Convergence analysis of a subband adaptive filter structure

This paper investigates the convergence properties of an adaptive FIR subband structure, where the input signal is decomposed by an analysis filter bank and each of the subband signals is modified by shorter adaptive filters operating at a lower rate. We consider here a subband structure with down-sampling factor smaller than the number of subbands. A convergence analysis is presented, where it is shown that the non-ideal filter bank characteristics cause a degradation in the adaptation speed. Such degradation increases with the number of subbands and calls for the use of more sophisticated adaptive algorithms than the LMS algorithm. Computer simulation results are presented with the objective of verifying the convergence analysis