The design of uniformly and nonuniformly spaced pseudoquadrature mirror filters

In the past, quadrature mirror filters (QMF´s) have been used to derive both uniformly and nonuniformly spaced filterbanks. A pair of QMF´s divides a signal into two equal bands which can be decimated at 2:1 and subsequently combined to reconstruct the original signal. In order to derive filterbanks with more than two bands, QMF´s are combined in a binary tree structure. Pseudoquadrature mirror filters are similar to QMF´s but can be designed to split a signal directly into any number of equally spaced bands, thus generalizing the QMF concept. In this paper, 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. An extension is made to the theory 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 analog scrambling of speech.