures

    Page(s): 3010 - 3023
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    A family of Schur-type spatial least-squares algorithms is presented for solving the spatial LS estimation problem, in which the correlation matrix is neither Toeplitz nor near-Toeplitz, by order recursion. Normalized spatial Levinson- and Schur-type algorithms are also derived. Highly pipelined architectures are designed to realize these recursions. The reflection coefficients are first computed using the spatial Schur type recursions. Then, the forward and backward filter parameters are calculated by the spatial Levinson-type recursions. A pyramid systolic array is demonstrated to calculate not only the filter parameters but also the LDU decomposition of the inverse cross-correlation matrix at every clock phase. This pyramid array can be mapped onto a two-dimensional systolic array which has a simpler structure. A square systolic array is developed to implement the Levinson- and Schur-type temporal recursive LS (RLS) algorithms. A highly concurrent architecture which exploits the parallelism of the spatial Schur-type recursions is illustrated to perform the LDU decomposition of the cross-correlation matrix View full abstract»

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  • Statistical analysis of morphological openings

    Page(s): 3052 - 3056
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    Statistical analysis of morphological openings is carried out to study noise-suppression and edge-preserving properties of binary and gray-scale structuring elements. Based on the fact that basis functions are a general representation of any morphological mapping that is translation-invariant and increasing, it is shown that a statistical analysis using this representation is feasible and more general than the threshold decomposition approach View full abstract»

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  • Multiple Fourier series procedures for extraction of nonlinear regressions from noisy data

    Page(s): 3062 - 3065
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    Three nonparametric procedures for the extraction of nonlinear regressions from noisy data are proposed. The procedures are based on the Dirichlet, Fejer, and de la Vallee Poussin multiple kernels. Convergence properties are investigated. In particular, it is shown that the algorithms are convergent in the mean-integrated-square-error sense. The appropriate theorem establishes a relation between the order of kernels and the number of observations. Special attention is focused on the two-dimensional case. It is proved that the procedures attain the optimal rate of convergence, which cannot be exceeded by any other nonparametric algorithm View full abstract»

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  • Fast cosine transform of Toeplitz matrices, algorithm and applications

    Page(s): 3057 - 3061
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    A fast algorithm for the discrete cosine transform (DCT) of a Toeplitz matrix of order N is derived. Only O(N log N)+O(M) time is needed for the computation of M elements. The storage requirement is O(N). The method carries over to other transforms (DFT, DST) and to Hankel or circulant matrices. Some applications of the algorithm are discussed View full abstract»

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  • ARMA model order estimation based on the eigenvalues of the covariance matrix

    Page(s): 3003 - 3009
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    An approach to model order determination based on the minimum description length (MDL) criterion is proposed and shown to depend on the minimum eigenvalues of a covariance matrix derived from the observed data. A selection procedure for estimating the model order by means of the MDL method is proposed. Examples are given to illustrate the significantly improved accuracy of the technique View full abstract»

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  • Finite-precision analysis of a covariance algorithm for least squares FIR filtering and AR modeling

    Page(s): 2990 - 3002
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    A numerically stable, fast, order-recursive algorithm for solving the covariance problem in signal modeling is described. The propagation of finite arithmetic errors as well as data acquisition errors is studied in detail. First, linearization of the main algorithmic recursions is carried out. Then, a suitable transformation converts the resulting state equations of the accumulated errors into their residual form. Subsequently, bounds for the residuals are computed. The derivation of these bounds depends heavily on the Levinson type structure of the algorithm and the low displacement rank of the problem. The main result is that the algorithm is weakly numerically stable. The proposed order-recursive algorithm is subsequently utilized as a block adaptive method. Its performance is also demonstrated by long run simulations View full abstract»

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  • Maximum likelihood estimation of the parameters of discrete fractionally differenced Gaussian noise process

    Page(s): 2977 - 2989
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    A maximum-likelihood estimation procedure is constructed for estimating the parameters of discrete fractionally differenced Gaussian noise from an observation set of finite size N. The procedure does not involve the computation of any matrix inverse or determinant. It requires N2/2+O(N) operations. The expected value of the loglikelihood function for estimating the parameter d of fractionally differenced Gaussian noise (which corresponds to a parameter of the equivalent continuous-time fractional Brownian motion related to its fractal dimension) is shown to have a unique maximum that occurs at the true value of d. A Cramer-Rao bound on the variance of any unbiased estimate of d obtained from a finite-sized observation set is derived. It is shown experimentally that the maximum-likelihood estimate of d is unbiased and efficient when finite-size data sets are used in the estimation procedure. The proposed procedure is extended to deal with noisy observations of discrete fractionally differenced Gaussian noise View full abstract»

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  • Regularized image reconstruction using SVD and a neural network method for matrix inversion

    Page(s): 3074 - 3077
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    Two methods of matrix inversion are compared for use in an image reconstruction algorithm. The first is based on energy minimization using a Hopfield neural network. This is compared with the inverse obtained using singular value decomposition (SVD). It is shown for a practical example that the neural network provides a more useful and robust matrix inverse 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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Meet Our Editors

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