Multidimensional multirate filters and filter banks : theory, design, and implementation

Citation

Chen, Tsuhan (1993) Multidimensional multirate filters and filter banks : theory, design, and implementation. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/XHE8-RB96. https://resolver.caltech.edu/CaltechETD:etd-08232007-095226

Abstract

Multidimensional (MD) multirate systems, which find applications in the coding and compression of image and video data, and in high definition television (HDTV) systems, have recently attracted much attention. Central to these systems is the idea of sampling lattices. The basic building blocks in an MD multirate system are the decimation matrix M, the expansion matrix L, and MD digital filters. When M and L are diagonal, most of the one-dimensional (1D) multirate results can be extended automatically, using separable approaches (i.e., separate operations in each dimension). Separable approaches are commonly used in practice due to their low complexity in implementation. However, nonseparable operations, with respect to nondiagonal decimation and expansion matrices, often provide more flexibility and better performance. Several applications, such as the conversion between progressive and interlaced video signals, actually require the use of nonseparable operations. For the nonseparable case, extensions of 1D results to the MD case are nontrivial. In this thesis, we will introduce some developments in these extensions. The three main results are: the design of nonseparable MD filters and filter banks derived from 1D filters, the commutativity of MD decimators and expanders and its applications to the efficient polyphase implementation of MD rational decimation systems, and the vector space framework for unifying MD filter bank and wavelet theory. In particular, properties of integer matrices like matrix fraction descriptions, coprimeness, the Bezout identity, etc., of which the polynomial versions are known in system theory, are used for the first time in the area of multirate signal processing.

Thesis Files