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By Topic

Signal Processing, IEEE Transactions on

Issue 2 • Date Feb 1997

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Displaying Results 1 - 23 of 23
  • A parameter estimation scheme for damped sinusoidal signals based on low-rank Hankel approximation

    Page(s): 481 - 486
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (184 KB)  

    Most of the existing algorithms for parameter estimation of damped sinusoidal signals are based only on the low-rank approximation of the prediction matrix and ignore the Hankel property of the prediction matrix. We propose a modified Kumaresan-Tufts (MKT) algorithm exploiting both rank-deficient and Hankel properties of the prediction matrix. Computer simulation results demonstrate that compared with the original Kumaresan-Tufts (1982) algorithm and the matrix pencil algorithm, the MKT algorithm has a lower noise threshold and can estimate the parameters of signal with larger damping factors View full abstract»

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  • Flexible tree-structured signal expansions using time-varying wavelet packets

    Page(s): 333 - 345
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (552 KB)  

    Addresses the problem of finding the best time-varying filter bank tree-structured representation for a signal. The tree is allowed to vary at regular intervals, and the spacing of these changes can be arbitrarily short. The question of how to choose tree-structured representations of signals based on filter banks is considered. Wavelets and their adaptive version, known as wavelet packets, represent one approach that is popular. Wavelet packets are subband trees where the tree is chosen to match the characteristics of the signal. Variations where the tree varies over time have been proposed as the double tree and the time-frequency tree algorithms. Time-variation adds a further level of adaptivity. In all of the approaches proposed so far, the tree must be either fixed for the whole duration of the signal or fixed for its dyadic subintervals. The solution that we propose, as it allows more flexible variation, is an advance on the wavelet packet algorithm, the double tree algorithm, and the recently proposed time-frequency tree algorithm. Our solution is based on casting it in a dynamic programming (DP) setting. Focusing on compression applications, we use a Lagrangian cost of distortion +λ×rate as the objective function and explain our algorithm in detail, pointing out its relation to existing approaches to the problem. We demonstrate that the new algorithm indeed searches a larger library of representations than previously possible and that overcoming the constraint of dyadic time segmentations gives a significant improvement in practice View full abstract»

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  • Application of filter sharpening to cascaded integrator-comb decimation filters

    Page(s): 457 - 467
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (260 KB)  

    A new architecture for the implementation of high-order decimation filters is described. It combines the cascaded integrator-comb (CIC) multirate filter structure with filter sharpening techniques to improve the filter's passband response. This allows the first-stage CIC decimation filter to be followed by a fixed-coefficient second-stage filter, rather than a programmable filter, thereby achieving a significant hardware reduction over existing approaches. Furthermore, the use of fixed-coefficient filters in place of programmable-coefficient filters improves the overall throughput rate. The resulting architecture is well suited for single-chip VLSI implementation with very high data-sample rates. We discuss an example with specifications suitable for use in a wideband satellite communication subband tuner system and for signal analysis View full abstract»

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  • The hyperbolic class of quadratic time-frequency representations. II. Subclasses, intersection with the affine and power classes, regularity, and unitarity

    Page(s): 303 - 315
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (736 KB)  

    For pt.I see ibid., vol.41, p.3425-444 (1993). Part I introduced the hyperbolic class (HC) of quadratic/bilinear time-frequency representations (QTFRs). The present paper defines and studies four subclasses of the HC: (1) The focalized-kernel subclass of the HC is related to a time-frequency concentration property of QTFRs. It is analogous to the localized-kernel subclass of the affine QTFR class. (2) The affine subclass of the HC (affine HC) consists of all HC QTFRs that satisfy the conventional time-shift covariance property. It forms the intersection of the HC with the affine QTFR class. (3) The power subclasses of the HC consist of all HC QTFRs that satisfy a “power time-shift” covariance property. They form the intersection of the HC with the recently introduced power classes. (4) The power-warp subclass of the HC consists of all HC QTFRs that satisfy a covariance to power-law frequency warpings. It is the HC counterpart of the shift-scale covariant subclass of Cohen's class. All of these subclasses are characterized by 1D kernel functions. The affine HC is contained in both the localized kernel hyperbolic subclass and the localized-kernel affine subclass and that any affine HC QTFR can be derived from the Bertrand unitary Po-distribution by a convolution. We furthermore consider the properties of regularity and unitarity in the HC. The calculus of inverse kernels is developed, and important implications of regularity and unitarity are summarized. The results comprise a general method for least-squares signal synthesis and new relations for the Altes-Marinovich Q-distribution View full abstract»

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  • A class of second-order stationary self-similar processes for 1/f phenomena

    Page(s): 396 - 410
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (572 KB)  

    We propose a class of statistically self-similar processes and outline an alternative mathematical framework for the modeling and analysis of 1/f phenomena. The foundation of the proposed class is based on the extensions of the basic concepts of classical time series analysis, in particular, on the notion of stationarity. We consider a class of stochastic processes whose second-order structure is invariant with respect to time scales, i.e., E[X(t)X(λt)]=t2HλHR(λ), t>0 for some -x<H<∞. For H=0, we refer to these processes as wide sense scale stationary. We show that any self-similar process can be generated from scale stationary processes. We establish a relationship between linear scale-invariant system theory and the proposed class that leads to a concrete analysis framework. We introduce new concepts, such as periodicity, autocorrelation, and spectral density functions, by which practical signal processing schemes can be developed. We give several examples of scale stationary processes including Gaussian, non-Gaussian, covariance, and generative models, as well as fractional Brownian motion as a special case. In particular, we introduce a class of finite parameter self-similar models that are similar in spirit to the ordinary ARMA models by which an arbitrary self-similar process can be approximated. Results from our study suggest that the proposed self-similar processes and the mathematical formulation provide an intuitive, general, and mathematically simple approach to 1/f signal processing View full abstract»

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  • Adaptive recovery of a chirped signal using the RLS algorithm

    Page(s): 363 - 376
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (604 KB)  

    This paper studies the performance of the recursive least squares (RLS) algorithm in the presence of a general chirped signal and additive white noise. The chirped signal, which is a moving average (MA) signal deterministically shifted in frequency at rate ψ, can be used to model a frequency shift in a received signal. General expressions for the optimum Wiener-Hopf coefficients, one-step recovery and estimation errors, noise and lag misadjustments, and the optimum adaptation constant (βopt) are found in terms of the parameters of the stationary MA signal. The output misadjustment is shown to be composed of a noise (ξ0Mβ/2) and lag term (κ/(β2ψ2)), and the optimum adaptation constant is proportional to the chirp rate as ψ2/3 . The special case of a chirped first-order autoregressive (AR1) process with correlation (α) is used to illustrate the effect the bandwidth (1/α) of the chirped signal on the adaptation parameters. It is shown that unlike for the chirped tone, where the βopt increases with the filter length (M), the adaptation constant reaches a maximum for M near the inverse of the signal correlation (1/α). Furthermore, there is an optimum filter length for tracking the chirped signal and this length is less than (1/α) View full abstract»

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  • On the generalized Cramer-Rao bound for the estimation of the location

    Page(s): 487 - 492
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (260 KB)  

    It is shown that the generalized Gaussian distribution maximizes the generalized Cramer-Rao (CR) bound for the pth absolute central moment of any classical location parameter unbiased estimator. The underlying maximization is taken over the class of distributions with fixed and finite pth-order moment and exhibits particular utility in minimax designs as well as in worst-case performance analysis. The relationship between the generalized Gaussian density and the generalized CR bound is further examined for the model of a mixture of generalized Gaussian distributions as well as for scenarios where multiple independent generalized Gaussian observations are involved View full abstract»

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  • Analysis of polynomial-phase signals by the integrated generalized ambiguity function

    Page(s): 316 - 327
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (512 KB)  

    The aim of this work is the performance analysis of a method for the detection and parameter estimation of mono or multicomponent polynomial-phase signals (PPS) embedded in white Gaussian noise and based on a generalized ambiguity function. The proposed method is shown to be asymptotically efficient for second-order PPS and nearly asymptotically efficient for third-order PPSs. The method presents some advantages with respect to similar techniques, like the polynomial-phase transform, for example, in terms of (i) a closer approach to the Cramer-Rao lower bounds, (ii) a lower SNR threshold, (iii) a better capability of discriminating multicomponent signals View full abstract»

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  • Blind intensity estimation from shot-noise data

    Page(s): 421 - 433
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (624 KB)  

    The estimation of the intensity function of an inhomogeneous Poisson process is considered when the observable data consists of sampled shot noise that results from passing the Poisson process through an unknown linear time-invariant system. The proposed method consists of first estimating a histogram of the underlying point process. The estimated histogram is used to construct a kernel estimate of the intensity function. An estimate of the unknown impulse response of the linear time-invariant system is constructed via a regularized backsubstitution of a discrete-time convolution with the estimated histogram View full abstract»

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  • A blind source separation technique using second-order statistics

    Page(s): 434 - 444
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (408 KB)  

    Separation of sources consists of recovering a set of signals of which only instantaneous linear mixtures are observed. In many situations, no a priori information on the mixing matrix is available: The linear mixture should be “blindly” processed. This typically occurs in narrowband array processing applications when the array manifold is unknown or distorted. This paper introduces a new source separation technique exploiting the time coherence of the source signals. In contrast with other previously reported techniques, the proposed approach relies only on stationary second-order statistics that are based on a joint diagonalization of a set of covariance matrices. Asymptotic performance analysis of this method is carried out; some numerical simulations are provided to illustrate the effectiveness of the proposed method View full abstract»

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  • Efficient approximation of Gaussian filters

    Page(s): 468 - 471
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (164 KB)  

    This article presents improvements to the efficient approximation of Gaussian filters by sequentially applying uniform box filters. For 1-D filters, a simple and nearly optimal fit criterion for the length S of the box filters to the approximated Gaussian is given. For 2-D filters, a new method is introduced to improve the circular symmetry and the lowpass properties of the approximation without increasing the computational complexity. Finally, a multirate implementation for large Gaussian filters is presented that requires significantly fewer floating-point operations than the standard technique View full abstract»

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  • Data analytic wavelet threshold selection in 2-D signal denoising

    Page(s): 496 - 500
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (396 KB)  

    A data adaptive scheme for wavelet shrinkage-based noise removal is developed. The method involves a statistical test of hypotheses that takes into account the wavelet coefficients' magnitudes and relative positions. The amount of smoothing performed during noise removal is controlled by the user-supplied confidence level of the tests View full abstract»

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  • New split-radix algorithm for the discrete Hartley transform

    Page(s): 297 - 302
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (180 KB)  

    This paper presents a split-radix algorithm that can flexibly compute the discrete Hartley transforms of various sequence lengths. Comparisons with previously reported algorithms are made in terms of the required number of additions and multiplications. It shows that the length-3*2m DHTs need a smaller number of multiplications than the length-2m DHTs. However, they both require about the same computational complexity in terms of the total number of additions and multiplications. Optimized computation of length-12, -16 and -24 DFTs are also provided View full abstract»

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  • An IIR adaptive line enhancer with controlled bandwidth

    Page(s): 477 - 481
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (168 KB)  

    A previously proposed IIR adaptive line enhancer (ALE) is explored further. We propose a mechanism for controlling the bandwidth of the ALE in an adaptive manner. The proposed mechanism increases the bandwidth of the ALE whenever its peak is not close to a spectral line of the input signal to assure its fast convergence and decreases the bandwidth of the ALE when its peak matches a spectral line of the input signal to enhance that spectral line further. In addition, a new algorithm for robust adaptation of the ALE is proposed View full abstract»

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  • Statistical performance analysis of track initiation techniques

    Page(s): 445 - 456
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (540 KB)  

    This paper analyzes the statistical performance of track initiation methods. It evaluates, by considering a track initiation as a problem of signal detection, the track detection probabilities and false track probabilities of four popular approaches: the rule-based method, the logic-based method, the Hough transform, and the modified Hough transform techniques. The first two methods detect the existence of tracks in a sequential fashion, and the fast two are image processing techniques that initiate tracks using a batch of frames. The analytical expressions for the track detection probability and false track probability of the four methods are derived to predict their capabilities in capturing new tracks and in rejecting false tracks due to false alarms and clutter background. Monte Carlo simulations are performed to confirm the analysis. It is observed that when the false track probability is held fixed, the logic-based and the modified Hough transform techniques have good detection performances View full abstract»

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  • Volterra filter equalization: a fixed point approach

    Page(s): 377 - 388
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    One important application of Volterra filters is the equalization of nonlinear systems. Under certain conditions, this problem can be posed as a fixed point problem involving a contraction mapping. We generalize the previously studied local inverse problem to a very broad class of equalization problems. We also demonstrate that subspace information regarding the response behavior of the Volterra filters can be incorporated to improve the theoretical analysis of equalization algorithms. To this end, a new “windowed” signal norm is introduced. Using this norm, we show that the class of allowable inputs is increased and the upper bounds on the convergence rate are improved when subspace information is exploited View full abstract»

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  • Second-order statistics of complex signals

    Page(s): 411 - 420
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (436 KB)  

    The second-order statistical properties of complex signals are usually characterized by the covariance function. However, this is not sufficient for a complete second-order description, and it is necessary to introduce another moment called the relation function. Its properties, and especially the conditions that it must satisfy, are analyzed both for stationary and nonstationary signals. This leads to a new perspective concerning the concept of complex white noise as well as the modeling of any signal as the output of a linear system driven by a white noise. Finally, this is applied to complex autoregressive signals, and it is shown that the classical prediction problem must be reformulated when the relation function is taken into consideration View full abstract»

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  • Implementation and perfect reconstruction of a maximally decimated FIR filter bank using parallel module decomposition

    Page(s): 328 - 332
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (176 KB)  

    This paper discusses an implementation and the perfect reconstruction (PR) of an M-channel maximally decimated FIR fitter bank. Using the polynomial module arithmetics, the filter bank is decomposed into a set of module filter banks of size M, independent of the filter length. When the filter bank is uniform, the computational cost is the same as the polyphase/FFT implementation. When it is not uniform, in which case the polyphase/FFT implementation is not applicable, the computational cost is still reduced by sharing among channel filtering computations. The parallel module configuration is favorable for hardware implementation because decomposing a large system into small subsystems is generally advantageous for many realizations. The PR analysis is greatly simplified by working on the module filter banks as well View full abstract»

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  • Reduced-rank adaptive filtering

    Page(s): 492 - 496
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    A novel rank reduction scheme is introduced for adaptive filtering problems. This rank reduction method uses a cross-spectral metric to select the optimal lower dimensional subspace for reduced-rank adaptive filtering as a function of the basis vectors of the full-rank space View full abstract»

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  • A realization method of an ARMAX lattice filter

    Page(s): 471 - 476
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (240 KB)  

    This paper proposes a realization method of an ARMAX lattice filter for frequency-weighting ARMAX model identification. The proposed lattice filter uses an exponentially weighted sliding window for the same application as the extended least squares (ELS) achieves. Based on the proposed structure, the algorithm can perform the frequency-weighting model identification more easily than the ELS. Further, applied to the ARMAX model identification, the proposed algorithm requires fewer multiplications than the ELS does View full abstract»

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  • Underdetermined-order recursive least-squares adaptive filtering: the concept and algorithms

    Page(s): 346 - 362
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (700 KB)  

    Underdetermined recursive least-squares (URLS) adaptive filtering is introduced. In particular, the URLS algorithm is derived and shown to be a direct consequence of the principle of minimal disturbance. By exploiting the Hankel structure of the filter input matrix, the fast transversal filter (FTF) version of the URLS algorithm (URLS-FTF) is derived including sliding window and growing window types. The computational complexity is reduced to O(N)+O(m), where N is the adaptive filter length, and m is the order of the URLS algorithm. In addition, the efficient URLS (EURLS) algorithm, which does not compute the filter coefficients explicitly, thereby significantly reducing the computational load, is presented. Some earlier adaptive algorithms such as the averaged LMS, filtered-X LMS, and fast conjugate gradient are shown to be suboptimal approximations of the URLS algorithm. Instrumental variable approximations are also discussed. The URLS algorithm has a whitening effect on the input, signal, which provides immunity to the eigenvalue spread of the input signal correlation matrix. Although the algorithm is sensitive to observation noise, it has good tracking characteristics, and tradeoffs can be found by tuning the step size. The utility of the URLS algorithms, in its basic form and FTF realization, depends heavily on the practical applicability of the mth-order sliding window estimate of the covariance matrix and mth-order PTF relations. The feasibility of the URLS family in practical applications is demonstrated in channel equalization and acoustic echo cancellation View full abstract»

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  • Pattern recognition using discriminative feature extraction

    Page(s): 500 - 504
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (108 KB)  

    We propose a new design method, called discriminative feature extraction for practical modular pattern recognizers. A key concept of discriminative feature extraction is the design of an overall recognizer in a manner consistent with recognition error minimization. The utility of the method is demonstrated in a Japanese vowel recognition task View full abstract»

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  • Fast digital locally monotonic regression

    Page(s): 389 - 395
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (268 KB)  

    Locally monotonic regression is the optimal counterpart of iterated median filtering. In a previous paper, Restrepo and Bovik (see ibid., vol.41, no.9, p.2796-2810, 1993) developed an elegant mathematical framework in which they studied locally monotonic regressions in RN. The drawback is that the complexity of their algorithms is exponential in N. We consider digital locally monotonic regressions, in which the output symbols are drawn from a finite alphabet and, by making a connection to Viterbi decoding, provide a fast O(|A|2αN) algorithm that computes any such regression, where |A| is the size of the digital output alphabet, a stands for lomo degree, and N is the sample size. This is linear in N, and it renders the technique applicable in practice 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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Meet Our Editors

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