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Signal Processing, IEEE Transactions on

Issue 9 • Date Sep 1995

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Displaying Results 1 - 25 of 27
  • A maximal invariant framework for adaptive detection with structured and unstructured covariance matrices

    Page(s): 2164 - 2175
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (940 KB)  

    We introduce a framework for exploring array detection problems in a reduced dimensional space by exploiting the theory of invariance in hypothesis testing. This involves calculating a low-dimensional basis set of functions called the maximal invariant, the statistics of which are often tractable to obtain, thereby making analysis feasible and facilitating the search for tests with some optimality property. Using this approach, we obtain a locally most powerful invariant test for the unstructured covariance case and show that all invariant tests can be expressed in terms of the previously published Kelly's generalized likelihood ratio (GLRT) and Robey's adaptive matched filter (AMF) test statistics. Applying this framework to structured covariance matrices, corresponding to stochastic interferers in a known subspace, for which the GLRT is unavailable, we obtain the maximal invariant and propose several new invariant detectors that are shown to perform as well or better than existing ad-hoc detectors. These invariant tests are unaffected by most nuisance parameters, hence the variation in the level of performance is sharply reduced. This framework facilitates the search for such tests even when the usual GLRT is unavailable View full abstract»

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  • Bounds for estimation of complex exponentials in unknown colored noise

    Page(s): 2176 - 2185
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    We consider the problem of estimating the parameters of complex exponentials in the presence of complex additive Gaussian noise with unknown covariance. Bounds are derived for the accuracy of jointly estimating the parameters of the exponentials and the noise. We first present an exact Cramer-Rao bound (CRB) for this problem and specialize it for the cases of circular Gaussian processes and autoregressive processes. We also derive an approximate expression for the CRB, which is related to the conditional likelihood function. Numerical evaluation of these bounds provides some insights on the effect of various signal and noise parameters on the achievable estimation accuracy View full abstract»

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  • Estimating 2-D DOA angles using nonlinear array configurations

    Page(s): 2212 - 2216
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    This paper modifies the direction-of-arrival matrix (DOAM) method for detecting 2-D direction-of-arrival (DOA) angles of narrowband far-field source signals using nonlinear array configurations. The key modification to the DOAM method is the replacement of the 1-D data model with a 2-D data model. The modified DOA matrix (MDOAM) method requires less computation, detects more sources with the same number of sensors, and removes the constraint on the spacing between subarrays View full abstract»

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  • Nonlinear adaptive IIR digital filter for linear system modeling

    Page(s): 2190 - 2193
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (320 KB)  

    The structure and adaptive algorithm of a nonlinear adaptive IIR digital filter is presented. It does not need stability monitoring in the adaptive process, which has always been a computational burden and disturbs the adaptive process in linear adaptive IIR filtering. The individual parameter adaptation scheme is incorporated into the adaptive algorithm to optimally adjust each parameter at every iteration to improve convergence speed. Simulation results are conducted for linear IIR system modeling View full abstract»

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  • Volterra filtering and higher order whiteness

    Page(s): 2209 - 2212
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    Some properties of Volterra filtering are established. Finite-order, finite-horizon Volterra filtering is investigated as well as its asymptotic properties. Next, the concepts of Volterra unpredictability and uninterpolability lead to generalizations of the notion of white noise to higher orders. These generalizations are introduced and relations are established between them View full abstract»

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  • Computationally efficient angle estimation for signals with known waveforms

    Page(s): 2154 - 2163
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    This paper presents a large sample decoupled maximum likelihood (DEML) angle estimator for uncorrelated narrowband plane waves with known waveforms and unknown amplitudes arriving at a sensor array in the presence of unknown and arbitrary spatially colored noise. The DEML estimator decouples the multidimensional problem of the exact ML estimator to a set of 1-D problems and, hence, is computationally efficient. We shall derive the asymptotic statistical performance of the DEML estimator and compare the performance with its Cramer-Rao bound (CRB), i.e., the best possible performance for the class of asymptotically unbiased estimators. We will show that the DEML estimator is asymptotically statistically efficient for uncorrelated signals with known waveforms. We will also show that for moderately correlated signals with known waveforms, the DEML estimator is no longer a large sample maximum likelihood (ML) estimator, but the DEML estimator may still be used for angle estimation, and the performance degradation relative to the CRB is small. We shall show that the DEML estimator can also be used to estimate the arrival angles of desired signals with known waveforms in the presence of interfering or jamming signals by modeling the interfering or jamming signals as random processes with an unknown spatial covariance matrix. Finally, several numerical examples showing the performance of the DEML estimator are presented in this paper View full abstract»

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  • Convergence analysis of finite length blind adaptive equalizers

    Page(s): 2120 - 2129
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    The paper presents some new analytical results on the convergence of two finite length blind adaptive channel equalizers, namely, the Godard equalizer and the Shalvi-Weinstein equalizer. First, a one-to-one correspondence in local minima is shown to exist between the Godard and Shalvi-Weinstein equalizers, hence establishing the equivalent relationship between the two algorithms. Convergence behaviors of finite length Godard and Shalvi-Weinstein equalizers are analyzed, and the potential stable equilibrium points are identified. The existence of undesirable stable equilibria for the finite length Shalvi-Weinstein equalizer is demonstrated through a simple example. It is proven that the points of convergence for both finite length equalizers depend on an initial kurtosis condition. It is also proven that when the length of equalizer is long enough and the initial equalizer setting satisfies the kurtosis condition, the equalizer will converge to a stable equilibrium near a desired global minimum. When the kurtosis condition is not satisfied, generally the equalizer will take longer to converge to a desired equilibrium given sufficiently many parameters and adequate initialization. The convergence analysis of the equalizers in PAM communication systems can be easily extended to the equalizers in QAM communication systems View full abstract»

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  • A new transform with symmetrical coding performance for Markov (1) signals

    Page(s): 2195 - 2198
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    Based on the DCT and DST-II, we present a new transform that provides a symmetrical performance for positively and negatively correlated Markov (1) signals (first-order stationary Markov process). A fast computational algorithm is presented. A sufficient condition of symmetrical transforms is also provided, and the idea of constructing the discrete cosine-sine transform (DCST) is then generalized to the Karhunen-Loeve transform (KLT) of any Markov (1) signal View full abstract»

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  • Incoherent receivers in alpha-stable impulsive noise

    Page(s): 2225 - 2229
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    We compute an incoherent receiver for demodulation of signals with random phase in additive impulsive noise modeled as a bivariate isotropic Cauchy process. Monte-Carlo simulation clearly shows that the proposed Cauchy receiver has a significantly improved operating characteristic over the corresponding Gaussian receiver. Moreover, the Cauchy receiver is very robust in the entire class of bivariate isotropic symmetric alpha-stable impulsive noises View full abstract»

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  • Digital filter bank design quadratic-constrained formulation

    Page(s): 2103 - 2108
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (472 KB)  

    Formulate the filter bank design problem as an quadratic-constrained least-squares minimization problem. The solution of the minimization problem converges very quickly since the cost function as well as the constraints are quadratic functions with respect to the unknown parameters. The formulations of the perfect-reconstruction cosine-modulated filter bank, of the near-perfect-reconstruction pseudo-QMF bank, and of the two-channel biorthogonal linear-phase filter bank are derived using the proposed approach. Compared with other design methods, the proposed technique yields PR filter banks with much higher stopband attenuation. The proposed technique can also be extended to design multidimensional filter banks View full abstract»

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  • On the principal domain of the discrete bispectrum of a stationary signal

    Page(s): 2130 - 2134
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    The paper presents a simplifying, yet general approach to determining the symmetry structure of a bispectrum. The principal domain (PD) of the bispectrum and its region of positive support are derived in a way that illuminates the controversy surrounding the triangle in the PD, which is called the outer triangle (OT) by Hinich and Wolinsky (1988), where the bispectrum is zero for a stationary random sampled process that is not aliased. The basic statistical issues of testing for nonzero bispectral structure are reviewed View full abstract»

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  • A geometric approach to multiple-channel signal detection

    Page(s): 2049 - 2057
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    The paper introduces the generalized coherence (GC) estimate and examines its application as a statistic for detecting the presence of a common but unknown signal on several noisy channels. The GC estimate is developed as a natural generalization of the magnitude-squared coherence (MSC) estimate-a widely used statistic for nonparametric detection of a common signal on two noisy channels. The geometrical nature of the GC estimate is exploited to derive its distribution under the H0 hypothesis that the data channels contain independent white Gaussian noise sequences. Detection thresholds corresponding to a range of false alarm probabilities are calculated from this distribution. The relationship of the H0 distribution of the GC estimate to that of the determinant of a complex Wishart-distributed matrix is noted. The detection performance of the three-channel GC estimate is evaluated by simulation using a white Gaussian signal sequence in white Gaussian noise. Its performance is compared with that of the multiple coherence (MC) estimate, another nonparametric multiple-channel detection statistic. The GC approach is found to provide better detection performance than the MC approach in terms of the minimum signal-to-noise ratio on all data channels necessary to achieve desired combinations of detection and false alarm probabilities View full abstract»

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  • A constrained notch Fourier transform

    Page(s): 2058 - 2067
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    The paper presents a new sliding algorithm for estimating the amplitude and phase of the Fourier coefficients of noise corrupted harmonic signals given a priori knowledge of the signal frequencies. The proposed method is similar in principle to the notch Fourier transform (NFT) technique suggested by Tadokoro et al. [1987] except that it employs an infinite impulse response (IIR) rather than a finite impulse response (FIR) notch filter parameterization. This modification provides bandwidth controlled bandpass (BP) filters whose center frequencies are equally spaced in the frequency spectrum. In this sense, the proposed technique can be regarded as a constrained notch Fourier transform (CNFT). Sliding algorithms have been derived for both the NFT and CNFT for the purpose of estimating the Fourier coefficients of the sinusoidal components. The paper also proposes a similar algorithm to the CNFT for the signals containing sinusoids at arbitrary known frequencies. The main feature of the modified CNFT is that it uses second-order IIR BP filters whose bandwidth and center frequency can be adjusted independently. The bandwidth control aspect provides the user with an efficient means of achieving the required resolution as well as reducing spectral leakage. In general, the proposed approach leads to considerable reduction in terms of computational burden and memory storage View full abstract»

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  • Time-frequency kernel design by the two-dimensional frequency transformation method

    Page(s): 2198 - 2202
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    A subclass of Cohen's class of time-frequency (TF) distributions is introduced in which the TF distribution kernels are provided via the frequency transformation method (FTM), used in two dimensional (2-D) filter design. The FTM kernels have finite extent in time and frequency and allow the TF distribution to be efficiently implemented in all four domains View full abstract»

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  • Finite impulse response estimator (FIRE)

    Page(s): 2186 - 2189
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    FIRE is an optimal filter structure combining a deterministic digital filter and a stochastic filter. A model of the system is described by a stale equation and the output of the system is modeled by an FIR filter. This integrated structure has demonstrated the capability of processing signals contaminated by deterministic band-limited harmonic noises as well as random Gaussian noises. This article shows the derivation of FIRE and provides the simulation results for its tracking application View full abstract»

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  • On the determination of the optimal pole position of Laguerre filters

    Page(s): 2079 - 2087
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    As is known in the literature, at each stationary point of the squared error (SE) curve of a Laguerre filter at least one of a pair of certain Laguerre coefficients (weights) vanishes. The author describes a very efficient way to compute the derivatives of each one of these coefficients with respect to the pole position of the Laguerre filter. The knowledge of these derivatives makes possible the computation of high-order approximations to the coefficients in question, such as truncated Taylor series and Pade approximants. The zeros of these approximations are usually good estimates of the location of the stationary points of the SE curve nearer to the center of the approximation. In this way, the position of these stationary points, in particular local minima, can be estimated without resorting to a numerical search algorithm. Both continuous time and discrete time Laguerre filters are discussed, excited either by an impulse or by an arbitrary signal. The authors illustrate the main results of the paper with a numerical example View full abstract»

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  • Parametric localization of distributed sources

    Page(s): 2144 - 2153
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    Most array processing algorithms are based on the assumption that the signals are generated by point sources. This is a mathematical constraint that is not satisfied in many applications. In this paper, we consider situations where the sources are distributed in space with a parametric angular cross-correlation kernel. We propose an algorithm that estimates the parameters of this model using a generalization of the MUSIC algorithm. The method involves maximizing a cost function that depends on a matrix array manifold and the noise eigenvectors. We study two particular cases: coherent and incoherent spatial source distributions. The spatial correlation function for a uniformly distributed signal is derived. From this, we find the array gain and show that (in contrast to point sources) it does not increase linearly with the number of sources. We compare our method to the conventional (point source) MUSIC algorithm. The simulation studies show that the new method outperforms the MUSIC algorithm by reducing the estimation bias and the standard deviation for scenarios with distributed sources. It is also shown that the threshold signal-to-noise ratio required for resolving two closely spaced distributed sources is considerably smaller for the new method View full abstract»

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  • Cyclostationary modeling, analysis, and optimal compensation of quantization errors in subband codecs

    Page(s): 2109 - 2119
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    The paper is concerned with the analysis and modeling of the effects of quantization of subband signals in subband codecs. Using cyclostationary representations, the authors derive equations for the autocorrelation and power spectral density (PSD) of the reconstructed signal y(n) in terms of the analysis/synthesis filters, the PSD of the input, and the pdf-optimized quantizer model. Formulas for the mean-square error (MSE) and for compaction gain are obtained in terms of these parameters. The authors constrain the filter bank to be perfect reconstruction (PR) (but not necessarily paraunitary) in the absence of quantization and transmission errors. These formulas set the stage for filter optimization (maximization of compaction gain and minimization of MSE) subject to PR and bit constraints. Optimal filters are designed, optimal compensation is performed, and the theoretical results are confirmed with simulations. The floating-point quantizer wherein only the mantissa is uniformly quantized is also analyzed and compared with the fixed point, pdf-optimized filter bank. For high bit rates, their performance is comparable View full abstract»

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  • Oversampled Gabor representation for transient signals

    Page(s): 2088 - 2094
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    Considers the Gabor representation that uses a one-sided exponential window for detection and analysis of transient signals. Earlier results on the critically sampled case are extended to the more practically useful oversampled case. For oversampling by an integer factor, the authors derive an explicit analytical expression for the dual window (dual frame) function required for computing the Gabor representation. Based on this expression they develop an efficient procedure for computing the Gabor coefficients. Finally, they demonstrate the performance of the method by numerical examples View full abstract»

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  • An adaptive notch filter with improved tracking properties

    Page(s): 2068 - 2078
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    An analysis of the properties of an adaptive notch filter (ANF) applied to time-varying frequency tracking is presented. Starting from the derivation of an expression for ANF output power, asymptotically optimal values for the pole contraction and forgetting factors are derived for recursive prediction error (RPE) type ANF algorithms. Based on the obtained results, a new ANF algorithm that includes adaptation of both pole contraction and forgetting factors is proposed. The given experimental results confirm the theoretical conclusions and show that the proposed algorithm is highly efficient in practice View full abstract»

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  • On the application of the jackknife to the estimation of the parameters of short multisinusoidal signals using the data-matrix formulation

    Page(s): 2135 - 2143
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (728 KB)  

    It is demonstrated that the jackknife can be applied to the estimation of the parameters of a single short segment of a noisy, complex multisinusoid signal where the estimation process itself is based on the data-matrix formulation. The parameters of interest are the frequency, amplitude, and initial phase of each sinusoid, and the key role of the jackknife is to provide an estimate of the standard deviation of the estimates of these parameters from the single record available. The jackknife is shown to be especially appropriate where the primary estimator is well-behaved and its performance is broadly optimum where the sub-segment length used in creating the data matrix is about one-half of the record length and improves somewhat as the data length itself increases. This is inferred from a series of simulations involving three different algorithms with one, two, and three complex sinusoids in complex white noise. The application of the jackknife in the presence of phase noise and additive colored noise is also briefly examined. Due to the correlation between the columns of the data matrix, the successful application of the jackknife to this problem cannot be assumed a priori View full abstract»

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  • Sampling rate conversion systems using a new generalized form of the discrete Fourier transform

    Page(s): 2095 - 2102
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    A recursive factorization of the polynomial 1-zN leads to an efficient algorithm for the computation of the discrete Fourier transform (DFT) and the cyclic convolution. The paper introduces a new recursive polynomial factorization of the polynomial when N is highly composite. The factorization is used to define a generalized form of the DFT and to derive an efficient algorithm for the computation. The generalized form of the DFT is shown to be closely related to the polyphase decomposition of a sequence, and is applied for the design of sampling rate conversion systems, it gives not only alternative derivations for the polyphase interpolation and the polyphase decimation by an integer factor, but also a new sampling rate conversion system by a rational factor, which is more efficient than the known rational polyphase implementation when the filter length is large View full abstract»

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  • H nonlinear filtering of discrete-time processes

    Page(s): 2205 - 2209
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    This correspondence investigates the problem of H estimation of a discrete-time nonlinear process. An estimator, which may be nonlinear, is introduced so that an H-norm-like of what we call a generalized estimation error is guaranteed to be bounded by a prescribed level. Conditions for the existence of such an estimator, and formulae for its derivation, are obtained utilizing a discrete-time analog of the Hamilton-Jacobi inequality. An approximate filter based on linearization is developed. This filter relates to the extended Kalman filter in the same way that the linear H filter relates to the Kalman filter View full abstract»

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  • Asymptotically efficient estimation of spectral moments

    Page(s): 2222 - 2225
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    The article studies parametric estimation of spectral moments of a zero-mean complex Gaussian stationary process immersed in independent Gaussian noise. With the merit of the maximum-likelihood (ML) approach as motivation, this work exploits a Whittle's (1953) type objective function that is able to capture the relevant features of the log-likelihood function while being much more manageable. The resulting estimates are strongly consistent and asymptotically efficient. As an example, application to Doppler weather radar data is considered View full abstract»

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  • On the digital filter associated with Daubechies' wavelets

    Page(s): 2203 - 2205
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    The magnitude of the filters associated with Daubechies' wavelets nψ is shown to monotonically converge to an ideal highpass filter when n→∞. The rate of the convergence is also given. The magnitude of each filter is shown to be monotonically increasing from [0,π]. The convergence does not have Gibbs' phenomenon 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