Transform domain adaptive filtering using Walsh transforms

Abstract

The purpose of this study is to investigate the behaviour of the transform domain adaptive filter in the Walsh domain. As it is well known, because of the binary nature of the basis functions, the computationally intensive frequency domain adaptive filter algorithm lends itself to easier implementation if Walsh transform is employed. This thesis starts with a brief review of Walsh functions, Walsh transforms and adaptive filtering. The Walsh domain adaptive filter has been simulated on the digital computer. Simulation results for various input signals embedded in noise are given. It is shown that better convergence can be achieved when the adaptive filter is operated in the Walsh domain, rather than time domain. The effect of initial weight on convergence has been investigated. It has been observed that small values of the initial weight are necessary for better convergence performance. Although the theoretical basis of the effect of small initial weight on convergence characteristics has not been established yet, simulation results indicate improved performance with a small initial weight. Since the Walsh transform requires only additions and subtractions. the digital implementation of Walsh domain adaptive filter is easily achievable, and can be thought as the scope of a further study.