A COMPLETE FACTORIZATION OF PARAUNITARY MATRICES WITH PAIRWISE MIRROR-IMAGE SYMMETRY IN THE FREQUENCY-DOMAIN

The problem of designing orthonormal (paraunitary) filter banks has be en addressed in the past, Several structures have been reported for im plementing such systems. One of the structures reported imposes a pair wise mirror-image symmetry constraint on the frequency responses of th e analysis (and synthesis) filters around pi/2. This structure require s fewer multipliers, and the design time is correspondingly less than most other structures, The filters designed also have much better atte nuation. In this correspodence, we characterize the polyphase matrix o f the above filters in terms of a matrix equation, We then prove that the structure reported in a paper by Nguyen and Vaidyanathan, with min or modifications, is complete, This means that every polyphase matrix whose filters satisfy the mirror-image property can be factorized in t erms of the proposed structure.