Analysis and design of FIR multirate filter banks

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This thesis is concerned with the analysis and design of FIR multirate filter banks. Focusing on the time-frequency relation of the filter bank structures, various design methods have been developed. Standard digital filtering techniques are used such as windowing, and least squares in conjunction with the multirate structures of the filter banks to obtain efficient designs that will allow a great degree of flexibility in controlling the frequency characteristics of the filters. A spectral factorisation technique is introduced to design three-channel based systems in the z-domain. This method extends the well known two-channel based design, and requires no numerical optimization. Time-domain algorithms are introduced to design M-channel systems with arbitrary length filters and arbitrary system delays. Aliasing cancellation and perfect reconstruction conditions in the time domain are addressed. A recursive technique is proposed which uses the synthesis filters from one iteration to update the analysis filters for the next. Wavelets provide a new method for time-scale analysis of non-stationary signals. Filter banks are used to construct several classes of wavelet transforms; orthonormal, bi-orthogonal, and new low delay wavelets using the time-domain formulation.

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