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EURASIP Journal on Applied Signal Processing 2001:4, 192205 2001 Hindawi Publishing Corporation
 

Summary: EURASIP Journal on Applied Signal Processing 2001:4, 192205
2001 Hindawi Publishing Corporation
Adaptive Filters with Error Nonlinearities: Mean-Square
Analysis and Optimum Design
Tareq Y. Al-Naffouri
Electrical Engineering Department, Stanford University, CA 94305, USA
Email: nafouri@stanford.edu
Ali H. Sayed
Electrical Engineering Department, University of California, Los Angeles, CA 90095, USA
Email: sayed@ee.ucla.edu
Received 7 August 2001 and in revised form 10 October 2001
This paper develops a unified approach to the analysis and design of adaptive filters with error nonlinearities. In particular, the
paper performs stability and steady-state analysis of this class of filters under weaker conditions than what is usually encountered
in the literature, and without imposing any restriction on the color or statistics of the input. The analysis results are subsequently
used to derive an expression for the optimum nonlinearity, which turns out to be a function of the probability density function of
the estimation error. Some common nonlinearities are shown to be approximations to the optimum nonlinearity. The framework
pursued here is based on energy conservation arguments.
Keywords and phrases: adaptive filter, mean-square error, energy conservation, transient analysis, steady-state analysis, stability,
error nonlinearity.
1. INTRODUCTION

  

Source: Al-Naffouri, Tareq Y. - Electrical Engineering Department, King Fahd University of Petroleum and Minerals
Sayed, Ali - Electrical Engineering Department, University of California at Los Angeles

 

Collections: Engineering