Gerald Larocque

Multi-Rate Adaptive Filters

Advisor: H. Lev-Ari

Date: Monday, April 30, 2001

In this thesis, the Block Least Mean Square (BLMS) algorithm is extended to include a general finite impulse response (FIR) interpolating filter, resulting in a new adaptive filter architecture (GLMS). The performance of the BLMS and GLMS algorithms is evaluated with respect to steady state error performance and ability to track in a non-stationary environment. Algorithm error is partitioned into Steady State and Lag Error components for which approximate expressions are developed. In the cases of BLMS and first order GLMS, closed form expressions for the algorithm performance are obtained using a "random walk" model for the variation in the desired tap weight vector. The results also provide a basis for evaluation of other filters and optimal tap weight dynamics by use of numerical methods. Evaluation of the resulting expressions for BLMS and first order GLMS demonstrate clear performance differences with respect to the two error components as a function of the algorithm's update rate. Additionally, it has been shown that, in the case of random walk dynamics for the desired tap weight vector, the best performance is obtained for a zero order interpolation filter that corresponds to the conventional BLMS algorithm.