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Signal Processing, IEEE Transactions on

Issue 8 • Date Aug 1999

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Displaying Results 1 - 25 of 29
  • Nonsymmetrical contrasts for sources separation

    Page(s): 2241 - 2252
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (344 KB)  

    In this paper, the problem of the blind separation of independent sources is considered. Our approach relies on high-order inverse criteria. After generalizing the definition of classical contrast functions, we exhibit a wide class of generally nonsymmetrical functions that will be called “generalized contrasts” and whose maximization is proved to be a sufficient condition for source separation. We also establish a connection with “cumulant matching,” showing an equivalence between the two approaches. Then, in the case of two sources, a statistical study of the estimated parameter based on one of these new contrasts is presented. Finally, computer simulations illustrate the results and demonstrate all the interest we can find in considering a nonsymmetrical contrast View full abstract»

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  • The evanescent field transform for estimating the parameters of homogeneous random fields with mixed spectral distributions

    Page(s): 2167 - 2180
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (424 KB)  

    Parametric modeling and estimation of complex valued homogeneous random fields with mixed spectral distributions is a fundamental problem in two-dimensional (2-D) signal processing. The parametric model under consideration results from the 2-D Wold-type decomposition of the random field. The same model naturally arises as the physical model in problems of space-time adaptive processing of airborne radar. A computationally efficient algorithm for estimating the parameters of the field components is presented. The algorithm is based on a nonlinear operator that uniquely maps each evanescent component to a single exponential. The exponential's spatial frequency is a function of the spectral support parameters of the evanescent component. Hence, employing this operator, the problem of estimating the spectral support parameters of an evanescent field is replaced by the simpler problem of estimating the spatial frequency of a 2-D exponential. The properties of the operator are analyzed. The algorithm performance is illustrated and investigated using Monte Carlo simulations View full abstract»

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  • Expectation maximization algorithms for MAP estimation of jump Markov linear systems

    Page(s): 2139 - 2156
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (504 KB)  

    In a jump Markov linear system, the state matrix, observation matrix, and the noise covariance matrices evolve according to the realization of a finite state Markov chain. Given a realization of the observation process, the aim is to estimate the state of the Markov chain assuming known model parameters. Computing conditional mean estimates is infeasible as it involves a cost that grows exponentially with the number of observations. We present three expectation maximization (EM) algorithms for state estimation to compute maximum a posteriori (MAP) state sequence estimates [which are also known as Bayesian maximum likelihood state sequence estimates (MLSEs)]. The first EM algorithm yields the MAP estimate for the entire sequence of the finite state Markov chain. The second EM algorithm yields the MAP estimate of the (continuous) state of the jump linear system. The third EM algorithm computes the joint MAP estimate of the finite and continuous states. The three EM algorithms optimally combine a hidden Markov model (HMM) estimator and a Kalman smoother (KS) in three different ways to compute the desired MAP state sequence estimates. Unlike the conditional mean state estimates, which require computational cost exponential in the data length, the proposed iterative schemes are linear in the data length View full abstract»

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  • Equivalence between voltage-processing methods and discrete orthogonal Legendre polynomial (DOLP) approach

    Page(s): 2273 - 2278
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (112 KB)  

    There are three methods for solving the least-squares estimation (LSE) problem. (1) the power method; (2) the voltage-processing method (square-root method); and (3) the discrete orthogonal Legendre polynomial (DOLP) method. The first involves a matrix inversion and is sensitive to computer round-off errors. The second and third do not require a matrix inversion and are not as sensitive to computer round-off errors. It is shown that the voltage-processing LSE methods (Givens, Householder, and Gram-Schmidt) become the discrete orthogonal Legendre polynomial (DOLP) LSE method when the data can be modeled by a polynomial function and the times between measurements are equal. Furthermore, when the data can be modeled by a polynomial function and the time between measurements are equal, the DOLP is the preferred method because it does not require an orthonormal transformation and it does not require the back-substitution method View full abstract»

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  • A two-sensor array blind beamformer for direct sequence spread spectrum communications

    Page(s): 2191 - 2199
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (188 KB)  

    We present an efficient blind beamformer dedicated to the problem of interference mitigation in direct sequence spread spectrum (DSSS) communication systems using a two-sensor array. A closed-form solution for the blind identification of the communication channel is derived by exploiting the temporal properties of the desired signal and the interference. The optimal beamformer is derived from the maximization of the signal-to-interference and noise ratio (SINR) at the output of the receiver in terms of the blindly estimated channel coefficients. Three structures of the DSSS receiver are presented. One structure consists of the blind beamformer followed by the spread spectrum demodulator. The other two structures consist of the spread spectrum demodulator followed by the blind beamformer. The performance of these structures is discussed in terms of the achieved SINR and the computational cost. Simulation results are provided to illustrate the effectiveness of the proposed blind beamformers in interference excision View full abstract»

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  • Transient and tracking performance bounds of the sign-sign algorithm

    Page(s): 2200 - 2210
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (284 KB)  

    The paper provides a rigorous tracking analysis of the sign-sign algorithm when used in the identification of a time-varying plant with a white Gaussian input. The plant parameters vary according to a random walk model. The assumptions allow nonstationarity of the plant input, plant noise, and increments of the plant parameters. Upper bounds are derived for the long-term averages of the mean of the weight misalignment norm, mean absolute error, mean square weight misalignment, and mean square error. These bounds hold for all values of the algorithm step size, all initial filter weight settings, and all degrees of nonstationarity of the plant input, plant noise, and plant parameter increments. Lower bounds of the mean square weight misalignment and mean square error are also derived. The step sizes that minimize the above bounds are derived. A transient analysis of the algorithm is done in the case of a time-invariant plant. A tight lower bound of the convergence time is derived. The above analytical results are supported by computer simulations View full abstract»

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  • The extended Kalman filter as an exponential observer for nonlinear systems

    Page(s): 2324 - 2328
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (132 KB)  

    We analyze the behavior of the extended Kalman filter as a state estimator for nonlinear deterministic systems. Using the direct method of Lyapunov, we prove that under certain conditions, the extended Kalman filter is an exponential observer, i.e., the dynamics of the estimation error is exponentially stable. Furthermore, we discuss a generalization of the Kalman filter with exponential data weighting to nonlinear systems View full abstract»

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  • New filter banks and more regular wavelets

    Page(s): 2220 - 2227
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (292 KB)  

    One of the most interesting features of a wavelet is its Sobolev regularity. In this paper, we construct new wavelets that are more regular than the Daubechies wavelets for a given support width. We tabulate the coefficients of the new filters to make them easily accessible. We show that these filters outperform the Daubechies filters in the L2 approximation of the ideal filter. An application for speech analysis, synthesis, and compression is provided View full abstract»

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  • A general class of nonlinear normalized adaptive filtering algorithms

    Page(s): 2262 - 2272
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (284 KB)  

    The normalized least mean square (NLMS) algorithm is an important variant of the classical LMS algorithm for adaptive linear filtering. It possesses many advantages over the LMS algorithm, including having a faster convergence and providing for an automatic time-varying choice of the LMS stepsize parameter that affects the stability, steady-state mean square error (MSE), and convergence speed of the algorithm. An auxiliary fixed step-size that is often introduced in the NLMS algorithm has the advantage that its stability region (step-size range for algorithm stability) is independent of the signal statistics. In this paper, we generalize the NLMS algorithm by deriving a class of nonlinear normalized LMS-type (NLMS-type) algorithms that are applicable to a wide variety of nonlinear filter structures. We obtain a general nonlinear NLMS-type algorithm by choosing an optimal time-varying step-size that minimizes the next-step MSE at each iteration of the general nonlinear LMS-type algorithm. As in the linear case, we introduce a dimensionless auxiliary step-size whose stability range is independent of the signal statistics. The stability region could therefore be determined empirically for any given nonlinear filter type. We present computer simulations of these algorithms for two specific nonlinear filter structures: Volterra filters and the previously proposed class of Myriad filters. These simulations indicate that the NLMS-type algorithms, in general, converge faster than their LMS-type counterparts View full abstract»

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  • Estimation of fractional Brownian motion embedded in a noisy environment using nonorthogonal wavelets

    Page(s): 2211 - 2219
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (232 KB)  

    We show that nonorthogonal wavelets can characterize the fractional Brownian motion (fBm) that is in white noise. We demonstrate the point that discriminating the parameter of fBm from that of noise is equivalent to discriminating the composite singularity formed by superimposing a peak singularity on a Dirac singularity. We characterize the composite singularity by formalizing this problem as a nonlinear optimization problem. This yields our parameter estimation algorithm. For fractal signal estimation, Wiener filtering is explicitly formulated as a function of the signal and noise parameters and the wavelets. We show that the estimated signal is a 1/f process. Comparative studies through numerical simulations of our methods with those of Wornell and Oppenheim (1992) are presented View full abstract»

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  • Improving the performance of Unitary ESPRIT via pseudo-noise resampling

    Page(s): 2305 - 2308
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (144 KB)  

    A new pseudo-noise resampling technique is proposed to mitigate the effect of outliers in Unitary ESPRIT. This algorithm improves the performance of Unitary ESPRIT in unreliable situations, where the so-called reliability test has a failure. For this purpose, we exploit a pseudo-noise resampling of a failed Unitary ESPRIT estimator with a censored selection of “successful” resamplings recovering the nonfailed outputs of the reliability test View full abstract»

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  • Density function approximation using reduced sufficient statistics for joint estimation of linear and nonlinear parameters

    Page(s): 2089 - 2099
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (320 KB)  

    A new algorithm is presented for the joint estimation of linear and nonlinear parameters of a deterministic signal embedded in additive Gaussian noise. The algorithm is an approximation to the reduced sufficient statistics (RSS) method introduced by Kulhavy (1990) which estimates the posterior parameter density via minimization of the cross-entropy (Kullback-Leibler distance). In the modified RSS algorithm presented, the components of the posterior density representing the nonlinear parameter are modeled using Haar basis scale functions, and the components corresponding to the linear parameters are represented by Gaussian densities. In the additive Gaussian noise measurement model, the RSS algorithm employs a parallel bank of modified least-squares estimators for the linear parameters, coupled with a nonlinear estimator for the nonlinear parameters. Simulation results are presented for the problem of estimating parameters of a chirp signal embedded in multipath, and the averaged squared error (ASE) of the parameter estimates is compared with the Cramer-Rao bound. Finally, an application of the algorithm is presented in which the delay, multipath coefficients, and Doppler shift of a digitally modulated waveform received over a fading channel are jointly estimated View full abstract»

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  • Algorithms for adaptive transform edge detection

    Page(s): 2313 - 2317
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (260 KB)  

    Edge detection in grayscale digital images based on the locations of zero crossings has been investigated. Samples of the image are transformed using the discrete symmetric cosine transform (DSCT) and filtered using truncated time or frequency sampled forms of the Laplacian-of-Gaussian (LOG) filter. This article presents and evaluates adaptive block-based filtering procedures to localize edges based on discrete circular and real transforms. Measures of the signal-to-noise ratio (SNR) and edge localization are provided View full abstract»

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  • Fourier series based nonminimum phase model for statistical signal processing

    Page(s): 2228 - 2240
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (688 KB)  

    In this paper, a parametric Fourier series based model (FSBM) for or as an approximation to an arbitrary nonminimum-phase linear time-invariant (LTI) system is proposed for statistical signal processing applications where a model for LTI systems is needed. Based on the FSBM, a (minimum-phase) linear prediction error (LPE) filter for amplitude estimation of the unknown LTI system together with the Cramer-Rao (CR) bounds is presented. Then, an iterative algorithm for obtaining the optimum LPE filter with finite data is presented that is also an approximate maximum-likelihood algorithm when data are Gaussian. Then three iterative algorithms using higher order statistics (HOS) with finite non-Gaussian data are presented to estimate parameters of the FSBM followed by some simulation results as well as some experimental results with real speech data to support the efficacy of the proposed algorithms using the FSBM. Finally, we draw some conclusions View full abstract»

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  • A numerically stable fast RLS algorithm for adaptive filtering and prediction based on the UD factorization

    Page(s): 2309 - 2313
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (168 KB)  

    The use of UD factorization in adaptive RLS algorithms is interesting for its numeric robustness and because no square-root operations at all are involved. We describe a square root free fast RLS algorithm based on the UD factorization of the autocorrelation matrix. Numerous finite precision simulations tend to indicate that this algorithm is numerically stable. The algorithm requires 𝒪(𝒩) operations, where 𝒩 is the linear filter order View full abstract»

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  • Serial updating rule for blind separation derived from the method of scoring

    Page(s): 2279 - 2285
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (228 KB)  

    In the context of blind source separation, the method of scoring based on the inverse of the Fisher information matrix (FIM) becomes the serial updating learning rule with an equivariant property. This learning rule can be simplified to a low-complexity algorithm by using the asymptotic form of the FTM around the equilibrium. The simplified learning rule is still general enough to include some existing equivariant blind separation algorithms as its special cases View full abstract»

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  • Detection of environmental mismatch in a shallow water waveguide

    Page(s): 2181 - 2190
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (272 KB)  

    Performance of source localization, particularly using matched-field processing techniques, is very sensitive to modeling mismatch. This paper presents a novel test for detecting modeling mismatch in a bounded propagation medium, such as shallow water. The test is based on the fact that when there are no model uncertainties, the modal spectrum of the received signal is strictly limited to an a priori known set of modes. Mismatch in the modal eigenfunction of the assumed model causes the modal spectrum out of this band to be nonzero. The proposed test requires no prior knowledge about the radiating sources. The performance of the proposed test is evaluated via computer simulations of a benchmark shallow water channel. It is shown that the test is sensitive to mismatch in the channel depth and in bottom sound speeds. The ability of the test to identify array tilt mismatch is also presented. An application of the test for validation of maximum-likelihood localization results is also discussed View full abstract»

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  • An adaptive spatial diversity receiver for non-Gaussian interference and noise

    Page(s): 2100 - 2111
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (332 KB)  

    Standard linear diversity combining techniques are not effective in combating fading in the presence of non-Gaussian noise. An adaptive spatial diversity receiver is developed for wireless communication channels with slow, flat fading and additive non-Gaussian noise. The noise is modeled as a mixture of Gaussian distributions and the expectation-maximization (EM) algorithm is used to derive estimates for the model parameters. The transmitted signals are detected using a likelihood ratio test based on the parameter estimates. The new adaptive receiver converges rapidly, its bit error rate performance is very close to optimum when relatively short training sequences are used, and it appears to be relatively insensitive to mismatch between the noise model and the actual noise distribution. Simulation results are included that illustrate various aspects of the adaptive receiver performance View full abstract»

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  • Some methods to evaluate the performance of Page's test as used to detect transient signals

    Page(s): 2112 - 2127
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (400 KB)  

    In the “classical” detection problem, a decision is to be made about the presence or absence of a target based on an observation sequence. Since this data is of a given length, we refer to this as fixed-sample-size testing. A pair of problems that are similar in spirit (but turn out to be considerably different mathematically) is that of quickest detection and transient detection. The former refers to timely notification of a statistical change; the latter, which is the subject of this paper, refers to detection of a temporary change. Much is known about the performance of Page's (1954) test in terms of average run lengths; however, more detailed statistical analysis is required to determine the detectability of a transient change. Techniques to calculate and approximate the probability of detection by Page's test for a transient of a given length and strength are developed through investigation of the probability distribution of the so-called stopping time of Page's test, which is the time between the starting instant of the test and the instant of the first alarm (false- or true-detection) View full abstract»

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  • Robust H2 filtering for uncertain systems with measurable inputs

    Page(s): 2286 - 2292
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (172 KB)  

    This paper deals with the robust minimum variance filtering problem for linear time-varying systems subject to a measurable input and to norm bounded parameter uncertainty in the state and/or the output matrices of the state-space model. The problem addressed is the design of linear filters having an error variance with a guaranteed upper bound for any allowed uncertainty and any input of bounded energy. Three types of input signals are considered: a signal that is a priori known for the whole time interval, an unknown signal of very large bandwidth that is perfectly measured on-line, and a large bandwidth signal that is measured ahead of time in a fixed preview time interval. Both the time-varying finite-horizon and stationary infinite-horizon cases are treated View full abstract»

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  • Modified B-splines for the sampling of bandlimited functions

    Page(s): 2328 - 2332
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (184 KB)  

    It is shown that there is an optimal finite linear combination of B-splines (denominated modified B-splines) such that a pertinent low frequency condition called M-flatness is satisfied. A profound relationship of the modified B-splines with the beta distribution implies an asymptotic sampling theorem with exact reconstruction requiring only small oversampling View full abstract»

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  • Generalized transfer function estimation using evolutionary spectral deblurring

    Page(s): 2335 - 2339
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (204 KB)  

    We present a method for estimating the generalized transfer function (GTF) of a time-varying filter from a time-frequency representation (TFR) of its output. This method uses the fact that many TFR's can be written as blurred versions of the GTF. The approach minimizes the error between the TFR found from the data and that found by blurring the GTF. The problem as such has many solutions. We, therefore, additionally constrain it to minimize the distance between the GTF-based spectrum and the autoterms of the Wigner distribution, suppressing the cross terms using an appropriate signal dependent mask function. To illustrate the performance of the proposed procedure, we apply it to the spectral representation of speech signals and to signal masking View full abstract»

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  • A note on Unser-Zeruhia generalized sampling theory applied to the linear interpolator

    Page(s): 2332 - 2335
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    In this correspondence, we calculate the condition number of the linear operator that maps sequences of samples f(2k), f(2k+a), k∈Z of an unknown continuous f∈L2 (R) consistently (in the sense of the Unser-Zeruhia generalized sampling theory) onto the set of continuous, piecewise linear functions in L2(R) with nodes at the integers as a function of a∈(0,2). It turns out that the minimum condition numbers occur at a=√2/3 and a=2-√2/3 and not at a=1 as we might have expected. The theory is verified using the example of video deinterlacing View full abstract»

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  • Optimal and self-tuning deconvolution in time domain

    Page(s): 2253 - 2261
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (256 KB)  

    This paper is concerned with both the optimal (minimum mean square error variance) and self-tuning deconvolution problems for discrete-time systems. When the signal model, measurement model, and noise statistics are known, a novel approach for the design of the optimal deconvolution filter, predictor, and smoother is proposed based on projection theory and innovation analysis in the time domain. The estimators are given in terms of an autoregressive moving average (ARMA) innovation model and one unilateral linear polynomial equation, where the ARMA innovation model is obtained by performing one spectral factorization. A self-tuning scheme can be incorporated when the noise statistics, the input model, and/or colored noise model are unknown. The self-tuning estimator is designed by identifying two ARMA innovation models View full abstract»

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  • Spatial signature estimation for uniform linear arrays with unknown receiver gains and phases

    Page(s): 2128 - 2138
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (236 KB)  

    The problem of spatial signature estimation using a uniform linear array (ULA) with unknown receiver gain and phase responses is studied. Sufficient conditions for identifying the spatial signatures are derived, and a closed-form ESPRIT-like estimator is proposed. The performance of the method is investigated by means of simulations and on experimental data collected with an antenna array in a suburban environment. The results show that the absence of receiver calibration is not critical for uplink signal waveform estimation using a plane wave model 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