UNITARY FIR FILTER BANKS AND SYMMETRY

Recently, unitary FIR filter banks with linear-phase have been complet ely parameterized [8] by exploiting the eigenstructure of the exchange matrix. This correspondence gives new characterizations of polyphase matrices of filter banks with various types of symmetry on the filters . Using matrix extensions of the well-known hyperbolic and orthogonal lattices, we give a alternative proof for the parameterization of line ar-phase unitary filter banks. A complete parameterization of FIR unit ary filter banks with each of the different types of symmetries consid ered (not just linear-phase) is also given. These results can also be used to generate non-unitary filter banks with symmetries, though no c ompleteness results can be obtained. In some cases implicit, and in ot hers explicit parameterization of wavelet tight frames associated with these filter banks are also given. This paper only considers filter b anks with an even number of channels. A similar theory can be develope d if the number of channels is an odd integer.