Signal Processing on Finite Groups

Abstract

A unified approach to the design and evaluation of fast algorithms for discrete signal processing is developed. Based on the theory of finite groups, it hence includes the familiar cases of the fast Fourier and Walsh- Hadamard transforms. However, the use of noncommutative groups reveals a large variety of novel methods. Some of these exhibit a superior performance, as measured by both reduced error rates and computational complexity, on nonstationary data. The recent history of this subject is reviewed first, followed by a detailed examination of the three principal ingredients of the present study: the underlying groups, the signal-processing tasks on which the group-based algorithms are to compete, and the signal models used to define the data environment. Test results and conclusions then follow, the former being based on the use of random correlation matrices. (kr)

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Document Details

Document Type
Technical Report
Publication Date
Feb 27, 1990
Accession Number
ADA221129

Entities

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  • Richard B. Holmes

Organizations

  • Massachusetts Institute of Technology

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  • Energy and Power Technologies
  • Sensors

DTIC Thesaurus Topics

  • Abstracts
  • Algorithms
  • Computational Complexity
  • Computational Science
  • Computer Programs
  • Data Compression
  • Hilbert Space
  • Information Theory
  • Mathematical Filters
  • Mathematics
  • Pattern Recognition
  • Probability
  • Random Variables
  • Signal Processing
  • Standards
  • Statistics
  • Stochastic Processes

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