Tree structure filter bank for wideband signal processing.

Abstract

A N-parallel branches maximally decimated filter bank is generally implemented using the polyphase components implementation. In this case, a N-th band lowpass filter is designed and its polyphase components are derived to constitute the branch 'subfilters.' This approach uses a N x N FFT matrix that will be the source of the complex (numbers) operations. Obviously, when the number of branches is equal to 2, the computations remain real. In a tree structure filter bank, the computations remain real with or without polyphase implementation. When the polyphase implementation is used, the branch signals at each stage are computed using a set of 2 x 2 FFT matrices leading to real computations. In this thesis, a new implementation approach based on the tree structured is proposed. The derivation of the structure is based on the equivalent parallel structure implementation of the tree structured filter bank. It uses the polyphase components of a given half-band lowpass filter (real coefficients) followed by a N x N Hadamard matrix. The computations, as in the original tree structured filter bank, remain real. A simplified version of the structure is a 'tree structure' followed by an N x N Hadamard matrix. A comparison between this new structure and the N parallel branch maximally decimated filter bank is made based on reconstruction error, computation complexity and processing delay.