The Use of Finite Fields and Rings to Compute Convolutions

Abstract

This note extends briefly the integer transforms of C.M. Radar (1972) to transforms over finite fields and rings. These transforms have direct application to digital filters and make possible digital filtering without round-off error. In some cases, the parameters of such number-theoretic transforms can be chosen so that substantial reductions in hardware are possible over what would be needed using classical digital filtering techniques.

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Document Details

Document Type
Technical Report
Publication Date
Jun 06, 1975
Accession Number
ADA016955

Entities

People

  • Irving S. Reed

Organizations

  • Massachusetts Institute of Technology

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Abstracts
  • Arithmetic
  • Binary Arithmetic
  • Complex Numbers
  • Delta Functions
  • Digital Filters
  • Fast Fourier Transforms
  • Filters
  • Filtration
  • Number Theory
  • Numbers
  • Polynomials
  • Prime Numbers
  • Rational Numbers
  • Theorems
  • Two Dimensional
  • United States Government

Readers

  • Computer Programming and Software Development.
  • Phased Array Antenna Design.
  • Theoretical Analysis.