A group theoretic approach to multidimensional filter banks: theory and applications

In this paper, we provide a new method for analyzing multidimensional filter banks. This method enables us to solve various open problems in multidimensional filter bank characterization and design. The essential element in this new approach is the redefinition of polyphase components. It will be shown that a rich set of mathematical tools, in particular algebraic group theory, will become available for use in the analysis of filter banks. We demonstrate the elegance and power of the tool set by employing it for the characterization of multidimensional filter banks and applying it to two open problems. The first problem is concerned with the development of a general method to design multichannel (⩾2), multidimensional filter banks using transformations, while the second problem is concerned with the derivation of general restrictions on group delays in linear phase filter banks. The treatment of these problems is only an illustration of the power of the tool set of algebraic group theory, employed for the first time in the context of multidimensional filter banks