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Signal Processing, IEEE Transactions on

Issue 1 • Date Jan. 2009

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Displaying Results 1 - 25 of 44
  • Table of contents

    Page(s): C1 - C4
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    Freely Available from IEEE
  • IEEE Transactions on Signal Processing publication information

    Page(s): C2
    Save to Project icon | Request Permissions | PDF file iconPDF (38 KB)  
    Freely Available from IEEE
  • A Message From the New Editor-in-Chief

    Page(s): 1
    Save to Project icon | Request Permissions | PDF file iconPDF (24 KB)  
    Freely Available from IEEE
  • Stochastic Resonance in Sequential Detectors

    Page(s): 2 - 15
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (677 KB) |  | HTML iconHTML  

    Stochastic resonance (SR) is a nonlinear phenomenon known in physics that has attracted recent interest in the signal-processing literature, and specifically in the context of detection. We investigate the SR effect arising in sequential detectors for shift-in-mean binary hypothesis testing and characterize the optimal resonance as the solution of specific optimization problems. One particular (and at first glance perhaps counterintuitive) finding is that certain sequential detection procedures can be made more efficient by randomly adding or subtracting a suitable constant value to the data at the input of the detector. View full abstract»

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  • Distributed Detection in the Presence of Byzantine Attacks

    Page(s): 16 - 29
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (746 KB) |  | HTML iconHTML  

    Distributed detection in the presence of cooperative (Byzantine) attack is considered. It is assumed that a fraction of the monitoring sensors are compromised by an adversary, and these compromised (Byzantine) sensors are reprogrammed to transmit fictitious observations aimed at confusing the decision maker at the fusion center. For detection under binary hypotheses with quantized sensor observations, the optimal attacking distributions for Byzantine sensors that minimize the detection error exponent are obtained using a ldquowater-fillingrdquo procedure. The smallest error exponent, as a function of the Byzantine sensor population, characterizes the power of attack. Also obtained is the minimum fraction of Byzantine sensors that destroys the consistency of detection at the fusion center. The case when multiple measurements are made at the remote nodes is also considered, and it is shown that the detection performance scales with the number of sensors differently from the number of observations at each sensor. View full abstract»

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  • Vehicle Speed Estimation Using Acoustic Wave Patterns

    Page(s): 30 - 47
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (2112 KB) |  | HTML iconHTML  

    We estimate a vehicle's speed, its wheelbase length, and tire track length by jointly estimating its acoustic wave pattern with a single passive acoustic sensor that records the vehicle's drive-by noise. The acoustic wave pattern is determined using the vehicle's speed, the Doppler shift factor, the sensor's distance to the vehicle's closest-point-of-approach, and three envelope shape (ES) components, which approximate the shape variations of the received signal's power envelope. We incorporate the parameters of the ES components along with estimates of the vehicle engine RPM, the number of cylinders, and the vehicle's initial bearing, loudness and speed to form a vehicle profile vector. This vector provides a fingerprint that can be used for vehicle identification and classification. We also provide possible reasons why some of the existing methods are unable to provide unbiased vehicle speed estimates using the same framework. The approach is illustrated using vehicle speed estimation and classification results obtained with field data. View full abstract»

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  • Detection of Multiple Changes in Fractional Integrated ARMA Processes

    Page(s): 48 - 61
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1555 KB) |  | HTML iconHTML  

    This paper addresses the problem of changepoint detection in FARIMA processes. The received signal is modeled as a FARIMA process, with abrupt changes in the Hurst and ARMA parameters. The proposed changepoint detection method first estimates the model parameters over small segments. The changes are then detected in the parameter vector sequence by minimizing an appropriate least-squares criterion. The cases of known, as well as unknown, number of changes are investigated. Dynamic programming is used to solve this optimization problem. A theoretical analysis of the statistical properties of the change point estimates is provided. Simulation results on synthetic data and real network traffic data are presented. View full abstract»

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  • Estimation of the Parameters of Sinusoidal Signals in Non-Gaussian Noise

    Page(s): 62 - 72
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (928 KB) |  | HTML iconHTML  

    Accurate estimation of the amplitude and frequency parameters of sinusoidal signals from noisy observations is an important problem in many signal processing applications. In this paper, the problem is investigated under the assumption of non-Gaussian noise in general and Laplace noise in particular. It is proven mathematically that the maximum likelihood estimator derived under the condition of Laplace white noise is able to attain an asymptotic Cramer-Rao lower bound which is one half of that achieved by periodogram maximization and nonlinear least squares. It is also proven that when applied to non-Laplace situations, the Laplace maximum likelihood estimator, which may also be referred to as the nonlinear least-absolute-deviations estimator, can achieve an even higher statistical efficiency especially when the noise distribution has heavy tails. A computational procedure is proposed to overcome the difficulty of local extrema in the likelihood function. Simulation results are provided to validate the analytical findings. View full abstract»

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  • Performance Limits of Alphabet Diversities for FIR SISO Channel Identification

    Page(s): 73 - 82
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (582 KB) |  | HTML iconHTML  

    Finite impulse responses (FIR) of single-input single-output (SISO) channels can be blindly identified from second-order statistics of transformed data, for instance when the channel is excited by binary phase shift keying (BPSK), minimum shift keying (MSK), or quadrature phase shift keying (QPSK) inputs. Identifiability conditions are derived by considering that noncircularity induces diversity. Theoretical performance issues are addressed to evaluate the robustness of standard subspace-based estimators with respect to these identifiability conditions. Then benchmarks such as asymptotically minimum variance (AMV) bounds based on various statistics are presented. Some illustrative examples are eventually given where Monte Carlo experiments are compared to theoretical performances. These comparisons allow to quantify limits to the use of the alphabet diversities for the identification of FIR SISO channels, and to demonstrate the robustness of algorithms based on high-order statistics. View full abstract»

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  • Data-Driven Spatio-Temporal Modeling Using the Integro-Difference Equation

    Page(s): 83 - 91
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (564 KB) |  | HTML iconHTML  

    A continuous-in-space, discrete-in-time dynamic spatio-temporal model known as the integro-difference equation (IDE) model is presented in the context of data-driven modeling. A novel decomposition of the IDE is derived, leading to state-space representation that does not couple the number of states with the number of observation locations or the number of parameters. Based on this state-space model, an expectation-maximization (EM) algorithm is developed in order to jointly estimate the IDE model's spatial field and spatial mixing kernel. The resulting modeling framework is demonstrated on a set of examples. View full abstract»

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  • Multitask Compressive Sensing

    Page(s): 92 - 106
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (2433 KB) |  | HTML iconHTML  

    Compressive sensing (CS) is a framework whereby one performs N nonadaptive measurements to constitute a vector v isin RN used to recover an approximation u isin RM desired signal u isin RM with N << M this is performed under the assumption that u is sparse in the basis represented by the matrix Psi RMtimesM. It has been demonstrated that with appropriate design of the compressive measurements used to define v, the decompressive mapping vrarru may be performed with error ||u-u||2 2 having asymptotic properties analogous to those of the best adaptive transform-coding algorithm applied in the basis Psi. The mapping vrarru constitutes an inverse problem, often solved using l1 regularization or related techniques. In most previous research, if L > 1 sets of compressive measurements {vi}i=1,L are performed, each of the associated {ui}i=1,Lare recovered one at a time, independently. In many applications the L ldquotasksrdquo defined by the mappings virarrui are not statistically independent, and it may be possible to improve the performance of the inversion if statistical interrelationships are exploited. In this paper, we address this problem within a multitask learning setting, wherein the mapping vrarru for each task corresponds to inferring the parameters (here, wavelet coefficients) associated with the desired signal vi, and a shared prior is placed across all of the L tasks. Under this hierarchical Bayesian modeling, data from all L tasks contribute toward inferring a posterior on the hyperparameters, and once the shared prior is thereby inferred, the data from each of the L individual tasks is then employed to estimate the task-dependent wavelet coefficients. An empirical Bayesian procedure for the estimation of hyperparameters is considered; two fast inference algorithms extending the relevance vector - - machine (RVM) are developed. Example results on several data sets demonstrate the effectiveness and robustness of the proposed algorithms. View full abstract»

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  • A Stochastic Model for a Pseudo Affine Projection Algorithm

    Page(s): 107 - 118
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1661 KB) |  | HTML iconHTML  

    This paper presents a statistical analysis of a Pseudo Affine Projection (PAP) algorithm, obtained from the Affine Projection algorithm (AP) for a step size alpha < 1 and a scalar error signal in the weight update. Deterministic recursive equations are derived for the mean weight and for the mean square error (MSE) for a large number of adaptive taps N compared to the order P of the algorithm. Simulations are presented which show good to excellent agreement with the theory in the transient and steady states. The PAP learning behavior is of special interest in applications where tradeoffs are necessary between convergence speed and steady-state misadjustment. View full abstract»

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  • Stability and Convergence Analysis of Transform-Domain LMS Adaptive Filters With Second-Order Autoregressive Process

    Page(s): 119 - 130
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1257 KB) |  | HTML iconHTML  

    In this paper, the stability and convergence properties of the class of transform-domain least mean square (LMS) adaptive filters with second-order autoregressive (AR) process are investigated. It is well known that this class of adaptive filters improve convergence property of the standard LMS adaptive filters by applying the fixed data-independent orthogonal transforms and power normalization. However, the convergence performance of this class of adaptive filters can be quite different for various input processes, and it has not been fully explored. In this paper, we first discuss the mean-square stability and steady-state performance of this class of adaptive filters. We then analyze the effects of the transforms and power normalization performed in the various adaptive filters for both first-order and second-order AR processes. We derive the input asymptotic eigenvalue distributions and make comparisons on their convergence performance. Finally, computer simulations on AR process as well as moving-average (MA) process and autoregressive-moving-average (ARMA) process are demonstrated for the support of the analytical results. View full abstract»

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  • Overcomplete Discrete Wavelet Transforms With Rational Dilation Factors

    Page(s): 131 - 145
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (555 KB) |  | HTML iconHTML  

    This paper develops an overcomplete discrete wavelet transform (DWT) based on rational dilation factors for discrete-time signals. The proposed overcomplete rational DWT is implemented using self-inverting FIR filter banks, is approximately shift-invariant, and can provide a dense sampling of the time-frequency plane. A straightforward algorithm is described for the construction of minimal-length perfect reconstruction filters with a specified number of vanishing moments; whereas, in the nonredundant rational case, no such algorithm is available. The algorithm is based on matrix spectral factorization. The analysis/synthesis functions (discrete-time wavelets) can be very smooth and can be designed to closely approximate the derivatives of the Gaussian function. View full abstract»

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  • Higher-Order Properties of Analytic Wavelets

    Page(s): 146 - 160
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1728 KB) |  | HTML iconHTML  

    The influence of higher-order wavelet properties on the analytic wavelet transform behavior is investigated, and wavelet functions offering advantageous performance are identified. This is accomplished through detailed investigation of the generalized Morse wavelets, a two-parameter family of exactly analytic continuous wavelets. The degree of time/frequency localization, the existence of a mapping between scale and frequency, and the bias involved in estimating properties of modulated oscillatory signals, are proposed as important considerations. Wavelet behavior is found to be strongly impacted by the degree of asymmetry of the wavelet in both the frequency and the time domain, as quantified by the third central moments. A particular subset of the generalized Morse wavelets, recognized as deriving from an inhomogeneous Airy function, emerge as having particularly desirable properties. These ldquoAiry waveletsrdquo substantially outperform the only approximately analytic Morlet wavelets for high time localization. Special cases of the generalized Morse wavelets are examined, revealing a broad range of behaviors which can be matched to the characteristics of a signal. View full abstract»

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  • A Fast Convergence Algorithm for Band-Limited Extrapolation by Sampling

    Page(s): 161 - 167
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1330 KB) |  | HTML iconHTML  

    In this paper, an algorithm for band-limited extrapolation is presented. This uses Shannon's sampling theorem and Fourier series. Error analysis is given by proof. The convergence rate is much faster than that of the Papoulis-Gerchberg algorithm. The procedure of the fast convergence algorithm is described in detail. The result is demonstrated by numerical examples. View full abstract»

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  • Functionally Weighted Lagrange Interpolation of Band-Limited Signals From Nonuniform Samples

    Page(s): 168 - 181
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (479 KB) |  | HTML iconHTML  

    A modification of the conventional Lagrange interpolator is proposed in this paper, that allows one to approximate a band-limited signal from its own nonuniform samples with high accuracy. The modification consists in applying the Lagrange method to the signal, but pre-multiplied by a fixed function, and then solving for the desired signal value. Its efficiency lies in the fact that the fixed function is independent of the sampling instants. It is shown in this paper that the function can be selected so that the interpolation error decreases exponentially with the number of samples, for the case in which the sampling instants have a maximum deviation from a uniform grid. This paper includes a low-complexity recursive implementation of the method. Its accuracy is validated in the numerical examples by comparison with several interpolators in the literature, and by deriving upper and lower bounds for its maximum error. View full abstract»

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  • On the Accuracy and Resolution of Powersum-Based Sampling Methods

    Page(s): 182 - 193
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (476 KB) |  | HTML iconHTML  

    Recently, several sampling methods suitable for signals that are sums of Diracs have been proposed. Though they are implemented through different acquisition architectures, these methods all rely on estimating the parameters of a powersum series. We derive Cramer-Rao lower bounds (CRBs) for estimation of the powersum poles, which translate to the Dirac positions. We then demonstrate the efficacy of simple algorithms due to Prony and Cornell for low-order powersums and low oversampling relative to the rate of innovation. The simulated performance illustrates the possibility of superresolution reconstruction and robustness to correlation in the powersum sample noise. View full abstract»

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  • Random Sampling Estimates of Fourier Transforms: Antithetical Stratified Monte Carlo

    Page(s): 194 - 204
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (748 KB) |  | HTML iconHTML  

    We estimate the Fourier transform of continuous-time signals on the basis of N discrete-time nonuniform observations. We introduce a class of antithetical stratified random sampling schemes and we obtain the performance of the corresponding estimates. We show that when the underlying function f(t) has a continuous second-order derivative, the rate of mean square convergence is 1/N 5, which is considerably faster that the rate of 1/N 3 for stratified sampling and the rate of 1/N for standard Monte Carlo integration. In addition, we establish joint asymptotic normality for the real and imaginary parts of the estimate and give an explicit expression for the asymptotic covariance matrix. The theoretical results are illustrated by examples for low-pass and high-pass signals. View full abstract»

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  • Algebraic Signal Processing Theory: Cooley–Tukey Type Algorithms for Real DFTs

    Page(s): 205 - 222
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (797 KB) |  | HTML iconHTML  

    In this paper, we systematically derive a large class of fast general-radix algorithms for various types of real discrete Fourier transforms (real DFTs) including the discrete Hartley transform (DHT) based on the algebraic signal processing theory. This means that instead of manipulating the transform definition, we derive algorithms by manipulating the polynomial algebras underlying the transforms using one general method. The same method yields the well-known Cooley-Tukey fast Fourier transform (FFT) as well as general radix discrete cosine and sine transform algorithms. The algebraic approach makes the derivation concise, unifies and classifies many existing algorithms, yields new variants, enables structural optimization, and naturally produces a human-readable structural algorithm representation based on the Kronecker product formalism. We show, for the first time, that the general-radix Cooley-Tukey and the lesser known Bruun algorithms are instances of the same generic algorithm. Further, we show that this generic algorithm can be instantiated for all four types of the real DFT and the DHT. View full abstract»

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  • Variational Bayesian Inference for a Nonlinear Forward Model

    Page(s): 223 - 236
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (973 KB) |  | HTML iconHTML  

    Variational Bayes (VB) has been proposed as a method to facilitate calculations of the posterior distributions for linear models, by providing a fast method for Bayesian inference by estimating the parameters of a factorized approximation to the posterior distribution. Here a VB method for nonlinear forward models with Gaussian additive noise is presented. In the case of noninformative priors the parameter estimates obtained from this VB approach are identical to those found via nonlinear least squares. However, the advantage of the VB method lies in its Bayesian formulation, which permits prior information to be included in a hierarchical structure and measures of uncertainty for all parameter estimates to be obtained via the posterior distribution. Unlike other Bayesian methods VB is only approximate in comparison with the sampling method of MCMC. However, the VB method is found to be comparable and the assumptions made about the form of the posterior distribution reasonable. Practically, the VB approach is substantially faster than MCMC as fewer calculations are required. Some of the advantages of the fully Bayesian nature of the method are demonstrated through the extension of the noise model and the inclusion of automatic relevance determination (ARD) within the VB algorithm. View full abstract»

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  • A Novel Adaptive Nonlinear Filter-Based Pipelined Feedforward Second-Order Volterra Architecture

    Page(s): 237 - 246
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (707 KB) |  | HTML iconHTML  

    Due to the computational complexity of the Volterra filter, there are limitations on the implementation in practice. In this paper, a novel adaptive joint process filter using pipelined feedforward second-order Volterra architecture (JPPSOV) to reduce the computational burdens of the Volterra filter is proposed. The proposed architecture consists of two subsections: nonlinear subsection performing a nonlinear mapping from the input space to an intermediate space by the feedforward second-order Volterra (SOV), and a linear combiner performing a linear mapping from the intermediate space to the output space. The corresponding adaptive algorithms are deduced for the nonlinear and linear combiner subsections, respectively. Moreover, the analysis of theory shows that these adaptive algorithms based on the pipelined architecture are stable and convergence under a certain condition. To evaluate the performance of the JPPSOV, a series of simulation experiments are presented including nonlinear system identification and predicting of speech signals. Compared with the conventional SOV filter, adaptive JPPSOV filter exhibits a litter better convergence performance with less computational burden in terms of convergence speed and steady-state error. View full abstract»

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  • Influence Function and Asymptotic Efficiency of Scatter Matrix Based Array Processors: Case MVDR Beamformer

    Page(s): 247 - 259
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (901 KB) |  | HTML iconHTML  

    In this paper, we consider array processors that are scale-invariant functions of the array covariance matrix. The emphasis is on Capon's MVDR beamformer. We call such an array processor as scatter matrix based (SMB) array processor since the covariance matrix is required only up to a constant scalar and thus a scatter matrix (proportional to covariance under finite covariance assumption) provides sufficient information. In order to establish interesting statistical robustness and large sample properties, we derive a general expression for the influence function and the asymptotic covariance structure of SMB-MVDR beamformer weights. Our results apply under the class of complex elliptically symmetric distributions, which includes the commonly used complex normal distribution as a special case. We illustrate the theory by deriving the IF and asymptotic relative efficiencies of the conventional SMB-MVDR beamformer that employs the sample covariance matrix and beamformers that employ robust M -estimators of scatter. Theoretical findings are confirmed by simulations. Our findings favor beamformers based upon M-estimators of scatter, since they combine a high efficiency with appealing robustness properties. View full abstract»

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  • A Novel Subspace Approach for Cooperative Localization in Wireless Sensor Networks Using Range Measurements

    Page(s): 260 - 269
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (488 KB) |  | HTML iconHTML  

    Estimating the positions of sensor nodes is a fundamental and crucial problem in wireless sensor networks. In this paper, three novel subspace methods for node localization in a fully connected network are devised with the use of range measurements. Biases and mean square errors of the sensor node position estimates are also derived. Computer simulations are included to contrast the performance of the proposed algorithms with the conventional subspace positioning method, namely, classical multidimensional scaling, as well as Cramer-Rao lower bound. View full abstract»

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  • Tail Extrapolation in MLSE Receivers Using Nonparametric Channel Model Estimation

    Page(s): 270 - 278
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (354 KB) |  | HTML iconHTML  

    This paper presents a method for determining the probability of rare events, in particular for probability density function (pdf) and bit error rate (BER) estimation. The derivation of the method is based on the presumption that the pdf is a member of a family of distributions very often named as the generalized exponential (GE) class of distributions. Based on high reliability estimations obtained in short simulation/measurement times, the low probably events are estimated accurately by extrapolation. The suggested method can be applied to some distributions that are different from GE distributions, such as noncentral chi-square distributions, to extrapolate to low probability events, with some extrapolation error. It can also be applied to BER estimation. The method is in particular helpful for estimating channels suffering from both severe signal distortion causing undesired intersymbol interference (ISI) of several symbols, and from severe noise. Such conditions prevail, for example, in metro and long haul high-speed optical fiber communication systems. So the method may be implemented in particular in maximum-likelihood sequence estimation (MLSE) optical receivers using nonparametric channel model estimation. A special use of the extrapolation method is explained for practical systems using trellis branch metrics derived from the estimated pdf to decode the transmitted sequence of symbols. 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

Full Aims & Scope

Meet Our Editors

Editor-in-Chief
Zhi-Quan (Tom) Luo
University of Minnesota