A sequentially operated periodic FIR filter for perfect reconstruction

This paper presents a sequentially operated periodic FIR filter to perform the functions of multirate filter banks for perfect reconstruction. This filter consists of an analysis filter and a synthesis filter. Each of these filters has a single-input/single-output FIR filter with periodically time-varying coefficients and a sequentially operated multichannel sampling scheme. As a result, the proposed filter can offer considerable improvements in computation and implementation. For the design of the filter, we provide a necessary and sufficient condition for perfect reconstruction in terms of the blocked transfer matrices and give a design procedure.