Theory of Two-Dimensional Multirate Filter Banks

Abstract

New results are presented on two-dimensional finite-im-pulse-response filter banks for multirate applications. The theory is valid for all sampling lattices, and conditions for alias-free and perfect signal reconstruction are derived. Synthesis structures for paraunitary and nonparaunitary polynomial matrices are derived, which yield perfect reconstruction filter banks. The degrees of freedom are given for these systems. Linear phase conditions are posed on the polyphase form of filter banks, which is used to derive a design structure for the restricted, but important, case of linear phase filter banks. © 1990 IEEE