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Signal Processing, IEEE Transactions on

Issue 4 • Date April 1995

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Displaying Results 1 - 25 of 26
  • Asymptotic maximum likelihood estimator performance for chaotic signals in noise

    Publication Year: 1995 , Page(s): 1009 - 1012
    Cited by:  Papers (25)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (317 KB)  

    The performance of the maximum likelihood estimator for a 1-D chaotic signal in white Gaussian noise is derived. It is found that the estimator is inconsistent and therefore the usual asymptotic distribution (large data record length) is invalid. However, for high signal-to-noise ratios (SNRs), the maximum likelihood estimator is asymptotically unbiased and attains the Cramer-Rao lower bound.<> View full abstract»

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  • On the effect of input signal correlation on weight misadjustment in the RLS algorithm

    Publication Year: 1995 , Page(s): 988 - 991
    Cited by:  Papers (10)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (364 KB)  

    New expressions are derived for the mean weight misadjustment in the recursive least squares (RLS) algorithm for first-order Markov channel estimation. The expressions derived are general in that they take into account the correlation in the input. It is shown that the additive system noise is amplified by a correlation amplification factor that is defined as a function of the input autocorrelation matrix eigenvalues. However, input correlation has almost no effect on the misadjustment due to time-varying system weights. These results are checked by simulations demonstrating excellent agreement with the theory View full abstract»

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  • Maximum likelihood DOA estimation and asymptotic Cramer-Rao bounds for additive unknown colored noise

    Publication Year: 1995 , Page(s): 938 - 949
    Cited by:  Papers (16)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (840 KB)  

    This paper is devoted to the maximum likelihood estimation of multiple sources in the presence of unknown noise. With the spatial noise covariance modeled as a function of certain unknown parameters, e.g., an autoregressive (AR) model, a direct and systematic way is developed to find the exact maximum likelihood (ML) estimates of all parameters associated with the direction finding problem, including the direction-of-arrival (DOA) angles Θ, the noise parameters α, the signal covariance Φs, and the noise power σ2. We show that the estimates of the linear part of the parameter set Φs and σ2 can be separated from the nonlinear parts Θ and α. Thus, the estimates of Φs and σ2 become explicit functions of Θ and α. This results in a significant reduction in the dimensionality of the nonlinear optimization problem. Asymptotic analysis is performed on the estimates of Θ and α, and compact formulas are obtained for the Cramer-Rao bounds (CRB's). Finally, a Newton-type algorithm is designed to solve the nonlinear optimization problem, and simulations show that the asymptotic CRB agrees well with the results from Monte Carlo trials, even for small numbers of snapshots View full abstract»

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  • Reconstruction of bandlimited signal with lost samples at its Nyquist rate-the solution to a nonuniform sampling problem

    Publication Year: 1995 , Page(s): 1008 - 1009
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (328 KB)  

    We present a formula for the sample values f(nj/2W), j=1, ..., N, of a W-bandlimited finite energy signal f in terms of the remaining sample values f(n/2W), n≠nj, j=1, ..., N, and N sample values f(yj), j=1, ..., N with yj≠n/2W, n∈Z but otherwise arbitrarily chosen View full abstract»

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  • New FFT bit-reversal algorithm

    Publication Year: 1995 , Page(s): 991 - 994
    Cited by:  Papers (6)  |  Patents (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (360 KB)  

    Presents a very short, simple, easy to understand bit-reversal algorithm for radix-2 fast Fourier transform (FFT), which is, furthermore, easily extendable to radix-M. In addition, when implemented together with Yong's (see IEEE Trans. Acoust., Speech, Signal Processing, vol.39, no.1O, p.2365-7, 1991) technique, the computing time is comparable to that of the fastest algorithms View full abstract»

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  • An algorithm for pole-zero system model order estimation

    Publication Year: 1995 , Page(s): 1013 - 1017
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (396 KB)  

    In system identification, estimates of the unknown system model orders are often required. An algorithm for estimating model orders is described that looks at input/output data covariance matrix eigenvectors. When model orders are overestimated, zeros appear in the noise subspace eigenvectors. The number of zeros present can be used to estimate model orders View full abstract»

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  • Detection of broadband planewaves in the presence of Gaussian noise of unknown covariance: asymptotically optimum tests using the 2-D autoregressive noise model

    Publication Year: 1995 , Page(s): 950 - 966
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1348 KB)  

    This paper addresses the problem of detecting a broadband planewave in noise of unknown spatial and temporal covariance at a linear array of sensors. Results of asymptotic detection theory are applied to derive detectors that approach optimal performance for large data records. A parametric approach is used to model the statistics of the data. A 2-D autoregressive (2DAR) model is chosen to model the noise process. Two broadband planewave signal models are considered. Both models represent the signal as a sum of monochromatic planewaves. In the Gaussian model, the amplitudes are assumed to be Gaussian with a single variance parameter, whereas in the deterministic assumption, they are individual unknown parameters. Detectors based on asymptotic theory are derived for both models. As part of the development of the asymptotically (AS) optimum detector, the Fisher information matrix (FIM) is derived. A proof of the locally asymptotic normal (LAN) property is provided for the Gaussian model probability density function (PDF). Both detectors, however, are AS equivalent to the generalized likelihood ratio test (GLRT), are AS of constant false alarm rate (CFAR), and perform AS as well as the GLRT constructed with full knowledge of the noise statistics. The performance of both detectors are compared with each other and to a standard spatially normalized beamformer in a computer simulation View full abstract»

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  • Perfect reconstruction with critically sampled filter banks and linear boundary conditions

    Publication Year: 1995 , Page(s): 994 - 997
    Cited by:  Papers (5)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (336 KB)  

    This work is concerned with the (image) boundary conditions involved in processing a finite discrete-time signal with a critically sampled perfect reconstruction filter bank. It is desirable that the boundary conditions reduce edge effects and define a transformation into a space having the same dimensionality as the original signal. The complication that arises is in the computation of the inverse transform. Although it is straightforward to reconstruct the signal values that were not influenced by the boundary conditions, recovering those values on the boundaries is nontrivial. The solution of this problem is discussed for general linear boundary conditions. No symmetry assumptions are made on the boundary conditions or on the impulse responses of the analysis filters. A low-rank linear transform is derived that expresses the boundary values in terms of the transform coefficients, which in turn provides a method for inverting the subband decomposition. The application of the results in the case of two-channel orthonormal wavelet filters is discussed, and the effects of the filter support on the conditioning of the inverse problem are investigated View full abstract»

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  • Parameter estimation for noncausal ARMA models of non-Gaussian signals via cumulant matching

    Publication Year: 1995 , Page(s): 886 - 893
    Cited by:  Papers (6)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (748 KB)  

    We consider the problem of estimating the parameters of a stable (stationary), scalar ARMA(p,q) signal model driven by an i.i.d. non-Gaussian sequence. The driving noise sequence is not observed. The signal is allowed to be nonminimum phase and/or noncausal (i.e., poles may lie both inside as well as outside the unit circle). We address the problem of parameter identifiability given the higher order cumulants of the signal on a finite set of lags. The sufficient set of lags required to achieve parameter identifiability is the smallest to date. The sufficient conditions for parameter identifiability are also the least restrictive to date. We also propose a frequency-domain approach for time-domain, nonlinear optimization of a quadratic cumulant matching criterion. Illustrative computer simulation results are presented View full abstract»

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  • Probability of resolution of the MUSIC algorithm

    Publication Year: 1995 , Page(s): 978 - 987
    Cited by:  Papers (31)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (736 KB)  

    The MUSIC algorithm is well known for its high-resolution capability, and various aspects of its statistical performance have been investigated. However, rigorous asymptotic analysis of one of its most important performance measures, the probability of resolution, is not available yet. We analyze the probability of the MUSIC algorithm resolving two spatially separated signal sources in the context of array processing. By formulating the resolution problem in the framework of statistical decision theory and directly determining the probability density function (PDF) of the indefinite and singular quadratic form that defines the resolution event, we arrive at an exact asymptotic formula for the probability of resolution. This is accomplished by a multistep procedure. Computer simulations have been performed to confirm the validity of the theory View full abstract»

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  • Adaptive algorithms for joint time delay estimation and IIR filtering

    Publication Year: 1995 , Page(s): 841 - 851
    Cited by:  Papers (7)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (928 KB)  

    A new class of gradient-based algorithms for joint adaptive time delay estimation and IIR filtering for the recursive identification of systems with long pure delays is introduced. The algorithms update an adaptive delay estimate and the coefficients of an IIR filter using familiar gradient-descent methods. In addition, interpolation of the input sequence is used to obtain delays that are not constrained to integer numbers of samples. Three algorithms using a direct form filter parametrization and one using a normalized lattice filter are derived, and computer simulations are used to demonstrate their convergence and tracking properties View full abstract»

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  • A framework for quality versus efficiency tradeoffs in STFT analysis

    Publication Year: 1995 , Page(s): 998 - 1001
    Cited by:  Papers (8)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (452 KB)  

    A framework is presented for increasing the computational efficiency of STFT analysis by sacrificing the quality of each signal frame's DFT in terms of SNR, frequency resolution, and frequency coverage. The resulting algorithms are dominated by a frame-adaptive vector summation process designed to ensure that the number of additions per frame does not exceed any desired limit View full abstract»

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  • A simple method for designing high-quality prototype filters for M-band pseudo QMF banks

    Publication Year: 1995 , Page(s): 1005 - 1007
    Cited by:  Papers (47)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (260 KB)  

    Discusses a new method for designing the prototype filters necessary to implement M-band pseudo QMF banks. This method does not rely on the traditional nonlinear optimization used in past work but rather optimizes a single parameter on a convex error surface, consistently delivering the best equiripple filter possible while minimizing the overlapped passband distortion. A very simple algorithm for designing lowpass prototype filters suitable for use in pseudo QMF banks is described. To illustrate the applicability of this algorithm, two different filters are designed, both for such applications as wideband audio coding that require high quality reconstructed signals View full abstract»

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  • Characterization of threshold for single tone maximum likelihood frequency estimation

    Publication Year: 1995 , Page(s): 817 - 821
    Cited by:  Papers (14)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (428 KB)  

    This paper presents a simple and direct approach to understanding the threshold effect associated with maximum likelihood estimation of the frequency of a single complex tone. Motivation for the approach, stemming from known results in the field of phase locked loops, is given. It is shown both theoretically and experimentally that the onset of threshold can be directly characterized by a single, easily computed parameter, namely the Cramer-Rao bound on the phase estimation error variance View full abstract»

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  • Stack filter design: a structural approach

    Publication Year: 1995 , Page(s): 831 - 840
    Cited by:  Papers (9)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (788 KB)  

    A new approach is developed for finding the optimal stack filter that minimizes noise subject to constraints on its structural behavior. Based on the output moments of stack filters, it is proven that the optimal stack filter is a combination of the median filter, which has the same window width as the stack filter, and a set of maximum and minimum filters, which are attributed to the structural constraints. Design examples for 1-D signal processing and image processing are provided View full abstract»

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  • Estimation of amplitude and phase parameters of multicomponent signals

    Publication Year: 1995 , Page(s): 917 - 926
    Cited by:  Papers (51)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (740 KB)  

    This paper considers the problem of estimating signals consisting of one or more components of the form a(t)ejφ(t), where the amplitude and phase functions are represented by a linear parametric model. The Cramer-Rao bound (CRB) on the accuracy of estimating the phase and amplitude parameters is derived. By analyzing the CRB for the single-component case, if is shown that the estimation of the amplitude and the phase are decoupled. Numerical evaluation of the CRB provides further insight into the dependence of estimation accuracy on signal-to-noise ratio (SNR) and the frequency separation of the signal components. A maximum likelihood algorithm for estimating the phase and amplitude parameters is also presented. Its performance is illustrated by Monte-Carlo simulations, and its statistical efficiency is verified View full abstract»

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  • Gaussian mixture density modeling of non-Gaussian source for autoregressive process

    Publication Year: 1995 , Page(s): 894 - 903
    Cited by:  Papers (19)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (780 KB)  

    A new approach is taken to model non-Gaussian sources of AR processes using Gaussian mixture densities that are known to be effective for approximating wide varieties of probability distributions. A maximum likelihood estimation algorithm is derived for estimating the AR parameters by solving a generalized normal equation, and a clustering algorithm is used for estimating the parameters of Gaussian mixture density of the source signals. The correlation matrix of the generalized normal equation is not Toeplitz but is symmetric and in general positive definite. Higher order statistics of skewness and kurtosis are used for identifying the source distribution as being Gaussian or non-Gaussian and, consequently, determining the parameter estimation technique between the conventional method and the proposed method. Experiments on non-Gaussian source AR processes demonstrate that under high SNR conditions (SNR⩾20 dB), the proposed algorithm outperforms the conventional AR estimation algorithm and the cumulant-based algorithm by an order-of-magnitude reduction of average estimation errors. The proposed algorithm also has very low estimation errors with short data records. Finally, a maximum likelihood prediction method is formulated for non-Gaussian source AR processes that has shown potential in achieving higher efficiency signal coding than linear predictive coding View full abstract»

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  • Sample cumulants of stationary processes: asymptotic results

    Publication Year: 1995 , Page(s): 967 - 977
    Cited by:  Papers (8)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (844 KB)  

    In this paper, we present the formulas of the covariances of the second-, third-, and fourth-order sample cumulants of stationary processes. These expressions are then used to obtain the analytic performance of FIR system identification methods as a function of the coefficients and the statistics of the input sequence. The lower bound in the variance is also compared for different sets of sample statistics to provide insight about the information carried by each sample statistic. Finally, the effect that the presence of noise has on the accuracy of the estimates is studied analytically. The results are illustrated graphically with plots of the variance of the estimates as a function of the parameters or the signal-to-noise ratio. Monte Carlo simulations are also included to compare their results with the predicted analytic performance View full abstract»

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  • A complete factorization of paraunitary matrices with pairwise mirror-image symmetry in the frequency domain

    Publication Year: 1995 , Page(s): 1002 - 1004
    Cited by:  Papers (8)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (220 KB)  

    The problem of designing orthonormal (paraunitary) filter banks has been addressed in the past. Several structures have been reported for implementing such systems. One of the structures reported imposes a pairwise mirror-image symmetry constraint on the frequency responses of the analysis (and synthesis) filters around π/2. This structure requires fewer multipliers, and the design time is correspondingly less than most other structures. The filters designed also have much better attenuation. We characterize the polyphase matrix of the above filters in terms of a matrix equation. We then prove that the structure reported in a paper by Nguyen and Vaidyanathan (1988), with minor modifications, is complete. This means that every polyphase matrix whose filters satisfy the mirror-image property can be factorized in terms of the proposed structure View full abstract»

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  • The estimation of time delay and Doppler stretch of wideband signals

    Publication Year: 1995 , Page(s): 904 - 916
    Cited by:  Papers (32)  |  Patents (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (916 KB)  

    The problem of estimating the time delay and the Doppler stretch for wideband signals from a moving target is considered. The Cramer-Rao bound and the maximum likelihood (ML) method of estimation are derived. Due to the uncertainty of the reflection coefficient, the ML method may not be practicable. An alternative method involving the location of the peak of the wideband ambiguity function of the signal is suggested. The performance of the method is analysed, and, under high signal-to-noise ratios (SNRs), the method is asymptotically unbiased, and the variances of the estimates are closed to the Cramer-Rao bound for a large variety of signals. Optimum signals for the joint estimation of the time delay and the Doppler stretch under practical constraints are designed and, through computer simulations, their performance are shown to be superior to the commonly used signals View full abstract»

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  • A class of high-precision multiplier-free FIR filter realizations with periodically time-varying coefficients

    Publication Year: 1995 , Page(s): 822 - 830
    Cited by:  Papers (4)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (752 KB)  

    Proposes a class of high-precision, multiplier-free realizations for FIR filters. These realizations use upsampling and downsampling in conjunction with a periodically time-varying system to achieve time-invariant, multiplier-free FIR filter operation. Nonbinary encoding schemes are used for obtaining the filter coefficients, which are periodically time-varying (PTV), i.e., they vary in a periodic fashion. Each target filter coefficient is directly mapped into a set of PTV coefficients so that the realizations are easy to obtain. The values of the PTV coefficients are restricted to either the ternary set {±1, 0} or the quinary set {±2, ±1, 0} so that the realizations can be implemented with only add/subtract and one-bit shift (for the quinary case) operations. A few shift-and-add operations are also needed at the beginning and the end of the structure. Coefficient precisions (in bits) of these realizations are given and they are sufficiently high for most applications. Advantages of the proposed realizations accrue at the expense of a higher clock rate View full abstract»

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  • On computing and implementing the running bispectra

    Publication Year: 1995 , Page(s): 1017 - 1021
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (396 KB)  

    The paper extends recursion to bispectrum estimation problems and presents the systolic array implementation of the recursive higher order spectrum in which the bispectrum estimate is updated every data sample. Forward and reverse sequence running Fourier transforms are first systolically realized. The results are then used to drive a second systolic array, whose outputs represent the FT of the data third-order moment. The proposed systolic arrays have no global communications with a number of processing elements independent of the size of the employed 2D lag window View full abstract»

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  • Direction finding with time-varying arrays

    Publication Year: 1995 , Page(s): 927 - 937
    Cited by:  Papers (17)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (900 KB)  

    This paper considers the problem of finding the directions of narrowband signals using a time-varying array, whose elements move during the observation interval in an arbitrary but known way. Assuming a Gaussian signal model, we derive the Cramer-Rao bound (CRB) and the maximum likelihood estimator for the directions of arrival. The single source case is studied in detail. Time-varying arrays are shown to be more robust to ambiguity errors than static arrays of comparable dimensions View full abstract»

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  • Cramer-Rao lower bounds for a damped sinusoidal process

    Publication Year: 1995 , Page(s): 878 - 885
    Cited by:  Papers (25)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (436 KB)  

    The Cramer-Rao lower bounds (CRLBs) for the parameter estimators of a damped sinusoidal process are derived in this paper. Succinct matrix expressions for CRLB's of frequency, damping factor, amplitude, and initial phase are given for both scalar and vector processes. The relationships between the CRLBs of the characteristic parameters are established in the general multimode case. In particular, explicit, closed-form expressions for the single mode scalar/vector-damped/undamped cases are provided View full abstract»

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  • Behavior of the partial correlation coefficients of a least squares lattice filter in the presence of a nonstationary chirp input

    Publication Year: 1995 , Page(s): 852 - 863
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (904 KB)  

    This paper studies the performance of the a posteriori recursive least squares lattice filter in the presence of a nonstationary chirp signal. The forward and backward partial correlation (PARCOR) coefficients for a Wiener-Hopf optimal filter are shown to be complex conjugates for the general case of a nonstationary input with constant power. Such an optimal filter is compared to a minimum mean square error based least squares lattice adaptive filter. Expressions are found for the behavior of the first stage of the adaptive filter based on the least squares algorithm. For the general nth stage, the PARCOR coefficients of the previous stages are assumed to have attained Wiener-Hopf optimal steady state. The PARCOR coefficients of such a least squares adaptive filter are compared with the optimal coefficients for such a nonstationary input. The optimal lattice fitter is seen to track a chirp input without any error, and the tracking lag in such an adaptive filter is due to the least squares update procedure. The expression for the least squares based PARCOR coefficients are found to contain two terms: a decaying convergence term due to the weighted estimation procedure and a tracking component that asymptotically approaches the optimal coefficient value. The rate of convergence is seen to depend inversely on the forgetting factor. The tracking lag of the filter is derived as a function of the rate of nonstationarity and the forgetting factor. It is shown that for a given chirp rate there is a threshold adaptation constant below which the total tracking error is negligible. For forgetting factors above this threshold, the error increases nonlinearly. Further, this threshold forgetting factor decreases with increasing chirp rate. Simulations are presented to validate the analysis 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
Sergios Theodoridis
University of Athens