A group of permutations that commute with the discrete Fouriertransform

  • Authors:

  • P.J.S.G. Ferreira

  • Affiliations:

  • Dept. de Electron. e Telecoms, Aveiro Univ.

  • Venue:
  • IEEE Transactions on Signal Processing
  • Year:
  • 1994

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Abstract

The authors characterize a potentially useful set of permutation matrices that commute with the Fourier matrix of order n. The set of all such permutation matrices is a group under matrix multiplication, and every element of the group is its own inverse. They study the number of these permutations as a function of the order n_ of the Fourier matrix and conclude that it is a multiplicative function of n