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

Machine-learning nonstationary noise out of gravitational-wave detectors

Signal extraction out of background noise is a common challenge in high-precision physics experiments, where the measurement output is often a continuous data stream. To improve the signal-to-noise ratio of the detection, witness sensors are often used to independently measure background noises and subtract them from the main signal. If the noise coupling is linear and stationary, optimal techniques already exist and are routinely implemented in many experiments. However, when the noise coupling is nonstationary, linear techniques often fail or are suboptimal. Inspired by the properties of the background noise in gravitational wave detectors, this work develops a novel algorithm to efficiently characterize and remove nonstationary noise couplings, provided there exist witnesses of the noise source and of the modulation. In this work, the algorithm is described in its most general formulation, and its efficiency is demonstrated with examples from the data of the Advanced LIGO gravitational-wave observatory, where we could obtain an improvement of the detector gravitational-wave reach without introducing any bias on the source parameter estimation

A Novel Method for Acoustic Noise Cancellation

Over the last several years Acoustic Noise Cancellation (ANC) has been an active area of research and various adaptive techniques have been implemented to achieve a better online acoustic noise cancellation scheme. Here we introduce the various adaptive techniques applied to ANC viz. the LMS algorithm, the Filtered-X LMS algorithm, the Filtered-S LMS algorithm and the Volterra Filtered-X LMS algorithm and try to understand their performance through various simulations. We then take up the problem of cancellation of external acoustic feedback in hearing aid. We provide three different models to achieve the feedback cancellation. These are - the adaptive FIR Filtered-X LMS, the adaptive IIR LMS and the adaptive IIR PSO models for external feedback cancellation. Finally we come up with a comparative study of the performance of these models based on the normalized mean square error minimization provided by each of these feedback cancellation schemes

Output-error LMS bilinear filters with stability monitoring

Journal ArticleABSTRACT This paper introduces output-error LMS bilinear filters with stability monitoring. Bilinear filters are recursive nonlinear systems that belong to the class of polynomial systems. Because of the feedback structure, such models are able to represent many nonlinear systems efficiently. However, the usefulness of adaptive bilinear filters is greatly restricted unless they are guaranteed to perform in a stable manner. A stability monitoring scheme is proposed to overcome the stability problem. The paper concludes with simulation results that demonstrate the usefulness of oiir technique

FAST IMPLEMENTATION TECHNIQUES OF MULTICHANNEL DIGITAL FILTERS FOR COLOR IMAGE PROCESSING USING MATRIX DECOMPOSITIONS

For the processing of color images, multivariable 3-input, 3-output 2-D digital filters are used, considering decomposition in the R, G and B components. Assuming that the three image components are decorrelated, three independent single-input, single-output (SISO) two-dimensional (2-D) digital filters are needed for the processing of each monochromatic image. Additional processing is needed for the correlated noise components in each chan- nel. The requirement of very fast processing dictates the use of special purpose hardware implementations. The VLSI array processors, which are special purpose, locally intercon- nected computing networks, are ideally suited for the fast implementation of digital filters, since they maximize concurrency by exploiting both parallelism and pipelining. In this paper fast implementation architectures of 3-input, 3-output 2-D multi-input digital filters for color image processing that are based on matrix decompositions are presented. The resulting structures are modular, regular, have high inherent parallelism and are easily pipelined, so that they may be implemented via VLSI array processors

Method and system for training dynamic nonlinear adaptive filters which have embedded memory

Described herein is a method and system for training nonlinear adaptive filters (or neural networks) which have embedded memory. Such memory can arise in a multi-layer finite impulse response (FIR) architecture, or an infinite impulse response (IIR) architecture. We focus on filter architectures with separate linear dynamic components and static nonlinear components. Such filters can be structured so as to restrict their degrees of computational freedom based on a priori knowledge about the dynamic operation to be emulated. The method is detailed for an FIR architecture which consists of linear FIR filters together with nonlinear generalized single layer subnets. For the IIR case, we extend the methodology to a general nonlinear architecture which uses feedback. For these dynamic architectures, we describe how one can apply optimization techniques which make updates closer to the Newton direction than those of a steepest descent method, such as backpropagation. We detail a novel adaptive modified Gauss-Newton optimization technique, which uses an adaptive learning rate to determine both the magnitude and direction of update steps. For a wide range of adaptive filtering applications, the new training algorithm converges faster and to a smaller value of cost than both steepest-descent methods such as backpropagation-through-time, and standard quasi-Newton methods. We apply the algorithm to modeling the inverse of a nonlinear dynamic tracking system 5, as well as a nonlinear amplifier 6

Volterra and general polynomial related filtering

Journal ArticleThis paper presents a review of polynomial filtering and, in particular, of tlie truncated Volterra filters. Following the introduction of the general properties of such filters, issues such as eficieiit realizations, design, adaptive algoritlims and stability are discussed

A simple algorithm for stable order reduction of z-domain Laguerre models

International audienceDiscrete-time Laguerre series are a well known and efficient tool in system identification and modeling. This paper presents a simple solution for stable and accurate order reduction of systems described by a Laguerre model