A complete factorization of paraunitary matrices with pairwise mirror-image symmetry in the frequency domain

Abstmct-The problem of designiiag orthonormal (paraunitary) filter banks has been addressed in the past. Several structures have been reported for implementing such systems. One of the structur es reported imposes a pairwise mirror-image symmetry constraint on the frequency responses of the analysis (and synthesis) filters around 7r/2. This shveture requires fewer multipliers, and the design time is correspondingly less than most other structures. The mters designed also have much better attenuation. In this compodence, we characterize the polyphase matrix of the above filters in terms of a mpMx equation. We then prove that the structure reported in a paper by Nguyen and Vaidyanathan, with minor modiUcations, is complete. This means that every polyphase matrix w h w filters satisfy the mirror-image property can be faaorized in terms of the proposed structure.