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

The problem of designing orthonormal (paraunitary) filter banks has been addressed in the past. Several structures have been reported for implementing such systems. One of the structures reported imposes a pairwise mirror-image symmetry constraint on the frequency responses of the analysis (and synthesis) filters around π/2. This structure requires fewer multipliers, and the design time is correspondingly less than most other structures. The filters designed also have much better attenuation. We characterize the polyphase matrix of the above filters in terms of a matrix equation. We then prove that the structure reported in a paper by Nguyen and Vaidyanathan (1988), with minor modifications, is complete. This means that every polyphase matrix whose filters satisfy the mirror-image property can be factorized in terms of the proposed structure