Design of oversampled multichannel filter banks

This thesis introduces a general approach for the design of oversampled multichannel filter banks including one-dimensional and nonseparable multidimensional filter banks, as well as filter banks with linear phase and complex-valued coefficients. The approach is carried within the framework of rectangular polyphase matrices, developed to design perfect reconstruction filter banks with uniform sampling in the subbands and finite impulse response filters.; This thesis introduces an approach for the design of two-dimensional oversampled filter banks that allows directional frequency selectivity with low redundancy. Directional two-dimensional filter banks find application in texture classification, denoising, segmentation, and enhancement. In several of these applications, the frequency directionality relies on oversampled filter banks with redundancy factors that range from two to four. This thesis uses non uniform frequency division of the unit frequency cell to design multichannel oversampled filter banks that have frequency directionality and redundancy factor less than two.; Additionally, this thesis expands the tools available for the design of wavelet systems by providing a formulation of the problem of filter bank design that covers polyphase matrices of one-dimensional perfect reconstruction filter banks, oversampled or critically sampled, with real- or complex-valued coefficients.; Although in the past the design of critically sampled filter banks was addressed using a formulation based either on the factorization of polyphase matrices or on the modulation of prototype windows, the design of oversampled filter banks was more restricted to modulation. No formulation based on the polyphase matrix existed in the oversampled case for multichannel filter banks with complex-valued coefficients. Furthermore, no approach in the oversampled case had a formulation for linear phase filter banks with non integer rational oversampling ratios for non uniform bandwidth filters.