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Signal Processing, IEEE Transactions on

Issue 5 • Date May 1999

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Displaying Results 1 - 25 of 40
  • Comments on "On a least-squares-based algorithm for identification of stochastic linear systems"

    Page(s): 1395 - 1396
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (74 KB)  

    The bias-eliminated least squares estimator proposed in the paper by Zheng (see ibid., vol.46, p.1631-8, 1998) is shown to be identical to a simple instrumental variable estimator, using delayed input values as instruments. View full abstract»

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  • The slantlet transform

    Page(s): 1304 - 1313
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    The discrete wavelet transform (DWT) is usually carried out by filterbank iteration; however, for a fixed number of zero moments, this does not yield a discrete-time basis that is optimal with respect to time localization. This paper discusses the implementation and properties of an orthogonal DWT, with two zero moments and with improved time localization. The basis is not based on filterbank iteration; instead, different filters are used for each scale. For coarse scales, the support of the discrete-time basis functions approaches two thirds that of the corresponding functions obtained by filterbank iteration. This basis, which is a special case of a class of bases described by Alpert (1992, 1993), retains the octave-band characteristic and is piecewise linear (but discontinuous). Closed-form expressions for the filters are given, an efficient implementation of the transform is described, and improvement in a denoising example is shown. This basis, being piecewise linear, is reminiscent of the slant transform, to which it is compared View full abstract»

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  • Estimation of fractional Brownian motion with multiresolution Kalman filter banks

    Page(s): 1431 - 1434
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (140 KB)  

    A filter bank design based on orthonormal wavelets and equipped with a multiscale Kalman filter was proposed for deconvolution of fractal signals. We use the same scheme for estimating fractional Brownian motion in noise considering (1) the effect of correlation in the sequence of wavelet coefficients; (2) the approximation term in the wavelet expansion; (3) aliasing effects; (4) the optimal number of scales in the filter bank. Considerations on the minimum number of filters in the bank are made, and comparisons between Wiener and Kalman filters are given. Explicit expressions of the mean-square error are given, and comparisons between theoretical and simulation results are shown View full abstract»

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  • A wavelet time-scale deconvolution filter design for nonstationary signal transmission systems through a multipath fading channel

    Page(s): 1441 - 1446
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (232 KB)  

    This study attempts to develop a time-scale deconvolution filter for optimal signal reconstruction of nonstationary processes with a stationary increment transmitted through a multipath fading and colored noisy channel with stochastic tap coefficients. A deconvolution filter based on wavelet analysis/synthesis filter bank is proposed to solve this problem via a three-stage filter bank. A fractal signal transmitted through a multipath fading and noisy channel is provided to demonstrate the design procedure's effectiveness and to exhibit the signal reconstruction performance of the proposed optimal time-scale deconvolution filter View full abstract»

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  • Estimation of continuous-time AR process parameters from discrete-time data

    Page(s): 1232 - 1244
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (544 KB)  

    The problem of estimating continuous-time autoregressive process parameters from discrete-time data is considered. The basic approach used here is based on replacing the derivatives in the model by discrete-time differences, forming a linear regression, and using the least squares method. Such a procedure is simple to apply, computationally flexible and efficient, and may have good numerical properties. It is known, however, that all standard approximations of the highest order derivative, such as repeated use of the delta operator, gives a biased least squares estimate, even as the sampling interval tends to zero. Some of our previous approaches to overcome this problem are reviewed. Then. two new methods, which avoid the shift in our previous results, are presented. One of them, which is termed bias compensation, is computationally very efficient. Finally, the relationship of the above least squares approaches with an instrumental variable method is investigated. Comparative simulation results are also presented View full abstract»

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  • Analysis of the convergence properties of self-normalized source separation neural networks

    Page(s): 1272 - 1287
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (508 KB)  

    An extended source separation neural network was derived by Cichocki et al. (see Proc. 1995 Int. Symp. Nonlinear Theory Appl. NOLTA, Las Vegas, NV, p.61-65, 1995) from the classical Herault-Jutten network. It claimed to have several advantages, but its convergence properties were not described. In this paper, we first consider the standard version of this network. We determine all its equilibrium points and analyze their stability for a small adaptation gain. We prove that the stationary independent sources that this network can separate are the globally sub-Gaussian signals. As the Herault-Jutten (1991) network applies to the same sources, we thus show that the advantages of the new network are not counterbalanced by a reduced field of application, which confirms its attractiveness in the considered conditions. Moreover, we then introduce and analyze a modified version of this network, which can separate the globally super-Gaussian source signals. These theoretical results are experimentally confirmed by computer simulations. As a result of our overall investigation, a method for processing each one of the two classes of signals (i.e. sub- and super-Gaussian) is available View full abstract»

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  • Fuzzy selection filters for image restoration with neural learning

    Page(s): 1446 - 1450
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (180 KB)  

    A novel class of nonlinear filters, called rank conditioned fuzzy selection (RCFS) filters, is proposed to improve the filtering capability of rank conditioned rank selection filters. In contrast to the selection filters, the output of RCFS filters is obtained from the center gravity of a selected fuzzy set of the observation samples View full abstract»

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  • Multichannel system identification and deconvolution: performance bounds

    Page(s): 1410 - 1414
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (200 KB)  

    We consider the problem of estimating the parameters of an unknown multi-input multi-output (MIMO) linear system and the related problem of deconvolving and recovering its inputs. Only the system outputs are assumed to be observable. The system inputs are assumed to be non-Gaussian. We derive simple closed-form asymptotic expressions for the Cramer-Rao lower bound (CRLB) for the system parameters, as well as lower bounds on the signal reconstruction performance. These show that the identification/deconvolution performance depend on the accuracy with which the location (mean) and the scale (standard deviation) parameters of the input probability density functions can be identified from observation of the input signals View full abstract»

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  • On computation of the discrete W transform

    Page(s): 1450 - 1453
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (148 KB)  

    This article presents new fast algorithms for the type-II, -III, and -IV discrete W transform (DWT). The type-II and -III DWT is decomposed into two length-N/2 type-I DWTs, and the type-IV is converted into two length-N/2, type-II or type-III DWTs. The proposed algorithms achieve a simple computational structure and naturally support a wide range of sequence lengths. Savings on the number of arithmetic operations are achieved for the type-II to -IV DWT when N=15*2r View full abstract»

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  • Improved estimation of hyperbolic frequency modulated chirp signals

    Page(s): 1384 - 1388
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (176 KB)  

    This article deals with parameter estimation of product signals consisting of hyperbolic FM and chirp factors. A computationally simple algorithm that decouples estimation of the chirp parameters from those of the hyperbolic FM part is presented. It relies on a simple data transformation that removes the hyperbolic FM component, leaving one with the simpler problem of estimating chirp parameters. For the latter, the high-order ambiguity function (HAF) is adopted. Schemes for estimating the hyperbolic FM parameter are also proposed. The method improves on existing approaches and is shown to provide performance close to the Cramer-Rao bound View full abstract»

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  • A modified QRD for smoothing and a QRD-LSL smoothing algorithm

    Page(s): 1414 - 1420
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (256 KB)  

    This paper introduces a modified QR-decomposition (QRD) that extends the method of QRD to a more general case to solve the least-squares lattice smoothing problems. We show that the conventional QRD is a special form of the modified QRD that occurs when no future data values are used. Within the framework of the modified QRD procedure, an order-recursive QRD based least-squares lattice (QRD-LSL) smoothing algorithm is formulated. The algorithm combines all the desirable features of the standard QRD-LSL filtering algorithm with a more accurate smoothing process. The results of some computer simulations of a channel equalizer are also presented View full abstract»

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  • Localization of wideband signals using least-squares and total least-squares approaches

    Page(s): 1213 - 1222
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (492 KB)  

    In this paper, we introduce a new focusing technique for localization of wideband signals. Relaxing the unitary assumption for the focusing matrices, we formulate the least-square (LS) and the total least-square (TLS) coherent signal-subspace methods. The TLS is an alternative to the conventional LS and uses the fact that errors can exist both in the focusing location matrix as well as in the estimated location matrix at a given frequency bin. To prevent the focusing loss, we use a class of focusing matrices that are constant under multiplication by their Hermitian transpose. The class of unitary matrices comports with this property. We then develop a new focusing technique based on a modification to the TLS (MTLS). It is shown that the computational complexity of the new technique is significantly lower than that for the rotational signal subspace method (RSS). The focusing gain of the new technique is also larger than the focusing gain of the RSS algorithm. The simulation study shows that, compared with the RSS, the new algorithm has a smaller resolution signal to-noise ratio (SNR) View full abstract»

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  • Maximum-likelihood symmetric α-stable parameter estimation

    Page(s): 1382 - 1384
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (112 KB)  

    Using the close relation between Fisher scoring and Newton maximization, and an efficient density function evaluation, we develop a fast maximum-likelihood parameter estimation method. Simulations show the algorithm to be superior in accuracy to McCulloch's (1986) method and to achieve the Cramer-Rao bound View full abstract»

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  • Methods for blind equalization and resolution of overlapping echoes of unknown shape

    Page(s): 1245 - 1254
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (300 KB)  

    This paper considers the related problems of using an uncalibrated antenna array to (1) recover an unknown signal transmitted over an unknown (but stationary) multipath channel and (2) resolve overlapping pulse echoes with unknown shape. Unlike previously proposed multichannel blind equalization techniques, the methods described herein employ a model based on physical channel parameters rather than unstructured single-input, multi-output FIR filters. The algorithms exploit similarities between a model for the data in the frequency domain and the standard direction-of-arrival estimation problem. This connection between the two problems suggests several different approaches based on, for example, maximum likelihood, MODE, IQML, and ESPRIT. These approaches are developed in some detail, and the results of several simulation examples are included to compare their performance View full abstract»

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  • On the LTI properties of adaptive feedforward systems with tap delay-line regressors

    Page(s): 1288 - 1296
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (420 KB)  

    It is shown that an adaptive system whose regressor is formed by tap delay-line (TDL) filtering of a multitone sinusoidal signal is representable as a parallel connection of a linear time-invariant (LTI) block and a linear time-varying (LTV) block. A norm-bound (induced 2-norm) is computed explicitly on the LTV block and is shown to decrease as N-1, where N is the number of taps. Hence, the adaptive system becomes LTI in the limit as the number of taps goes to infinity. In the more realistic case where the number of taps N is finite, the new “LTI plus norm-bounded perturbation” representation renders, for the first time, the adaptive system analyzable by standard robust control methods View full abstract»

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  • Hybrid nonlinear moments subspace processing for wireless communication systems using antenna arrays

    Page(s): 1434 - 1441
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (436 KB)  

    It is shown that hybrid nonlinear (HKL) moments matrices can be used to identify a multichannel FIR system. The method outperforms the popular subspace method based on second-order statistics in low SNR and/or correlated noise, and it is fundamentally equivalent in terms of computational complexity. The method is applied to the channel identification problem in a cellular base-station receiver employing antenna arrays View full abstract»

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  • The probability density of spectral estimates based on modified periodogram averages

    Page(s): 1255 - 1261
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (284 KB)  

    Welch's (1967) method for spectral estimation of averaging modified periodograms has been widely used for decades. Because such an estimate relies on random data, the estimate is also a random variable with some probability density function. Here, the PDF of a power estimate is derived for an estimate based on an arbitrary number of frequency bins, overlapping data segments, amount of overlap, and type of data window, given a correlated Gaussian input sequence. The PDFs of several cases are plotted and found to be distinctly non-Gaussian (the asymptotic result of averaging frequency bins and/or data segments), using the Kullback-Leibler distance as a measure. For limited numbers of frequency bins or data segments, the precise PDF is considerably skewed and will be important in applications such as maximum likelihood tests View full abstract»

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  • A general efficient method for chaotic signal estimation

    Page(s): 1424 - 1428
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (204 KB)  

    This article presents a general, computationally efficient method for chaotic signal estimation based on the connection between the symbolic sequence and the initial condition of a chaotic system. The performance of the method in white Gaussian noise is evaluated. The new method is asymptotically unbiased and attains the Cramer-Rao lower bound at high signal-to-noise ratios View full abstract»

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  • Complexity reduction of the NLMS algorithm via selective coefficient update

    Page(s): 1421 - 1424
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (180 KB)  

    This article proposes an algorithm for partial update of the coefficients of the normalized least mean square (NLMS) finite impulse response (FIR) adaptive filter. It is shown that while the proposed algorithm reduces the complexity of the adaptive filter, it maintains the closest performance to the full update NLMS filter for a given number of updates. Analysis of the MSE convergence and steady-state performance for independent and identically distributed (i.i.d.) signals is provided for the extreme case of one update/iteration View full abstract»

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  • On computing the 2-D FFT

    Page(s): 1428 - 1431
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (140 KB)  

    A a new implementation of the two-dimensional FFT (2-D FFT) is proposed. Compared with the usual separable solution, the new realization of the 2-D FFT has reduced arithmetic complexity. Computational savings are achieved because the 2-D case enables, after some modifications of the basic separable algorithm, scaling and inverse scaling of butterfly operators. The new improvement is also applied to other 2-D transforms: DCT-IV, DCT, and lapped transforms View full abstract»

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  • Realization of 2-D linear-phase FIR filters by using the singular-value decomposition

    Page(s): 1349 - 1358
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (440 KB)  

    The singular-value decomposition (SVD) technique is investigated for the realization of a general two-dimensional (2-D) linear-phase FIR filter with an arbitrary magnitude response. A parallel realization structure consisting of a number of one-dimensional (1-D) FIR subfilters is obtained by applying the SVD to the impulse response of a 2-D filter. It is shown that by using the symmetry property of the 2-D impulse response and by developing an appropriate unitary transformation, an SVD yielding linear-phase constituent 1-D filters can always be obtained so that the efficient structures of the 1-D linear-phase filters can be exploited for 2-D realization. It is shown that when the 2-D filter to be realized has some specified symmetry in its magnitude response, the proposed SVD realization would yield a magnitude characteristic with the same symmetry. An analysis is carried out to obtain tight upper bounds for the errors in the impulse response as well as in the frequency response of the realized filter. It is shown that the number of parallel sections can be reduced significantly without introducing large errors, even in the case of 2-D filters with nonsymmetric magnitude response View full abstract»

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  • On the recursive solution of the normal equations of bilateral multivariate autoregressive models

    Page(s): 1388 - 1390
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (120 KB)  

    A multivariate version of the bilateral autoregressive (AR) model is proposed, and a recursive algorithm is presented to solve the normal equations of the bilateral multivariate AR models. The recursive algorithm is computationally efficient and easy to implement as a computer program. The recursive algorithm is useful for identifying and smoothing not only bilateral multivariate AR processes but multidimensional multivariate AR processes and multivariate spatio-temporal processes as well View full abstract»

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  • On adaptive EVD asymptotic distribution of centro-symmetric covariance matrices

    Page(s): 1402 - 1406
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (272 KB)  

    This article investigates the gain in statistical performance/complexity of the adaptive estimation of the eigenvalue decomposition (EVD) of covariance matrices when the centro-symmetric (CS) structure of such matrices is utilized. After deriving the asymptotic distribution of the EVD estimators, it is shown, in particular, that the closed-form expressions for the asymptotic covariance of batch and adaptive EVD estimators are very similar, provided that the number of samples is replaced by the inverse of the step size View full abstract»

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  • Discrete fractional Fourier transform based on orthogonal projections

    Page(s): 1335 - 1348
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (580 KB)  

    The continuous fractional Fourier transform (FRFT) performs a spectrum rotation of signal in the time-frequency plane, and it becomes an important tool for time-varying signal analysis. A discrete fractional Fourier transform has been developed by Santhanam and McClellan (see ibid., vol.42, p.994-98, 1996) but its results do not match those of the corresponding continuous fractional Fourier transforms. We propose a new discrete fractional Fourier transform (DFRFT). The new DFRFT has DFT Hermite eigenvectors and retains the eigenvalue-eigenfunction relation as a continous FRFT. To obtain DFT Hermite eigenvectors, two orthogonal projection methods are introduced. Thus, the new DFRFT will provide similar transform and rotational properties as those of continuous fractional Fourier transforms. Moreover, the relationship between FRFT and the proposed DFRFT has been established in the same way as the conventional DFT-to-continuous-Fourier transform View full abstract»

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  • A modified path-following algorithm using a known algebraic path

    Page(s): 1407 - 1409
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (120 KB)  

    A new computationally efficient path-following algorithm is presented for source localization that uses a uniform linear sensor array. An algebraic relation is demonstrated between the bearing of a source under a plane wave assumption and the actual source bearing and range. This relation can be used as a path to follow to the peak of the 2-D MUSIC spectrum. As a result, in the case of an array that has m sensors with n sources, this new algorithm can reduce the number of searches to n independent 1-D searches following the known algebraic path 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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Editor-in-Chief
Zhi-Quan (Tom) Luo
University of Minnesota