Adaptive Filtering Using Filter Banks and Sparse Subfilters

Some convergence properties of an adaptive filter structure which employs an analysis filter bank and sparse adaptive subfilters are investigated in this paper. By properly choosing the filter bank and the number of adaptive coefficients, such a structure is capable of modeling any linear system with finite impulse response (FIR). Using the analysis results derived in this paper, an optimization procedure is described to select the prototype filter of a cosine modulated filter bank that results in the best convergence rate for a given input signal statistics. The convergence behavior of the proposed subband adaptation algorithm is verified by computer simulations and compared to the behavior of previously proposed algorithms. It is shown that significant improvement in the convergence rate can be obtained with the sparse subband structure using very simple filter banks, when compared to the conventional direct-form LMS algorithm, for colored input signals. Key–Words: Adaptive filtering, Filter banks, Filter design, Convergence analysis, Multirate processing.