Structural sub-band decomposition for adaptive filters

Abstract

The theory of structural sub-band decomposition of an FIR filters is extended to adaptive filters. It is shown that this sub-band decomposition is equivalent to the transform of input data by orthogonal matrices, of which the Walsh-Hadamard Transform (WHT) is a special case. Thus, the proposed method is a generalization of the transform domain adaptive filtering (TDAF) using WHT, which is already known to enhance the convergence speed of adaptive filters. Furthermore, our method yields one possible hardware implementation of the fast WHT. The convergence behavior of the proposed sub-band adaptive filters is simulated using the Least Mean Squares (LMS) and Recursive Least Squares (RLS) algorithms. The results show the faster convergence speed of the proposed adaptive filters compared to conventional adaptive filters.