Residue Number System Recursive Digital Filtering With Error Correction Capabilities

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Electrical Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• Etzel, Mark Howard

• Engineering, Electronics and Electrical

Language dc:language

eng

Identifier

(UMI)AAI8026489

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/66230