Residue Number System Recursive Digital Filtering With Error Correction Capabilities
Etzel, Mark Howard
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https://hdl.handle.net/2142/66230
Description
Title
Residue Number System Recursive Digital Filtering With Error Correction Capabilities
Author(s)
Etzel, Mark Howard
Issue Date
1980
Department of Study
Electrical Engineering
Discipline
Electrical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Electronics and Electrical
Language
eng
Abstract
Residue number system (RNS) digital filters are obtained by encoding all filter arithmetic and signals in a residue number system, creating an architecture consisting of a set of parallel arithmetic operations. To prevent overflow, the design and realization of recursive RNS digital filters require scaling, generally a difficult operation in an RNS. This research presents specialized residue classes in which scaling is a simple operation that can be easily mechanized. The resulting hierarchy of useful two-, three-, and four-modulus classes are described with an analysis of the quantization error due to scaling. Computer simulations illustrate the filter performance in these RNS classes. Despite much recent work in the design and realization of digital filters, little attention has been given to problems of error detection and correction in digital filters. This research examines inherent properties of RNS digital filters that can be used for such purposes. Theory is presented for handling overflow suppression and single error detection and correction both separately and simultaneously, and conditions for distinguishing single and double errors are discussed. The concept of gradual system degradation is described including results of computer simulations of filters with error handling capabilities and which are capable of continued operation in the presence of recurring errors. Possible hardware implementation of such a system are explored.
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