New results in subband decomposition techniques and multirate filter design

In digital filtering one of the main areas of investigation has been the search for computationally efficient structures. Another important research focus has been in the development of the simple techniques for approximating a desired function within a given structure. This dissertation is concerned with these two aspects of digital filtering in multirate systems.; A part of the dissertation deals with the design of multirate filters. Two specific types of multirate filters are considered here with a distinct design objective in each case. The first type we consider is halfband filters, and we provide simple approximation techniques. The other type we consider is approximately linear-phase multirate filters. The design objective here resides in efficient filter structures.; The rest of the dissertation is devoted to the design of two-channel perfect reconstruction filter banks. We consider both one-dimensional filter banks and two-dimensional filter banks. A two-channel filter bank plays a central role in multiresolution signal decomposition or hierarchical signal decomposition; these have been extensively studied in recent years in speech/image processing, computer vision, and applied mathematics. Though the properties and theoretical aspects of a two-channel perfect reconstruction filter bank have been well understood for some years, there are yet some important design issues to be resolved. For constructing linear-phase FIR perfect reconstruction filter banks, a few design techniques do exist although these methods have some deficiencies. For causal IIR filter bank, adequate design methods do not seem to exist. In the dissertation we present a new framework for perfect reconstruction filter banks which provides solutions to the linear-phase FIR filter bank problem and causal IIR filter filter bank problem. The proposed filter bank structure is computationally efficient, flexible, and simple to design.