Adaptive FIR filters based on structural subband decomposition for system identification problems

LMS (least-mean-square) adaptive filtering algorithms using FIR (finite-impulse-response) filter structures based on structural subband decomposition are developed. It is shown that the subband decomposition is equivalent to transformation of input data by orthogonal matrices of which the Walsh-Hadamard transform (WHT) is a special case. The proposed method is a generalization of WHT-based transform domain adaptive filtering, which is known to enhance the convergence speed of adaptive filters. It is also shown that the interpolator network of the subband structure is a fast implementation of the required transform and is therefore attractive from a practical standpoint. The convergence properties of subband FIR adaptive filters are studied for system identification applications. The results demonstrate the advantages of the proposed structure compared to conventional adaptive filters