THE GENERALIZED MULTIDELAY ADAPTIVE FILTER - STRUCTURE AND CONVERGENCE ANALYSIS

Frequency-domain adaptive filters have long been recognized as an attr active alternative to time-domain algorithms when dealing with systems with large impulse response and/or correlated input. Recently, new fr equency-domain LMS adaptive schemes have been proposed. These algorith ms essentially retain the attractive features of frequency-domain impl ementations, while requiring a processing delay considerably smaller t han the length of the impulse response. The first purpose of this cont ribution is to show that these algorithms can be seen as particular im plementations of a more general scheme, the generalized multidelay fil ter (GMDF). Within this general class of algorithms, we focus on imple mentations based on the weighted overlap and add reconstruction algori thms; these variants, overlooked in previous contributions, provide an independent control of the overall processing delay and of the rate o f update of the filter coefficients, allowing a trade-off between the computational complexity and the rate of convergence. The second purpo se of this work is to present a comprehensive analysis of the performa nce of this new scheme and to provide insight into the influence of im pulse response segmentation on the behavior of the adaptive algorithm. Exact analytical expressions for the steady-state mean-square error a re first derived. Necessary and sufficient conditions for the converge nce of the algorithm to the optimal solution within finite variance ar e then obtained, and are translated into bounds for the stepsize param eter. Simulations are presented to support our analysis and to demonst rate the practical usefulness of the GMDF algorithm in applications wh ere large impulse response has to be processed.