BANKS SATISFYING PERFECT RECONSTRUCTION
R. David Koilpillai, Palghat P. Vaidyanathan · 1991
It is well known that M-channel FIR filter banks, satisfying the perfect reconstruction (PR) property, can be obtained by the modulation of a linear-phase prototype of length N = 2M when certain constraints are imposed on the prototype. Recently, this result was extended to the case when N = 2mM, m 2 1. In this paper, we present a necessary and sufficient condition on the 2M polyphase components of the prototype filter (length N = 2mM) such that the polyphase component matrix of the filter bank is lossless. The losslessness of the polyphase component matrix ensures that the analysis/synthesis system satisfies PR. Based on this, we present a design procedure which enables the design of a large class of FIR-PR filter banks. It is shown that in this approach, there are significantly fewer parameters to be optimized than other M-channel QMF designs (for prototypes of equal length). This advantage becomes significant when designing long filters for large M. The design procedure is described a.nd a design example is included.