Design of conjugate quadrature filters having specified zeros

Conjugate quadrature filters (CQF) with multiple zeros at 1 have classical applications to unitary subband coding of signals using exact reconstruction filter banks. Previous work shows how to construct, given a set of n negative numbers, a CQF whose degree does not exceed 2n-1 and whose zeros contain the specified negative numbers, and applies such filters to interpolatory subdivision and to wavelet construction in Sobelov spaces. This paper describes a previous result of the authors which extends this construction for an arbitrary set of n nonzero complex numbers that contains no negative or negative reciprocal conjugate pairs. Detailed derivations are given elsewhere. We design several filters using an exchange algorithm to illustrate a conjecture concerning the minimal degree and we discuss an application to coding transient acoustic signals