THE DESIGN OF UNIFORMLY AND NONUNIFORMLY SPACED PSEUDOQUADRATURE MIRROR FILTERS

A pair of quadrature mirror filters (QMFs) divides a signal into two equal bands which can be decimated at 2:1 and subsequently combined to reconstruct the original signal. To derive banks with more than two bands, QMFs are combined in a binary tree structure. Pseudoquadrature mirror filters are similar to QMFs but can be designed to split a signal directly into any number of equally spaced bands, thus generalizing the QMF concept. The theory of pseudoquadrature mirror filters is reviewed. These filters retain the desirable property that the channel signals from a uniformly spaced bank of M filters can be decimated by M:1, then interpolated and reassembled to reproduce the original signal. The theory is extended to allow a set of nonuniformly spaced filters to be derived from a uniformly spaced set and still retain all the desirable characteristics. Another extension to the theory is the derivation of a family of different sized filterbanks, all derived from the same original prototype. Potential applications for the new filterbanks include improvements in subband coding of speech and music, and the analog scrambling of speech.