A Procedure to Adapt Filter Banks to Finite-Length Signals

In this paper, we consider the problem of processing finite-length signals by means of critically sampled or oversampled filter banks. Based on a polyphase matrix factorization of the filter bank, we propose a realization adaptation that does not make any assumption about the signal values outside the support of the input signal, contrary to what is done, for instance, when using zero padding, periodic repetition or extension by symmetry. The proposed procedure has several advantages. In particular, we show that it preserves the perfect reconstruction and the general properties of the filter bank.