A comparison of design methods for 2-D FIR orthogonal perfect reconstruction filter banks

This paper examines the design of nonseparable 2-D FIR perfect reconstruction filter banks. We restrict our attention to orthogonal filter banks, i.e., analysis and synthesis filter banks with paraunitary polyphase matrices. The design problem reduces to the selection of a 2-D FIR paraunitary polyphase matrix, such that the filtering characteristics of the analysis or synthesis filters approximate as closely as possible the ideal bandpass characteristics of their desired frequency bands. Three design methods are compared. The first method, which was developed by Viscito and Allebach (1991), designs the impulse response of the polyphase matrix in the space-domain. A second technique was proposed in a paper by Karlsson Vetterli (1990) and relies on the subclass of 2-D paraunitary transfer matrices which can be represented as a product of paraunitary matrices of McMillan degree one in each variable. Finally, we develop a third approach based on a parametrization of 2-D FIR paraunitary matrices in terms of orthonormal minimal 2-D state-space realizations. The design examples that we present indicate that the third approach may have significant advantages, at least for the design of orthogonal filter banks with small spatial support