A Group Theoretic Approach

Keywords| Filter banks, bi-orthogonal, linear phase, McClellan transformations, multirate systems. EDICS| Filter Bank Theory 2.4.2. Abstract| In this paper we provide a new method for analyzing multidimensional lter banks. This method enables us to solve various open problems in multidimensional l-ter bank characterization and design. The essential element in this new approach is the redeenition 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 lter banks. We demonstrate the elegance and power of the tool set by employing it for the characterization of multidimensional lter banks, and by applying it to two open problems. The rst problem is concerned with the development of a general method to design multichannel (2) multidimensional lter banks using transformations, while the second problem is concerned with the derivation of general restrictions on group delays in linear phase lter banks. The treatment of these problems is only an illustration of the power of the tool set of algebraic group theory, employed for the rst time in the context of multidimensional lter banks.