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Signal Processing, IEEE Transactions on

Issue 6 • Date June 1997

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Displaying Results 1 - 25 of 28
  • Corrections to "Matched Subspace Detectors"

    Page(s): 1669
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  • Comparative study of four adaptive frequency trackers

    Page(s): 1473 - 1484
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    We study and compare four algorithms for adaptive retrieval of slowly time-varying multiple cisoids in noise: the adaptive notch filter, the multiple frequency tracker, the adaptive estimation scheme, and the hyperstable adaptive line enhancer. The local behavior of the algorithms in a neighborhood of their equilibrium state [assuming high signal-to-noise ratio (SNR) and large data sample] for a two-cisoid signal is treated in a similar way to the linear filter approximation technique used for a single-cisoid case. The validity of the results is confirmed by computer simulations View full abstract»

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  • LMS-like AR modeling in the case of missing observations

    Page(s): 1574 - 1583
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    This paper presents a new recursive algorithm for the time domain reconstruction and spectral estimation of uniformly sampled signals with missing observations. An autoregressive (AR) modeling approach is adopted. The AR parameters are estimated by optimizing a mean-square error criterion. The optimum is reached by means of a gradient method adapted to the nonperiodic sampling. The time-domain reconstruction is based on the signal prediction using the estimated model. The power spectral density is obtained using the estimated AR parameters. The development of the different steps of the algorithm is discussed in detail, and several examples are presented to demonstrate the practical results that can be obtained. The spectral estimates are compared with those obtained by known AR estimators applied to the same signals sampled periodically. We note that this algorithm can also be used in the case of nonstationary signals View full abstract»

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  • Cumulant-based blind identification of linear multi-input-multi-output systems driven by colored inputs

    Page(s): 1543 - 1552
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    The blind identification problem of a linear multi-input-multi-output (MIMO) system is widely noticed by many researchers in diverse fields due to its relevance to blind signal separation. However, such a problem is ill-posed and has no unique solution. Therefore, we can only find a solution of the problem within an equivalence class. We address the blind identification problem of the linear MIMO system driven by unobservable colored inputs using higher order statistics (HOS), particularly the fourth-order cumulants, of the outputs, where the unobservable inputs are mutually independent but temporally colored linear processes. We first define the set, which is denoted by S, of stable scalar transfer functions and then define the notion of a generalized permutation matrix (which is abbreviated by a g-matrix) over S. Then, it is shown that the transfer function matrix of an unknown system is identified only up to post-multiplication by a g matrix. This result is applied to identifying FIR systems for blind signal separation View full abstract»

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  • Short-time Fourier analysis via optimal harmonic FIR filters

    Page(s): 1535 - 1542
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    The Fourier coefficients (FCs) of quasiperiodic signals are assumed to be in random walk motion in order to represent a broader class. A state model for such quasiperiodic signals is derived. The optimal short-time estimate of the Fourier coefficients is obtained via the suggested optimal harmonic FIR filter (OHFF) based on this state-space signal model. The optimal harmonic FIR filter can be considered to be a generalization of the discrete Fourier transform (DFT) in the sense that it becomes the same as the DFT when the state model is for periodic signals and the filter length is equal to the order of the state model. The optimal harmonic FIR filter derived from the model, even with nonzero state noise and measurement noise, gives an exact harmonic estimate when an incoming signal is periodic and noiseless. It is shown by examples that the ability to suppress noise and the ability to resolve changes of the Fourier coefficients can be adjusted by the filter length and the noise covariance of the state model. Finally, the suggested scheme is compared with existing short-time Fourier analysis methods in a test signal that has time-varying Fourier coefficients View full abstract»

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  • Robustness of oversampled Gabor transient detectors: a comparison of energy and known location detectors

    Page(s): 1638 - 1641
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    This correspondence provides a “context” for previous studies on the use of linear time-frequency transforms for transient signal detection in the case where signal component locations are assumed to be known. The robustness of a known-location detector (KLD) based on the oversampled Gabor transform is compared with that of the corresponding energy detector in the Gabor domain. As expected, the KLD was sensitive to location mismatch; unexpectedly, it was extremely sensitive to location mismatch View full abstract»

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  • Detection of cisoids using least square error function

    Page(s): 1584 - 1590
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    In this paper, we propose a new hypothesis testing method for detection of cisoids (complex sinusoids) from a single measurement of data. The testing is performed on the least square error. The least square error is shown to exhibit χ 2 distribution, which leads to an efficient threshold setup for the proposed method. The new method is a combined detection-estimation technique and provides improved performance over several existing techniques View full abstract»

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  • Multiscale deconvolution of sensor array signals via sum-of-cumulants

    Page(s): 1656 - 1659
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    This correspondence presents a solution to a multiscale deconvolution problem using higher order spectra where the data to be deconvolved consist of noise-corrupted sensor array measurements. We assume that the data are generated as a convolution of an unknown wavelet with reflectivity sequences that are linearly time-scaled versions of an unknown reference reflectivity sequence. This type of data occurs in many signal processing applications, including sonar and seismic processing. Our approach relies on exploiting the redundancy in the measurements due to time scaling and does not require knowledge of the wavelet or the reflectivity sequences. We formulate and solve the deconvolution problem as a quadratic minimization subject to a quadratic constraint in the sum-of-cumulants (SOC) domain. The formulation using the SOC approach reduces the effect of additive Gaussian noise on the accuracy of the results when compared with the standard time-domain formulation. We demonstrate this improvement using a simulation example View full abstract»

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  • Further results on the minimum variance time-frequency distribution kernels

    Page(s): 1650 - 1655
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    Results for the minimum variance kernel, presented by Hearon and Amin (see ibid., vol.43, p.1258, 1995), for the complex Gaussian white noise with independent real and imaginary parts remain valid for real noise and approximately valid for analytic noise. These results are extended to the real and analytic noisy signals cases View full abstract»

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  • Robust detection with the gap metric

    Page(s): 1591 - 1604
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    In a multipath communication channel, the optimal receiver is matched to the maximum likelihood (ML) estimate of the multipath signal. In general, this leads to a computationally intensive multidimensional nonlinear optimization problem that is not feasible in most applications. We develop a detection algorithm that avoids finding the ML estimates of the channel parameters while still achieving good performance. Our approach is based on a geometric interpretation of the multipath detection problem. The ML estimate of the multipath signal is the orthogonal projection of the received signal on a suitable signal subspace S. We design a second subspace G, which is the representation subspace, that is close to S but whose orthogonal projection is easily computed. The closeness is measured by the gap metric. The subspace G is designed by using wavelet analysis tools coupled with a reshaping algorithm in the Zak transform domain. We show examples where our approach significantly outperforms the conventional correlator receiver (CR) and other alternative suboptimal detectors View full abstract»

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  • An accurate error analysis model for fast Fourier transform

    Page(s): 1641 - 1645
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    An error propagation model is proposed for the in-place decimation-in-time version of the radix-2 FFT algorithm. With the model, an accurate error expression and error variance for the computation of FFT are derived. This correspondence deals with fixed-point and block floating-point arithmetic. Simulation results agree closely with the theoretical predicted ones. We find that some roundoff errors at different stages correlate with each other. The density of correlations is closely associated with the round-off approach used in butterfly calculations View full abstract»

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  • A unified minimum variance spectrum-based approach for simultaneous identification of both harmonic and stationary random noise fields

    Page(s): 1659 - 1663
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    The technique presented in this correspondence uses the MV spectrum's convergence properties to identify unknown and arbitrary harmonic signal fields. The correlation sequence for the identified harmonic signal field is then combined with the observed overall correlation sequence to obtain a spectral model of the random noise field View full abstract»

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  • A structural view of asymptotic convergence speed of adaptive IIR filtering algorithm. II. Finite precision implementation

    Page(s): 1458 - 1472
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    For pt.I see ibid., vol.41, no.4, p.1493-1517, 1993. Finite precision (FP) implementation is the ultimately inevitable reality of all adaptive filters, including adaptive infinite impulse response (IIR) filters. This paper continues to examine the asymptotic convergence speed of adaptive IIR filters of various structures and algorithms, including the simple constant gain type and the Newton type, but under FP implementation. A stochastic differential equation (SDE) approach is used in the analysis. Such an approach not only greatly simplifies the FP analysis, which is traditionally very involved algebraically, but it also provides valuable information about the first-order as well as the second-order moments that (the latter) are not available using the ordinary differential equation (ODE) approach. The asymptotic convergence speed, as well as the convergent values, of the pertinent moments of FP errors are examined in terms of unknown system pole-zero locations. The adverse effects of lightly damped low-frequency (LDLF) poles resulting from fast sampling on the local transient and convergent behavior of various structures and algorithms are analyzed and compared. The new results agree with the existing ones when reduced to the finite impulse response (FIR) case. In particular, the explosive behavior of pertinent error variances of Newton-type IIR algorithms when the forgetting factor λ=1 is also concluded. Computer simulation verifies the predicted theoretical results View full abstract»

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  • An exact maximum likelihood registration algorithm for data fusion

    Page(s): 1560 - 1573
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    Data fusion is a process dealing with the association, correlation, and combination of data and information from multiple sources to achieve refined position and identity estimates. We consider the registration problem, which is a prerequisite process of a data fusion system to accurately estimate and correct systematic errors. An exact maximum likelihood (EML) algorithm for registration is presented. The algorithm is implemented using a recursive two-step optimization that involves a modified Gauss-Newton procedure to ensure fast convergence. Statistical performance of the algorithm is also investigated, including its consistency and efficiency discussions. In particular, the explicit formulas for both the asymptotic covariance and the Cramer-Rao bound (CRB) are derived. Finally, simulated and real-life multiple radar data are used to evaluate the performance of the proposed algorithm View full abstract»

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  • Modular learning strategy for signal detection in a nonstationary environment

    Page(s): 1619 - 1637
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    We describe a novel modular learning strategy for the detection of a target signal of interest in a nonstationary environment, which is motivated by the information preservation rule. The strategy makes no assumptions on the environment. It incorporates three functional blocks: (1) time-frequency analysis, (2) feature extraction, and (3) pattern classification, the delineations of which are guided by the information preservation rule. The time-frequency analysis, which is implemented using the Wigner-Ville distribution (WVD), transforms the incoming received signal into a time-frequency image that accounts for the time-varying nature of the received signal's spectral content. This image provides a common input to a pair of channels, one of which is adaptively matched to the interference acting alone, and the other is adaptively matched to the target signal plus interference. Each channel of the receiver consists of a principal components analyzer (for feature extraction) followed by a multilayer perceptron (for feature classification), which are implemented using self-organized and supervised forms of learning in feedforward neural networks, respectively. Experimental results based on real-life radar data are presented to demonstrate the superior performance of the new detection strategy over a conventional detector using constant false-alarm rate (CFAR) processing. The data used in the experiment pertain to an ocean environment, representing radar returns from small ice targets buried in sea clutter; they were collected with an instrument quality coherent radar and properly ground truthed View full abstract»

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  • Paraunitary filter banks over finite fields

    Page(s): 1443 - 1457
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    In real and complex fields, unitary and paraunitary (PU) matrices have found many applications in signal processing. There has been interest in extending these ideas to the case of finite fields. We study the theory of PU filter banks (FBs) in GF(q) with q prime. Various properties of unitary and PU matrices in finite fields are studied. In particular, a number of factorization theorems are given. We show that (i) all unitary matrices in GF(q) are factorizable in terms of Householder-like matrices and permutation matrices, and (ii) the class of first-order PU matrices (the lapped orthogonal transform in finite fields) can always be expressed as a product of degree-one or degree-two building blocks. If q>2, we do not need degree-two building blocks. While many properties of PU matrices in finite fields are similar to those of PU matrices in complex field, there are a number of differences. For example, unlike the conventional PU systems, in finite fields, there are PU systems that are unfactorizable in terms of smaller building blocks. In fact, in the special case of 2×2 systems, all PU matrices that are factorizable in terms of degree-one building blocks are diagonal matrices. We derive results for both the cases of GF(2) and GF(Q) with q>2. Even though they share some similarities, there are many differences between these two cases View full abstract»

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  • Generalized evolutionary spectral analysis and the Weyl spectrum of nonstationary random processes

    Page(s): 1520 - 1534
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    The evolutionary spectrum (ES) is a “time-varying power spectrum” of nonstationary random processes. Starting from an innovations system interpretation of the ES, we introduce the generalized evolutionary spectrum (GES) as a novel family of time-varying power spectra. The GES contains the ES and the transitory evolutionary spectrum as special cases. We consider the problem of finding an innovations system for a process characterized by its correlation function, and we discuss the connection between GES analysis and the class of underspread processes. Furthermore, we show that another special case of the GES-a novel time-varying power spectrum that we call the Weyl spectrum-has substantial advantages over all other members of the GES family. The properties of the Weyl spectrum are discussed, and its superior performance is verified experimentally for synthetic and real-data processes View full abstract»

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  • Time-frequency distribution kernels using FIR filter design techniques

    Page(s): 1645 - 1650
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    In this correspondence, time-frequency distribution (TFD) kernels are obtained using finite impulse response (FIR) filter design methods, namely, the windowing method and the equiripple approximation method based on Chebyshev criterion. It is shown that the class of the window-designed kernels are simple to obtain and can handle most time-varying environments View full abstract»

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  • Statistical analysis and spectral estimation techniques for one-dimensional chaotic signals

    Page(s): 1495 - 1506
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    Signals arising out of nonlinear dynamics are compelling models for a wide range of both natural and man-made phenomena. In contrast to signals arising out of linear dynamics, extremely rich behavior is obtained even when we restrict our attention to one-dimensional (1-D) chaotic systems with certain smoothness constraints. An important class of such systems are the so-called Markov maps. We develop several properties of signals obtained from Markov maps and present analytical techniques for computing a broad class of their statistics in closed form. These statistics include, for example, correlations of arbitrary order and all moments of such signals. Among several results, we demonstrate that all Markov maps produce signals with rational spectra, and we can therefore view the associated signals as “chaotic ARMA processes,” with “chaotic white noise” as a special case. Finally, we also demonstrate how Markov maps can be used to approximate to arbitrary accuracy the statistics any of a broad class of non-Markov chaotic maps View full abstract»

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  • Discrete multiwindow Gabor-type transforms

    Page(s): 1428 - 1442
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    The discrete (finite) Gabor scheme is generalized by incorporating multiwindows. Two approaches are presented for the analysis of the multiwindow scheme: the signal domain approach and the Zak transform domain approach. Issues related to undersampling, critical sampling, and oversampling are considered. The analysis is based on the concept of frames and on generalized (Moore-Penrose) inverses. The approach based on representing the frame operator as a matrix-valued function is far less demanding from a computational complexity viewpoint than a straightforward matrix algebra in various operations such as the computation of the dual frame. DFT-based algorithms, including complexity analysis, are presented for the calculation of the expansion coefficients and for the reconstruction of the signal in both signal and transform domains. The scheme is further generalized and incorporates kernels other than the complex exponential. Representations other than those based on the dual frame and nonrectangular sampling of the combined space are considered as well. An example that illustrates the advantages of the multiwindow scheme over the single-window scheme is presented View full abstract»

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  • On fast FIR filters implemented as tail-canceling IIR filters

    Page(s): 1415 - 1427
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    We have developed an algorithm based on synthetic division for deriving the transfer function that cancels the tail of a given arbitrary rational (IIR) transfer function after a desired number of time steps. Our method applies to transfer functions with repeated poles, whereas previous methods of tail-subtraction cannot. We use a parallel state-variable technique with periodic refreshing to induce finite memory in order to prevent accumulation of quantization error in cases where the given transfer function has unstable modes. We present two methods for designing linear-phase truncated IIR (TIIR) filters based on antiphase filters. We explore finite-register effects for unstable modes and provide bounds on the maximum TIIR filter length. In particular, we show that for unstable systems, the available dynamic range of the registers must be three times that of the data. Considerable computational savings over conventional FIR filters are attainable for a given specification of linear-phase filter. We provide examples of filter design. We show how to generate finite-length polynomial impulse responses using TIIR filters. We list some applications of TIIR filters, including uses in digital audio and an algorithm for efficiently implementing Kay's optimal high-resolution frequency estimator View full abstract»

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  • Conjugate gradient projection subspace tracking

    Page(s): 1664 - 1668
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    In this correspondence, we develop a new subspace tracking algorithm called the conjugate gradient projection subspace tracker (CGPST). The algorithm is based on a recently introduced RLS-like subspace cost function, which we recursively minimize using conjugate gradient iterations. Subspace averaging concepts are used to produce an O(r2m) algorithm that updates an r-dimensional subspace of Cm. The algorithm is parallelizable, rapidly convergent, numerically stable, and computationally efficient. Simulation studies test the algorithm's performance and show it to compare favorably with other subspace trackers View full abstract»

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  • Optimizing synchronization in multiprocessor DSP systems

    Page(s): 1605 - 1618
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    This paper is concerned with multiprocessor implementations of embedded applications specified as iterative dataflow programs in which synchronization overhead can be significant. We develop techniques to alleviate this overhead by determining a minimal set of processor synchronizations that are essential for correct execution. Our study is based in the context of self-timed execution of iterative dataflow programs. An iterative dataflow program consists of a dataflow representation of the body of a loop that is to be iterated an indefinite number of times; dataflow programming in this form has been studied and applied extensively, particularly in the context of signal processing software. Self-timed execution refers to a combined compile-time/run-time scheduling strategy in which processors synchronize with one another based only on interprocessor communication requirements, and thus, synchronization of processors at the end of each loop iteration does not generally occur. We introduce a new graph-theoretic framework based on a data structure called the synchronization graph for analyzing and optimizing synchronization overhead in self-timed, iterative dataflow programs. We show that the comprehensive techniques that have been developed for removing redundant synchronizations in noniterative programs can be extended in this framework to optimally remove redundant synchronizations in our context. We also present an optimization that converts a feedforward dataflow graph into a strongly connected graph in such a way as to reduce synchronization overhead without slowing down execution View full abstract»

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  • Maximum a posteriori maximum entropy order determination

    Page(s): 1553 - 1559
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    An instance crucial to most problems in signal processing is the selection of the order of a presupposed model. Examples are the determination of the putative number of signals present in white Gaussian noise or the number of noise-contaminated sources impinging on a passive sensor array. It is shown that maximum a posteriori Bayesian arguments, coupled with maximum entropy considerations, offer an operational and consistent model order selection scheme, competitive with the minimum description length criterion 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