Date of Award
Electrical and Computer Engineering
Engineering, Electronics and Electrical.
CC BY-NC-ND 4.0
This work is an investigation into the use of the number theoretic techniques for implementing digital signal processing algorithms. In particular, residue coding principles are applied to fast digital convolution via the Number Theoretic Transform (NTT) and to digital filtering via recursive digital filters. The initial study of implementing the NTT using the residue number system (RNS) leads to the idea of implementing the transform over a direct sum of several extension fields, or rings, with the RNS architectures of ROM arrays or microprocessor arrays. New results and theorems are obtained for transform parameters that have a simple form which allows a reduction in the number of binary operations and allowing efficient implementation. These results are verified by computer programs. The application of the RNS for second order recursive digital filter sections is also investigated. Some of the design problems associated with read-only-memory implementation of second order sections, which can be used as building blocks for higher order recursive filters are considered along with a study of quantization error and limit cycle behavior. A new scheme for translation of the residue coded output into a binary representation is also developed in this thesis.Dept. of Electrical and Computer Engineering. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis1980 .B373. Source: Dissertation Abstracts International, Volume: 41-03, Section: B, page: 1048. Thesis (Ph.D.)--University of Windsor (Canada), 1980.
BARANIECKA, ANNA Z., "DIGITAL FILTERING USING NUMBER-THEORETIC TECHNIQUES." (1980). Electronic Theses and Dissertations. 1744.