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Multichannel Blind Deconvolution: Fir Matrix Algebra And Separation Of Multipath Mixtures
, 1996
"... A general tool for multichannel and multipath problems is given in FIR matrix algebra. With Finite Impulse Response (FIR) filters (or polynomials) assuming the role played by complex scalars in traditional matrix algebra, we adapt standard eigenvalue routines, factorizations, decompositions, and mat ..."
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A general tool for multichannel and multipath problems is given in FIR matrix algebra. With Finite Impulse Response (FIR) filters (or polynomials) assuming the role played by complex scalars in traditional matrix algebra, we adapt standard eigenvalue routines, factorizations, decompositions, and matrix algorithms for use in multichannel /multipath problems. Using abstract algebra/group theoretic concepts, information theoretic principles, and the Bussgang property, methods of single channel filtering and source separation of multipath mixtures are merged into a general FIR matrix framework. Techniques developed for equalization may be applied to source separation and vice versa. Potential applications of these results lie in neural networks with feedforward memory connections, wideband array processing, and in problems with a multiinput, multioutput network having channels between each source and sensor, such as source separation. Particular applications of FIR polynomial matrix alg...
Affine OrderStatistic Filters: "Medianization" of Linear FIR Filters
"... This paper introduces a novel, dataadaptive filtering framework: affine orderstatistic filters. Affine orderstatistic filters operate effectively on a wide range of signal statistics, are sensitive to the dispersion of the observed data, and are therefore particularly useful in the processing ..."
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This paper introduces a novel, dataadaptive filtering framework: affine orderstatistic filters. Affine orderstatistic filters operate effectively on a wide range of signal statistics, are sensitive to the dispersion of the observed data, and are therefore particularly useful in the processing of nonstationary signals. These properties result from the introduction of a tunable affinity function that measures the affinity, or closeness, of observation samples in their natural order to their corresponding orderstatistics. The obtained affinity measures are utilized to control the influence of individual samples in the filtering process. Depending on the spread of the affinity function, which is controlled by a single parameter fl, affine orderstatistic filters operate effectively in various environments ranging from Gaussian to impulsive. The class of affine orderstatistic filters subsumes the family of weighted order statistic (WOS) affine filters and the class of FIR affin...
Adaptive Weighted Myriad Filter Optimization for Robust Signal Processing
 in Proc. of the 1996 CISS
, 1996
"... Weighted Myriad Filters have been proposed recently as a class of robust, nonlinear filters based on the statistical properties of ffstable processes. These processes are very effective in modeling many realworld signals that are impulsive in nature. The class of Weighted Myriad Filters includes l ..."
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Weighted Myriad Filters have been proposed recently as a class of robust, nonlinear filters based on the statistical properties of ffstable processes. These processes are very effective in modeling many realworld signals that are impulsive in nature. The class of Weighted Myriad Filters includes linear normalized FIR filters and is inherently more powerful than weighted median filters (which are constrained to be selection filters). This paper addresses the problem of optimizing the weights of the weighted myriad filter under the mean absolute error criterion. Necessary conditions for optimality of the filter are determined. Using an implicit formulation of the filter output, a gradientbased adaptive algorithm to obtain the optimal filter weights is derived. A simplification of this algorithm is then proposed in order to reduce the computational burden. The effective performance of the algorithms in impulsive environments is illustrated through computer simulations involving the fil...
A Sliding Window RLSlike Adaptive Algorithm for Filtering alphastable Noise
"... Weintroduce a sliding window adaptive RLSlike algorithm for filtering alphastable noise. Unlike previously introduced stochastic gradienttype algorithms, the new adaptation algorithm minimizes the Lp norm of the error exactly in a sliding window of fixed size. Therefore, it behaves much like the RL ..."
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Weintroduce a sliding window adaptive RLSlike algorithm for filtering alphastable noise. Unlike previously introduced stochastic gradienttype algorithms, the new adaptation algorithm minimizes the Lp norm of the error exactly in a sliding window of fixed size. Therefore, it behaves much like the RLS algorithm in terms of convergence speed and computational complexity compared to previously introduced stochastic gradient based algorithms which behavelike the LMS algorithm. It is shown that the new algorithm achieves superior convergence rate at the expense of increased computational complexity. I. Introduction In the vast majority of signal processing applications it has been assumed that the signal or noise under investigation can be modeled by a Gaussian distribution law. This assumption has been justified by the central limit theorem and strong analytical properties of Gaussian pdf which leads to linear algorithms. However, in many realworld problems the noise encountered is more...
Adaptive Algorithms for Weighted Myriad Filter Optimization
 in Proc. of the 1997 IEEE ICASSP
, 1997
"... Stochastic gradientbased adaptive algorithms are developed for the optimization of Weighted Myriad Filters, a class of nonlinear filters, motivated by the properties of ffstable distributions, that have been proposed for robust nonGaussian signal processing in impulsive noise environments. An im ..."
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Stochastic gradientbased adaptive algorithms are developed for the optimization of Weighted Myriad Filters, a class of nonlinear filters, motivated by the properties of ffstable distributions, that have been proposed for robust nonGaussian signal processing in impulsive noise environments. An implicit formulation of the filter output is used to derive an expression for the gradient of the mean absolute error (MAE) cost function, leading to necessary conditions for the optimal filter weights. An adaptive steepest descent algorithm is then derived to optimize the filter weights. This is modified to yield an algorithm with a very simple weight update, computationally comparable to the update in the classical LMS algorithm. Simulations demonstrate the robust performance of these algorithms. I INTRODUCTION Classical statistical signal processing has been dominated by the assumption of the Gaussian model for the underlying signals. However, a large number of physical processes are impu...
Traffic Characterisation and Modelling for Call Admission Control Schemes on Asynchronous Transfer Mode Networks
, 1997
"... Allocating resources to variable bitrate (VBR) teletraffic sources is not a trivial task because the impact of such sources on a buffered switch is difficult to predict. This problem has repercussions for call admission control (CAC) on asynchronous transfer mode (ATM) networks. In this thesis we re ..."
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Allocating resources to variable bitrate (VBR) teletraffic sources is not a trivial task because the impact of such sources on a buffered switch is difficult to predict. This problem has repercussions for call admission control (CAC) on asynchronous transfer mode (ATM) networks. In this thesis we report on investigations into the nature of several types of VBR teletraffic. The purpose of these investigations is to identify parameters of the traffic that may assist in the development of CAC algorithms. As such we concentrate on the correlation structure and marginal distribution; the two aspects of a teletraffic source that affect its behaviour through a buffered switch. The investigations into the correlation structure consider whether VBR video is selfsimilar or nonstationary. This question is significant as the exponent of selfsimilarity has been identified as being useful for characterising VBR teletraffic. Although results are inconclusive with regards to the original question, t...
A MAP equaliser for impulsive noise environments
"... The maximum a posteriori probability (MAP) criterion for channel equalisation has been used with the assumption of additive Gaussian white noise. In this study, we investigate the MAP criterion in the presence of finite intersymbol interference and additive impulsive noise modelled as an ffstable p ..."
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The maximum a posteriori probability (MAP) criterion for channel equalisation has been used with the assumption of additive Gaussian white noise. In this study, we investigate the MAP criterion in the presence of finite intersymbol interference and additive impulsive noise modelled as an ffstable process. The optimum symbolbysymbol estimator is presented and it's performance is then discussed. The experimental results suggest that the proposed estimator outperforms the traditional Bayesian estimator based on the Gaussian noise assumption. I. Introduction T HE Gaussian stochastic process has been the dominant noise model in communications and signal processing literature, mainly because of the Central Limit Theorem. In addition, the Gaussian assumption often leads to analytically tractable solutions [1]. Unfortunately, in many communication channels, the observation noise exhibits Gaussian, as well as impulsive 1 characteristics. The sources of impulsive noise may be either natur...
Robust TimeFrequency Representations in Impulsive Noise Using Fractional Lower Order Moments
"... Timefrequency representations (TFRs) allow nonstationary signals to be characterized simultaneously in the time and frequency domains, and are useful tools for a variety of signal processing applications, such as signal detection, synthetic aperture radar, and tracking instantaneous frequency. They ..."
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Timefrequency representations (TFRs) allow nonstationary signals to be characterized simultaneously in the time and frequency domains, and are useful tools for a variety of signal processing applications, such as signal detection, synthetic aperture radar, and tracking instantaneous frequency. They function well in additive Gaussian noise because they spread the noise energy over the entire timefrequency plane, allowing signals of interest to be isolated. In the presence of impulsive noise, which is wellmodeled by the family of alphastable distributions, TFRs are severely corrupted by impulserelated artifacts, which tend to obscure the essential details of the desired signal. In this paper we show that by using fractional lowerorder moments (FLOMs), which are used as robust measures of the statistical properties of impulsive processes, we can produce a class of TFRs that are resistant to impulses and yet retain many of the desirable mathematical properties associated with Cohen's...