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Signal Processing, IEEE Transactions on

Issue 2 • Date Feb 2001

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Displaying Results 1 - 21 of 21
  • Convergence analysis of adaptive filtering algorithms with singular data covariance matrix

    Publication Year: 2001 , Page(s): 334 - 343
    Cited by:  Papers (4)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (220 KB)  

    The paper provides a rigorous analysis of the behavior of adaptive filtering algorithms when the covariance matrix of the filter input is singular. The analysis is done in the context of adaptive plant identification. The considered algorithms are LMS, RLS, sign (SA), and signed regressor (SRA) algorithms. Both the signal and weight behavior of the algorithms are considered. The signal behavior is evaluated in terms of the moments of the excess output error of the filter. The weight behavior is evaluated in terms of the moments of the filter weight misalignment vector. It is found that the RLS and SRA diverge when the input covariance matrix is singular. The steady-state signal behavior of the LMS and SA can be made arbitrarily fine by using sufficiently small step sizes of the algorithms. Indeed, the long-term average of the mean square excess error of the LMS is proportional to the algorithm step size. The long-term average of the mean absolute excess error of the SA is proportional to the square root of the algorithm step size. On the other hand, the steady-state weight behavior of both the LMS and SA have biases that depend on the weight initialization. The analytical results of the paper are supported by simulations View full abstract»

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  • 2-D and 1-D multipaired transforms: frequency-time type wavelets

    Publication Year: 2001 , Page(s): 344 - 353
    Cited by:  Papers (23)  |  Patents (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (292 KB)  

    A concept of multipaired unitary transforms is introduced. These kinds of transforms reveal the mathematical structure of Fourier transforms and can be considered intermediate unitary transforms when transferring processed data from the original real space of signals to the complex or frequency space of their images. Considering paired transforms, we analyze simultaneously the splitting of the multidimensional Fourier transform as well as the presentation of the processed multidimensional signal in the form of the short one-dimensional (1-D) “signals”, that determine such splitting. The main properties of the orthogonal system of paired functions are described, and the matrix decompositions of the Fourier and Hadamard transforms via the paired transforms are given. The multiplicative complexity of the two-dimensional (2-D) 2r×2r-point discrete Fourier transform by the paired transforms is 4r/2(r-7/3)+8/3-12 (r>3), which shows the maximum splitting of the 5-D Fourier transform into the number of the short 1-D Fourier transforms. The 2-D paired transforms are not separable and represent themselves as frequency-time type wavelets for which two parameters are united: frequency and time. The decomposition of the signal is performed in a way that is different from the traditional Haar system of functions View full abstract»

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  • Statistical analysis of a signal separation method based on second-order statistics

    Publication Year: 2001 , Page(s): 441 - 444
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (140 KB)  

    This correspondence explores a method for separation of dynamically mixed sources, which is based on second-order statistics. Here, a statistical analysis is given of a generalized version of the original algorithm. The generalized method includes a weighting matrix, and a result of the statistical analysis is that the best possible weighting is found. In cases where the sources have similar color, the weighted algorithm significantly improves the estimates of the mixing parameters. The problem of model validation is discussed as well View full abstract»

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  • Gibbs phenomenon removal and digital filtering directly through the fast Fourier transform

    Publication Year: 2001 , Page(s): 444 - 448
    Cited by:  Papers (17)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (136 KB)  

    The Gibbs phenomenon in the Fourier transform is due to a periodicity discrepancy between the waveform and its sinusoidal representations in the time domain. Data flipping, baseline tilting, or digital comparison completes the periodicity of the waveform and thus removes the Gibbs phenomenon. This facilitates digital filtering directly through the fast Fourier transform. Such a filtering is unique and exact, with its stop-band totally zeroed out and passband fully passed. It accomplishes lowpass, bandpass, highpass, bandstop, notch, or single-frequency-pass simply by manipulating the band limits View full abstract»

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  • Multiple window time-varying spectral analysis

    Publication Year: 2001 , Page(s): 448 - 453
    Cited by:  Papers (13)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (484 KB)  

    A multiwindow method for generating a time-varying spectrum of nonstationary signals is presented The time-varying spectrum is computed from an optimally weighted average of multiple orthogonal windowed spectrograms. The weights are determined using linear least squares estimation with respect to a reference time-frequency distribution. Examples are provided, with performance criteria measures, to demonstrate and quantify the effectiveness of the method View full abstract»

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  • A unified approach to the steady-state and tracking analyses of adaptive filters

    Publication Year: 2001 , Page(s): 314 - 324
    Cited by:  Papers (82)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (280 KB)  

    Most adaptive filters are inherently nonlinear and time-variant systems. The nonlinearities in the update equations tend to lead to difficulties in the study of their steady-state performance as a limiting case of their transient performance. This paper develops a unified approach to the steady-state and tracking analyses of adaptive algorithms that bypasses many of these difficulties. The approach is based on the study of the energy flow through each iteration of an adaptive filter, and it relies on a fundamental error variance relation View full abstract»

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  • Moving target feature extraction for airborne high-range resolution phased-array radar

    Publication Year: 2001 , Page(s): 277 - 289
    Cited by:  Papers (11)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (300 KB)  

    We study the feature extraction of moving targets in the presence of temporally and spatially correlated ground clutter for airborne high-range resolution (HRR) phased-array radar. To avoid the range migration problems that occur in HRR radar data, we first divide the HRR range profiles into low-range resolution (LRR) segments. Since each LRR segment contains a sequence of HRR range bins, no information is lost due to the division, and hence, no loss of resolution occurs. We show how to use a vector auto-regressive (VAR) filtering technique to suppress the ground clutter, Then, a parameter estimation algorithm is proposed for target feature extraction. From the VAR-filtered data, the target Doppler frequency and the spatial signature vectors are first estimated by using a maximum likelihood (ML) method. The target phase history and direction-of-arrival (DOA) (or the array steering vector for an unknown array manifold) are then estimated from the spatial signature vectors by minimizing a weighted least squares (WLS) cost function. The target radar cross section (RCS)-related complex amplitude and range-related frequency of each target scatterer are then extracted from the estimated target phase history by using RELAX, which is a relaxation-based high-resolution feature extraction algorithm. Numerical results are provided to demonstrate the performance of the proposed algorithm View full abstract»

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  • An iterative algorithm for the computation of the MVDR filter

    Publication Year: 2001 , Page(s): 290 - 300
    Cited by:  Papers (88)  |  Patents (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (304 KB)  

    Statistical conditional optimization criteria lead to the development of an iterative algorithm that starts from the matched filter (or constraint vector) and generates a sequence of filters that converges to the minimum-variance-distortionless-response (MVDR) solution for any positive definite input autocorrelation matrix. Computationally, the algorithm is a simple, noninvasive, recursive procedure that avoids any form of explicit autocorrelation matrix inversion, decomposition, or diagonalization. Theoretical analysis reveals basic properties of the algorithm and establishes formal convergence. When the input autocorrelation matrix is replaced by a conventional sample-average (positive definite) estimate, the algorithm effectively generates a sequence of MVDR filter estimators; the bias converges rapidly to zero and the covariance trace rises slowly and asymptotically to the covariance trace of the familiar sample-matrix-inversion (SMI) estimator. In fact, formal convergence of the estimator sequence to the SMI estimate is established. However, for short data records, it is the early, nonasymptotic elements of the generated sequence of estimators that offer favorable bias covariance balance and are seen to outperform in mean-square estimation error, constraint-LMS, RLS-type, orthogonal multistage decomposition, as well as plain and diagonally loaded SMI estimates. An illustrative interference suppression example is followed throughout this presentation View full abstract»

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  • Optimality of the myriad filter in practical impulsive-noise environments

    Publication Year: 2001 , Page(s): 438 - 441
    Cited by:  Papers (30)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (144 KB)  

    Linear filtering theory has been largely motivated by the characteristics of Gaussian signals. In the same manner, the proposed myriad filtering methods are motivated by the need for a flexible filter class with high statistical efficiency in non-Gaussian impulsive environments that can appear in practice. We introduce several important properties of the myriad filter and prove its optimality in the family of α-stable distributions View full abstract»

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  • A cumulant matrix subspace algorithm for blind single FIR channel identification

    Publication Year: 2001 , Page(s): 325 - 333
    Cited by:  Papers (10)  |  Patents (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (256 KB)  

    Blind identification of discrete-time single-user FIR channels with nonminimum phase is studied here. Exploiting higher order cumulants of output signals of unknown channels, a new closed-form solution to the FIR channel impulse response is derived. The algorithm is simple and fast. It relies only on nullspace decomposition of some cumulant matrices. This method neither involves the difficult task of iterative global minimization of nonunimodal cost functions, nor does it require overparametrization, which poses consistency difficulties. It can be used either as the final channel estimate or as a good initial point in nonlinear cumulant matching techniques. The application of this identification method is broad and not limited to the use of any fixed-order cumulants. Its application in identifying data communication systems shows great potential and promise View full abstract»

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  • Stochastic gradient identification of polynomial Wiener systems: analysis and application

    Publication Year: 2001 , Page(s): 301 - 313
    Cited by:  Papers (19)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (316 KB)  

    This paper presents analytical, numerical, and experimental results for a stochastic gradient adaptive scheme that identifies a polynomial-type nonlinear system with memory for noisy output observations. The analysis includes the computation of the stationary points, the mean square error surface, and the stability regions of the algorithm for Gaussian data. Convergence of the mean is studied using L 2 and Euclidian norms. Monte Carlo simulations confirm the theoretical predictions that show a small sensitivity to the observation noise. An application is presented for the identification of a nonlinear time-delayed feedback system View full abstract»

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  • M-estimation in exponential signal models

    Publication Year: 2001 , Page(s): 373 - 380
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (248 KB)  

    In this paper, we propose an M-estimation of the parameters in an undamped exponential signal model. Its asymptotic performance is investigated. Under mild assumptions, the estimation is consistent. The simulation studies of the performance of the M-estimation using Huber's function are provided when the sample size is small, and the comparisons between the performances of the M-estimation and the least squares estimation are also presented View full abstract»

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  • Criteria of convergence of median filters and perturbation theorem

    Publication Year: 2001 , Page(s): 360 - 363
    Cited by:  Papers (5)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (132 KB)  

    Repeated application of the median filter to any finite length sequence converges to a root in a finite number of passes. This requires padding on each end of the sequence. In some applications, such padding may be inappropriate because of the overemphasis on the endpoints. However, there are some of infinite-length sequences whose median filters are not convergent. In this paper, necessary and/or sufficient conditions on infinite-length sequences are derived in order that their median filters converge to roots of category I. Moreover, we study convergence of median filters of perturbed sequences. The results obtained extend the previous theory on convergence of median filters View full abstract»

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  • Theoretical aspects of radar imaging using stochastic waveforms

    Publication Year: 2001 , Page(s): 394 - 400
    Cited by:  Papers (19)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (184 KB)  

    In this work, we develop the theory of radar imaging using stochastic waveforms, such as random noise or chaotic signals. Specifically, we consider one-dimensional (1-D) (range profiles) and two-dimensional (2-D) (range-Doppler) radar imaging performed with a random signal radar, in which the transmit signals are assumed to be stationary random processes. We calculate the 1-D and 2-D point-spread functions as the expected value of the radar return. We show that the 2-D point-spread function is spatially invariant; however, the reduction in height and broadening of the mainlobe is small in the case of bandlimited noise. We also derive a formula that is useful in calculating the variance of the radar return under the assumption that the transmit signal is real valued and Gaussian View full abstract»

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  • Fast computation of the ambiguity function and the Wigner distribution on arbitrary line segments

    Publication Year: 2001 , Page(s): 381 - 393
    Cited by:  Papers (17)  |  Patents (4)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (632 KB)  

    By using the fractional Fourier transformation of the time-domain signals, closed-form expressions for the projections of their auto or cross ambiguity functions are derived. Based on a similar formulation for the projections of the auto and cross Wigner distributions and the well known two-dimensional (2-D) Fourier transformation relationship between the ambiguity and Wigner domains, closed-form expressions are obtained for the slices of both the Wigner distribution and the ambiguity function. By using discretization of the obtained analytical expressions, efficient algorithms are proposed to compute uniformly spaced samples of the Wigner distribution and the ambiguity function located on arbitrary line segments. With repeated use of the proposed algorithms, samples in the Wigner or ambiguity domains can be computed on non-Cartesian sampling grids, such as polar grids View full abstract»

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  • A unified algebraic transformation approach for parallel recursive and adaptive filtering and SVD algorithms

    Publication Year: 2001 , Page(s): 424 - 437
    Cited by:  Papers (4)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (488 KB)  

    In this paper, a unified algebraic transformation approach is presented for designing parallel recursive and adaptive digital filters and singular value decomposition (SVD) algorithms. The approach is based on the explorations of some algebraic properties of the target algorithms' representations. Several typical modern digital signal processing examples are presented to illustrate the applications of the technique. They include the cascaded orthogonal recursive digital filter, the Givens rotation-based adaptive inverse QR algorithm for channel equalization, and the QR decomposition-based SVD algorithms. All three examples exhibit similar throughput constraints. There exist long feedback loops in the algorithms' signal flow graph representation, and the critical path is proportional to the size of the problem. Applying the proposed algebraic transformation techniques, parallel architectures are obtained for all three examples. For cascade orthogonal recursive filter, retiming transformation and orthogonal matrix decompositions (or pseudo-commutativity) are applied to obtain parallel filter architectures with critical path of five Givens rotations. For adaptive inverse QR algorithm, the commutativity and associativity of the matrix multiplications are applied to obtain parallel architectures with critical path of either four Givens rotations or three Givens rotations plus two multiply-add operations, whichever turns out to be larger. For SVD algorithms, retiming and associativity of the matrix multiplications are applied to derive parallel architectures with critical path of eight Givens rotations. The critical paths of all parallel architectures are independent of the problem size as compared with being proportional to the problem size in the original sequential algorithms. Parallelism is achieved at the expense of slight increase (or the same for the SVD case) in the algorithms' computational complexity View full abstract»

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  • A mixed norm performance measure for the design of multirate filterbanks

    Publication Year: 2001 , Page(s): 354 - 359
    Cited by:  Papers (7)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (144 KB)  

    A mixed norm performance measure is presented to design the synthesis filters of a multirate filterbank. The mixed norm performance measure is based on the energy as well as the peak value of the error signal. Mathematically, the performance measure minimizes the l2 -norm of the error signal subject to the l-norm of the error being bounded by some positive value v (this imposes a bound on the peak value of the error signal). The design problem is shown to be that of a mixed ℋ2/ℋ optimization problem. The theory of linear matrix inequalities (LMIs) offers a tractable solution to such multiobjective synthesis problems. The synthesis filters designed with the new performance measure are compared with those obtained by similar induced norm minimization techniques in terms of degree of reconstruction, order of the synthesis filters, SNR, and aliasing distortion View full abstract»

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  • A signal subspace-based subband approach to space-time adaptive processing for mobile communications

    Publication Year: 2001 , Page(s): 401 - 413
    Cited by:  Papers (7)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (308 KB)  

    In this paper, we present a novel space-time signal subspace-based subband approach to space-time adaptive processing (STAP) that has been shown to be an effective method to suppress both the intersymbol interference (ISI) and the cochannel interference (CCI) in mobile communications. We first study the performance of STAP and make clear the conditions of perfect processing (i.e., perfect equalization of the desired user signal and perfect suppression of CCI signals). Based on the polyphase representation and the subspace analysis of the signal channels, we propose a space-time signal subspace-based subband approach to STAP, namely the subband STAP, which highly improves the convergence rate without loss of the steady-state performance. Simulation results show its effectiveness under the procedure of signal subspace estimation and detection View full abstract»

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  • Direction-of-arrival estimation of an amplitude-distorted wavefront

    Publication Year: 2001 , Page(s): 269 - 276
    Cited by:  Papers (7)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (172 KB)  

    In a number of array signal processing applications, such as underwater source localization, the propagation medium is not homogeneous, which causes a distortion of the wavefront received by the array. There has been some interest in the direction-of-arrival (DOA) estimation of such distorted wavefronts. Most works on this problem considered the so-called multiplicative noise scenario based on the rather strong assumption that the distortion is random and can be parameterized by a small number of parameters. To gain robustness against mismodeling, we assume a scenario in which the wavefront amplitude is distorted in a completely arbitrary way. Our main contribution consists of showing how to eliminate all nuisance (distortion) parameters from the likelihood function corresponding to such a scenario and obtain a robust maximum likelihood DOA estimate by means of a simple one-dimensional (1-D) search. Despite its simplicity, it is shown that the estimator has a performance close to the Cramer-Rao Bound (CRB), for which we derive a closed-form expression. Moreover, its accuracy is comparable with that of estimators that require knowledge of the form of amplitude distortions View full abstract»

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  • Block-median pyramidal transform: analysis and denoising applications

    Publication Year: 2001 , Page(s): 364 - 372
    Cited by:  Papers (8)  |  Patents (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (240 KB)  

    A nonlinear multiscale pyramidal transform based on nonoverlapping block decompositions using the median operation and a polynomial approximation is considered. It is shown that this structure can be useful for denoising of oneand two-dimensional (1-D and 2-D) signals. Various denoising techniques are analyzed, including methods based on spatially adaptive thresholding and partial cycle-spinning algorithms. An analytical method for deriving the distribution function of the transform coefficients is also presented. This, in turn, can be used for the selection of thresholds for denoising applications View full abstract»

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  • Markovian diffusive representation of 1/fα noises and application to fractional stochastic differential models

    Publication Year: 2001 , Page(s): 414 - 423
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (256 KB)  

    This paper is devoted to linear stochastic differential systems with fractional noise (or fractional Brownian motion) input. On the basis of a convenient Markovian description of such noises, elaborated from a diffusive representation of fractional integrators previously introduced in a deterministic context, the fractional differential system is equivalently transformed into a standard (but infinite-dimensional) one, with white-noise input. Finite dimensional approximations may easily be obtained from classical discretization schemes. With this equivalent representation, the correlation function of processes described by linear fractional stochastic differential systems may be expressed from the solution of standard differential systems, which generalizes, in some way, the well-known differential Lyapunov equation, which appears when computing the covariance matrix associated with standard linear stochastic systems View full abstract»

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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
Sergios Theodoridis
University of Athens