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Signal Processing, IEEE Transactions on

Issue 5 • Date May 2001

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Displaying Results 1 - 20 of 20
  • Call for papers

    Page(s): 1107 - 1109
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    Freely Available from IEEE
  • Comment on the "Unnecessary assumption of statistical independence between reference signal and filter weights in feedforward adaptive systems"

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    Minkoff (see IEEE Trans. Signal Processing, vol.45, p.2993-3004, 1997) presented a formulation in which the time-evolving weight-iteration equation for random signals is derived without the necessity of invoking the usual unsatisfactory assumption that is customarily made, namely, that the weights W and the reference signal X the weight-iteration equation are statistically independent. Minkoff neglected, however, to give a physical argument for it. That is, in this derivation, it is not necessary for W to be independent of X but only of XX which does not contain the phase information of X. The off-diagonal terms of XX contain only phase differences, which could be produced by an infinite number of different, arbitrary Xs. View full abstract»

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  • Generalized rectification of cross spectral matrices for arrays of arbitrary geometry

    Page(s): 972 - 978
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    In high-resolution methods applied to uniform linear arrays (ULA), the preprocessing that consists of forcing the estimated cross spectral matrix (CSM) to be Toeplitz by averaging its elements along its diagonals is known to increase the resolving power drastically. That is why it is always done in practice. However, this approach is limited to linear arrays because of the required Toeplitz structure for the CSM. This paper generalizes this technique to arrays of arbitrary geometry; the developed method is referred to as rectification. It proceeds by searching first for a vector subspace of Hermitian matrices that contains the manifold generated by the CSMs when the angle of arrival (AOA) varies. This preliminary step is performed only once for a given array geometry. Next, rectification of estimated CSMs is achieved by projecting them onto this subspace, resulting in denoising and increased resolving power of source localization methods at a very low computational cost. As a byproduct, the storage requirements for the CSMs are greatly reduced View full abstract»

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  • Stability analysis of 1-D and 2-D fixed-point state-space digital filters using any combination of overflow and quantization nonlinearities

    Page(s): 1097 - 1105
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    A new criterion, together with its frequency-domain interpretation for the global asymptotic stability of zero-input one-dimensional (1-D) state-space digital filters under various combinations of overflow and quantization nonlinearities and for the situation where quantization occurs after summation only, is presented. A condition in closed form involving solely the parameters of the state transition matrix for the nonexistence of limit cycles in second-order digital filters is derived. Improved versions of some of the stability results due to Leclerc and Bauer (1994) are established. Finally, the approach is extended to two-dimensional (2-D) digital filters described by the Roesser and the Fornasini-Marchesini second local state-space models View full abstract»

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  • Reply to “Comments on adaptive IIR filtering with monic normalization”

    Page(s): 1106 - 1107
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    Kim and Song (see IEEE Signal Processing Lett., vol.6, p.35-37, 1999) focused on the bias removal capability of the monic normalization equation error (MNEE) algorithm and showed in another paper (see IEEE Signal Processing Lett., vol.7, p.54-56, 2000) that the parameter estimated by the MNEE algorithm converges to the solution of the well-known eigenvalue equation presented by Regalia (1994), which is based on the unit-norm constraint. However, the convergence properties of the MNEE have not been fully understood. Some of its convergence issues were commented upon by Soderstrom (see vol.48, p.892-94, 2000). In the MNEE, there is a small bias of order O(μ). Under a certain condition, the MNEE may not be convergent. In this reply to Soserstrom's comments, we provide some remarks related to the above issues View full abstract»

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  • An optimal filter of the second order

    Page(s): 1044 - 1048
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    We present a new technique allowing us to find an optimal filter in the class of so-called second-order filters. The new filter is generated by a best-approximation operator of the second degree and generalizes and improves an optimal linear filter associated with the concept of Wiener filtering. This article provides a strict justification of the technique proposed, demonstrates its advantages, and describes numerous useful extensions and applications View full abstract»

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  • nth-order fractional Brownian motion and fractional Gaussian noises

    Page(s): 1049 - 1059
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    A generalization of fractional Brownian motion (fBm) of parameter H in ]0, 1[ is proposed. More precisely, this work leads to nth-order fBm (n-fBm) of H parameter in ]n-1, n[, where n is any strictly positive integer. They include fBm for the special case n=1. Properties of these new processes are investigated. Their covariance function are given, and it is shown that they are self similar. In addition, their spectral shape is assessed as 1/fα with α belonging to ]1; +∞[, providing a larger framework than classical fBm. Special interest is given to their nth-order stationary increments, which extend fractional Gaussian noises. The covariance function and power spectral densities are calculated. The properties and signal processing tasks such as a Cholesky-type synthesis technique and a maximum likelihood estimation method of the H parameter are presented. The results show that the estimator is efficient (unbiased and reaches the Cramer-Rao lower bound) for a large majority of tested values View full abstract»

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  • Quasi-nonparametric blind inversion of Wiener systems

    Page(s): 917 - 924
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    An efficient procedure for the blind inversion of a nonlinear Wiener system is proposed. We show that the problem can be expressed as a problem of blind source separation in nonlinear mixtures for which a solution has been previously proposed. Based on a quasi-nonparametric relative gradient descent, the proposed algorithm can perform efficiently even in the presence of hard distortions View full abstract»

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  • Fast matching pursuit with a multiscale dictionary of Gaussian chirps

    Page(s): 994 - 1001
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    We introduce a modified matching pursuit algorithm, called fast ridge pursuit, to approximate N-dimensional signals with M Gaussian chirps at a computational cost O(MN) instead of the expected O(MN2 logN). At each iteration of the pursuit, the best Gabor atom is first selected, and then, its scale and chirp rate are locally optimized so as to get a “good” chirp atom, i.e., one for which the correlation with the residual is locally maximized. A ridge theorem of the Gaussian chirp dictionary is proved, from which an estimate of the locally optimal scale and chirp is built. The procedure is restricted to a sub-dictionary of local maxima of the Gaussian Gabor dictionary to accelerate the pursuit further. The efficiency and speed of the method is demonstrated on a sound signal View full abstract»

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  • Bearing estimation in a Ricean channel .I. Inherent accuracy limitations

    Page(s): 925 - 937
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    This paper considers the problem of estimating the bearing of a single, far-field source using passive sensor array measurements when the spatial propagation channel formed between the source and the array may be described as “Ricean.” Such a channel consists of a direct, line-of-sight (LOS) component as well as an indirect, nonline-of-sight (NLOS) component due to scattering. A parametric description of the resulting spatial propagation channel is presented. A related source-bearing estimation problem is formulated, and the associated Cramer-Rao lower bound (CRLB) is evaluated. The bound is used to study the relationship among the bearing estimation problems under the Ricean (LOS/NLOS), point source (LOS), and scattered source (NLOS) models. Exact and simplified approximate forms of the bound are derived explicitly in terms of the point source and scattered source CRLBs. A number of properties of the bound are presented. In particular, it is shown that the bound is a monotonically decreasing function of the Rice factor (the ratio of the LOS component power to the NLOS component power). This implies that for a given signal-to-noise ratio (SNR), the CRLB is bounded from below by the point source bound and bounded from above by the scattered source bound. It is also shown that given a NLOS component, the addition of a LOS component necessarily makes the bearing estimation problem easier. On the other hand, given an LOS component, the addition of an NLOS component does not necessarily make the bearing estimation problem easier (and may even make it harder). Lastly, the CRLB for estimation of the Rice factor is considered, and some of its properties are studied View full abstract»

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  • Theory and lattice structure of complex paraunitary filterbanks with filters of (Hermitian-)symmetry/antisymmetry properties

    Page(s): 1028 - 1043
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    The theory of the real-coefficient linear-phase filterbank (LPFB) is extended to the complex case in two ways, leading to two generalized classes of M-channel filterbanks. One is the symmetric/antisymmetric filterbank (SAFB), where all filters are symmetric or antisymmetric. The other is the complex linear phase filterbank (CLPFB), where all filters are Hermitian symmetric or Hermitian antisymmetric and, hence, have the linear-phase property. Necessary conditions on the filter symmetry polarity and lengths for the existence of permissible solutions are investigated. Complete and minimal lattice structures are developed for the paraunitary SAFB and paraunitary CLPFB, where the channel number M is arbitrary (even or odd), and the subband filters could have different lengths. With the elementary unitary matrices in the structure of the paraunitary SAFB constrained to be real and orthogonal, the structure covers the most general real-coefficient paraunitary LPFBs. Compared with the existing results, the number of parameters is reduced significantly View full abstract»

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  • Closed-form correlative coding (CFC2) blind identification of MIMO channels: isometry fitting to second order statistics

    Page(s): 1073 - 1086
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    We present a blind closed-form consistent channel estimator for multiple-input multiple-output (MIMO) systems that uses only second order statistics. We spectrally modulate the output of each source by correlative coding it with a distinct filter. The correlative filters are designed to meet the following desirable characteristics: no additional power or bandwidth is required; no synchronization between the sources is needed; the original data rate is maintained. We first prove an identifiability theorem: under a simple spectral condition on the transmitted random processes, the MIMO channel is uniquely determined, up to a phase offset per user, from the second order statistics of the received data. We then develop the closed-form algorithm that attains this identifiability bound. We show that minimum-phase finite impulse response filters with arbitrary memory satisfy our sufficient spectral identifiability condition. This results in a computationally attractive scheme for retrieving the data information sequences after the MIMO channel has been identified. We assess the performance of the proposed algorithms by computer simulations. In particular, the results show that our technique outperforms the previously introduced transmitter-induced conjugate cyclostationarity approach when there are carrier frequency misadjustments View full abstract»

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  • Fractional convolution and correlation via operator methods and an application to detection of linear FM signals

    Page(s): 979 - 993
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    Using operator theory methods together with our previously introduced unitary fractional operator, we derive explicit definitions of fractional convolution and correlation operations in a systematic and comprehensive manner. Via operator manipulations, we also provide alternative formulations of those fractional operations that suggest efficient algorithms for discrete implementation. Through simulation examples, we demonstrate how well the proposed efficient method approximates the continuous formulation of fractional autocorrelation. It is also shown that the proposed fractional autocorrelation corresponds to radial slices of the ambiguity function (AF). We also suggest an application of the fast fractional autocorrelation for detection and parameter estimation of linear FM signals View full abstract»

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  • Optimized signal expansions for sparse representation

    Page(s): 1087 - 1096
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    Traditional signal decompositions such as transforms, filterbanks, and wavelets generate signal expansions using the analysis-synthesis setting: the expansion coefficients are found by taking the inner product of the signal with the corresponding analysis vector. In this paper, we try to free ourselves from the analysis-synthesis paradigm by concentrating on the synthesis or reconstruction part of the signal expansion. Ignoring the analysis issue completely, we construct sets of synthesis vectors, which are denoted waveform dictionaries, for efficient signal representation. Within this framework, we present an algorithm for designing waveform dictionaries that allow sparse representations: the objective is to approximate a training signal using a small number of dictionary vectors. Our algorithm optimizes the dictionary vectors with respect to the average nonlinear approximation error, i.e., the error resulting when keeping a fixed number n of expansion coefficients but not necessarily the first n coefficients. Using signals from a Gaussian, autoregressive process with correlation factor 0.95, it is demonstrated that for established signal expansions like the Karhunen-Loeve transform, the lapped orthogonal transform, and the biorthogonal 7/9 wavelet, it is possible to improve the approximation capabilities by up to 30% by fine tuning of the expansion vectors View full abstract»

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  • Detection-estimation of more uncorrelated Gaussian sources than sensors in nonuniform linear antenna arrays .I. Fully augmentable arrays

    Page(s): 959 - 971
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    Previous studies dealing with direction-of-arrival (DOA) estimation for uncorrelated planes waves incident on nonuniform M-sensor arrays assumed that the number of signal sources m was known or had already been estimated. In the “conventional” case (m<M), traditional detection techniques such as Akaike's information criterion (AIC) and minimum description length (MDL) that are based on the equality of several smallest eigenvalues in the covariance matrix may be applied, although we demonstrate that these results can be misleading for nonuniform arrays. In the “superior” case (m⩾M), these standard techniques are not applicable. We introduce a new approach to the detection problem for “fully augmentable” arrays (whose set of intersensor differences is complete). We show that the well-known direct augmentation approach applied to the sample covariance matrix is not a solution by itself since the resulting Toeplitz matrix is generally not positive definite for realistic sample volumes. We propose a transformation of this augmented matrix into a positive definite Toeplitz matrix Tμ with the proper number of equal minimum eigenvalues that are appropriate for the candidate number of sources μ. Comparison of the results of these best-fit transformations over the permissible range of candidates then allows us to select the most likely number of sources mˆ using traditional criteria and yields uniquely defined DOAs. Simulation results demonstrate the high performance of this method. Since detection techniques for superior scenarios have not been previously described in the literature, we compare our method with the standard AIC and MDL techniques in a conventional case with similar Cramer-Rao bound (CRB) and find that it has a similar detection performance View full abstract»

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  • Analysis of stochastic gradient identification of Wiener-Hammerstein systems for nonlinearities with Hermite polynomial expansions

    Page(s): 1060 - 1072
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    This paper investigates the statistical behavior of a sequential adaptive gradient search algorithm for identifying an unknown Wiener-Hammerstein (1958) system (WHS) with Gaussian inputs. The WHS nonlinearity is assumed to be expandable in a series of orthogonal Hermite polynomials. The sequential procedure uses (1) a gradient search for the unknown coefficients of the Hermite polynomials, (2) an LMS adaptive filter to partially identify the input and output linear filters of the WHS, and (3) the higher order terms in the Hermite expansion to identify each of the linear filters. The third step requires the iterative solution of a set of coupled nonlinear equations in the linear filter coefficients. An alternative scheme is presented if the two filters are known a priori to be exponentially shaped. The mean behavior of the various gradient recursions are analyzed using small step-size approximations (slow learning) and yield very good agreement with Monte Carlo simulations. Several examples demonstrate that the scheme provides good estimates of the WHS parameters for the cases studied View full abstract»

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  • Biorthogonal partners and applications

    Page(s): 1013 - 1027
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    Two digital filters H(z) and F(z) are said to be biorthogonal partners of each other if their cascade H(z)F(z) satisfies the Nyquist or zero-crossing property. Biorthogonal partners arise in many different contexts such as filterbank theory, exact and least squares digital interpolation, and multiresolution theory. They also play a central role in the theory of equalization, especially, fractionally spaced equalizers in digital communications. We first develop several theoretical properties of biorthogonal partners. We also develop conditions for the existence of biorthogonal partners and FIR biorthogonal pairs and establish the connections to the Riesz basis property. We then explain how these results play a role in many of the above-mentioned applications View full abstract»

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  • High-resolution direction finding: the missing data case

    Page(s): 950 - 958
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    This paper considers the problem of estimating the direction-of-arrival (DOA) of one or more signals using an array of sensors, where some of the sensors fail to work before the measurement is completed. Methods for estimating the array output covariance matrix are discussed. In particular, the maximum-likelihood (ML) estimate of this covariance matrix and its asymptotic accuracy are derived and discussed. Different covariance matrix estimates are used for DOA estimation together with the MUSIC algorithm and with a covariance matching technique. In contrast to MUSIC, the covariance matching technique can utilize information on the estimation accuracy of the array covariance matrix, and it is demonstrated that this yields a significant performance gain View full abstract»

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  • A generalization of weighted subspace fitting to full-rank models

    Page(s): 1002 - 1012
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    The idea of subspace fitting provides a popular framework for different applications of parameter estimation and system identification. Previously, some algorithms have been suggested based on similar ideas, for a sensor array processing problem where the underlying data model is not low rank. We show that two of these algorithms (DSPE and DISPARE) fail to give consistent estimates and introduce a general class of subspace fitting-like algorithms for consistent estimation of parameters from a possibly full-rank data model. The asymptotic performance is analyzed, and an optimally weighted algorithm is derived. The result gives a lower bound on the estimation performance for any estimator based on a low-rank approximation of the linear space spanned by the sample data. We show that in general, for full-rank data models, no subspace-based method can reach the Cramer-Rao lower bound (CRB) View full abstract»

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  • Multipath delay estimation using a superresolution PN-correlation method

    Page(s): 938 - 949
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    This paper addresses the problem of high-resolution estimation of a multipath channel delay profile. We propose several improvements to the so-called superresolution pseudo-noise sequence correlation method (SPM) and analyze its performance on time-varying channels. SPM is based on the multiple signal classification (MUSIC) algorithm, which requires decorrelation of the multipath echoes. The proposed improvements enable SPM-based delay estimation in the presence of narrowband interference, and they reduce the necessary transmission window while preserving multipath echo decorrelation. These improvements are analyzed and are applied to underwater acoustic experimental data 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