A perfect reconstruction filter bank with irrational down-sampling factors

Most of the existing methods designed to implement fractional interpolation and decimation are limited by rational scaling factors such as L/M, where L and M are positive integers. The general procedure is usually done with up-sampling by L first, and then followed by down-sampling by M. This scheme, however, requires two steps to fulfill and is not capable in dealing with irrational scaling factors, which can not be represented by L/M. In this paper, we propose a new method to solve the above two difficulties by a single step. Furthermore, a perfect reconstruction filter bank is derived using this new method and the experimental results are presented.