Cosine-modulated FIR filter banks satisfying perfect reconstruction

Abstract

The authors obtain a necessary and sufficient condition on the 2M (M = number of channels) polyphase components of a linear-phase prototype filter of length N = 2mM (where m = an arbitrary positive integer), such that the polyphase component matrix of the modulated filter is lossless. The losslessness of the polyphase component matrix, in turn, is sufficient to ensure that the analysis/synthesis system satisfies perfect reconstruction (PR). Using this result, a novel design procedure is presented based on the two-channel lossless lattice. This enables the design of a large class of FIR (finite impulse response)-PR filter banks, and includes the N = 2M case. It is shown that this approach requires fewer parameters to be optimized than in the pseudo-QMF (quadrature mirror filter) designs and in the lossless lattice based PR-QMF designs (for equal length filters in the three designs). This advantage becomes significant when designing long filters for large M. The design procedure and its other advantages are described in detail. Design examples and comparisons are included.