On the Eigenvectors of the Matrix That Performs the Discrete Finite Fourier Transform

Abstract

The discrete finite Fourier transform can be regarded as a matrix operation, since each element of one member of the pair is a linear combination of all the elements of the other member. A remarkably simple relation between a periodic function of a discrete variable and its discrete finite Fourier transform, namely that the absolute values of their expansion coefficients in these eigenvectors are the same, has been demonstrated. A canonical form for such functions (with respect to the finite Fourier transform) is suggested in which the transform can be done by inspection.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Mar 12, 1973
Accession Number
AD0758892

Entities

People

  • D. W. Mccowan
  • E. A. Flinn
  • G. M. Molchan

Tags

DTIC Thesaurus Topics

  • Air Force
  • Algebra
  • Contracts
  • Data Processing
  • Digital Data
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Fast Fourier Transforms
  • Functions (Mathematics)
  • Inspection
  • Integral Equations
  • New York
  • Numbers
  • Periodic Functions
  • Scientific Research
  • Vector Spaces

Fields of Study

  • Engineering

Readers

  • Approximation Theory.