Design of perfect reconstruction multi-dimensional filter banks using cascaded Smith form matrices

The theory and design of multidimensional perfect reconstruction filter banks are discussed. A necessary and sufficient condition for perfect reconstruction in multidimensional filter banks is derived, and an approach to filter-bank design using cascaded polyphase matrices and a statistical filter design method is presented. The approach is applicable to arbitrary (not necessarily rectangular) decimation and interpolation schemes and any number of channels. The results of a preliminary numerical design example are presented.<>