On adaptive filter structure and performance

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Adaptive polynomial filters

Journal ArticleWhile linear filter are useful in a large number of applications and relatively simple from conceptual and implementational view points. there are many practical situations that require nonlinear processing of the signals involved. This article explains adaptive nonlinear filters equipped with polynomial models of nonlinearity. The polynomial systems considered are those nonlinear systems whose output signals can be related to the input signals through a truncated Volterra series expansion, or a recursive nonlinear difference equation. The Volterra series expansion can model a large class of nonlinear systems and is attractive in filtering applications because the expansion is a linear combination of nonlinear functions of the input signal. The basic ideas behind the development of gradient and recursive least-squares adaptive Volterra filters are first discussed. followed by adaptive algorithms using system models involving recursive nonlinear difference equations. Such systems are attractive because they may be able to approximate many nonlinear systems with great parsimony in the use pf coefficients. Also discussed are current research trends and new results and problem areas associated with these nonlinear filters. A lattice structure for polynomial models is also described

Stochastic Behavior Analysis of the Gaussian Kernel Least-Mean-Square Algorithm

The kernel least-mean-square (KLMS) algorithm is a popular algorithm in nonlinear adaptive filtering due to its simplicity and robustness. In kernel adaptive filters, the statistics of the input to the linear filter depends on the parameters of the kernel employed. Moreover, practical implementations require a finite nonlinearity model order. A Gaussian KLMS has two design parameters, the step size and the Gaussian kernel bandwidth. Thus, its design requires analytical models for the algorithm behavior as a function of these two parameters. This paper studies the steady-state behavior and the transient behavior of the Gaussian KLMS algorithm for Gaussian inputs and a finite order nonlinearity model. In particular, we derive recursive expressions for the mean-weight-error vector and the mean-square-error. The model predictions show excellent agreement with Monte Carlo simulations in transient and steady state. This allows the explicit analytical determination of stability limits, and gives opportunity to choose the algorithm parameters a priori in order to achieve prescribed convergence speed and quality of the estimate. Design examples are presented which validate the theoretical analysis and illustrates its application

LMS Adaptive Filters for Noise Cancellation: A Review

This paper reviews the past and the recent research on Adaptive Filter algorithms based on adaptive noise cancellation systems. In many applications of noise cancellation, the change in signal characteristics could be quite fast which requires the utilization of adaptive algorithms that converge rapidly. Algorithms such as LMS and RLS proves to be vital in the noise cancellation are reviewed including principle and recent modifications to increase the convergence rate and reduce the computational complexity for future implementation. The purpose of this paper is not only to discuss various noise cancellation LMS algorithms but also to provide the reader with an overview of the research conducted

A kepstrum approach to filtering, smoothing and prediction

The kepstrum (or complex cepstrum) method is revisited and applied to the problem of spectral factorization where the spectrum is directly estimated from observations. The solution to this problem in turn leads to a new approach to optimal filtering, smoothing and prediction using the Wiener theory. Unlike previous approaches to adaptive and self-tuning filtering, the technique, when implemented, does not require a priori information on the type or order of the signal generating model. And unlike other approaches - with the exception of spectral subtraction - no state-space or polynomial model is necessary. In this first paper results are restricted to stationary signal and additive white noise

A study on adaptive filtering for noise and echo cancellation.

The objective of this thesis is to investigate the adaptive filtering technique on the application of noise and echo cancellation. As a relatively new area in Digital Signal Processing (DSP), adaptive filters have gained a lot of popularity in the past several decades due to the advantages that they can deal with time-varying digital system and they do not require a priori knowledge of the statistics of the information to be processed. Adaptive filters have been successfully applied in a great many areas such as communications, speech processing, image processing, and noise/echo cancellation. Since Bernard Widrow and his colleagues introduced adaptive filter in the 1960s, many researchers have been working on noise/echo cancellation by using adaptive filters with different algorithms. Among these algorithms, normalized least mean square (NLMS) provides an efficient and robust approach, in which the model parameters are obtained on the base of mean square error (MSE). The choice of a structure for the adaptive filters also plays an important role on the performance of the algorithm as a whole. For this purpose, two different filter structures: finite impulse response (FIR) filter and infinite impulse response (IIR) filter have been studied. The adaptive processes with two kinds of filter structures and the aforementioned algorithm have been implemented and simulated using Matlab.Dept. of Electrical and Computer Engineering. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2005 .J53. Source: Masters Abstracts International, Volume: 44-01, page: 0472. Thesis (M.A.Sc.)--University of Windsor (Canada), 2005

Adaptive filtering algorithms for noise cancellation

Tese de mestrado. Mestrado Integrado em Engenharia Electrotécnica e de Computadores - Major Automação. Faculdade de Engenharia. Universidade do Porto. 201

Sparse Nonlinear MIMO Filtering and Identification

In this chapter system identification algorithms for sparse nonlinear multi input multi output (MIMO) systems are developed. These algorithms are potentially useful in a variety of application areas including digital transmission systems incorporating power amplifier(s) along with multiple antennas, cognitive processing, adaptive control of nonlinear multivariable systems, and multivariable biological systems. Sparsity is a key constraint imposed on the model. The presence of sparsity is often dictated by physical considerations as in wireless fading channel-estimation. In other cases it appears as a pragmatic modelling approach that seeks to cope with the curse of dimensionality, particularly acute in nonlinear systems like Volterra type series. Three dentification approaches are discussed: conventional identification based on both input and output samples, semi–blind identification placing emphasis on minimal input resources and blind identification whereby only output samples are available plus a–priori information on input characteristics. Based on this taxonomy a variety of algorithms, existing and new, are studied and evaluated by simulation

Sparseness-controlled adaptive algorithms for supervised and unsupervised system identification

In single-channel hands-free telephony, the acoustic coupling between the loudspeaker and the microphone can be strong and this generates echoes that can degrade user experience. Therefore, effective acoustic echo cancellation (AEC) is necessary to maintain a stable system and hence improve the perceived voice quality of a call. Traditionally, adaptive filters have been deployed in acoustic echo cancellers to estimate the acoustic impulse responses (AIRs) using adaptive algorithms. The performances of a range of well-known algorithms are studied in the context of both AEC and network echo cancellation (NEC). It presents insights into their tracking performances under both time-invariant and time-varying system conditions. In the context of AEC, the level of sparseness in AIRs can vary greatly in a mobile environment. When the response is strongly sparse, convergence of conventional approaches is poor. Drawing on techniques originally developed for NEC, a class of time-domain and a frequency-domain AEC algorithms are proposed that can not only work well in both sparse and dispersive circumstances, but also adapt dynamically to the level of sparseness using a new sparseness-controlled approach. As it will be shown later that the early part of the acoustic echo path is sparse while the late reverberant part of the acoustic path is dispersive, a novel approach to an adaptive filter structure that consists of two time-domain partition blocks is proposed such that different adaptive algorithms can be used for each part. By properly controlling the mixing parameter for the partitioned blocks separately, where the block lengths are controlled adaptively, the proposed partitioned block algorithm works well in both sparse and dispersive time-varying circumstances. A new insight into an analysis on the tracking performance of improved proportionate NLMS (IPNLMS) is presented by deriving the expression for the mean-square error. By employing the framework for both sparse and dispersive time-varying echo paths, this work validates the analytic results in practical simulations for AEC. The time-domain second-order statistic based blind SIMO identification algorithms, which exploit the cross relation method, are investigated and then a technique with proportionate step-size control for both sparse and dispersive system identification is also developed