Variance of Signals and Their Finite Fourier Transforms

  • D. V. ChudnovskyEmail author
  • G. V. Chudnovsky
  • T. Morgan


The study of properties of the finite Fourier matrix can be traced back to I. Schur and his use of the Gauss reciprocity law to determine the spectral properties of the finite Fourier matrix. Unlike the continuous Fourier transform, there is no widely accepted eigenvector basis. We present different approaches to eigenvector construction for the finite Fourier matrix, and a new set of extremality principles for the finite Fourier transform. One of the consequences of this construction is a new discrete uncertainty principle, analogous to a classical Heisenberg–Weyl formulation.


Eigenvectors Fourier matrix Fractional fourier transform 


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • D. V. Chudnovsky
    • 1
    Email author
  • G. V. Chudnovsky
    • 1
  • T. Morgan
    • 1
  1. 1.Polytechnic Institute of NYU, IMASBrooklynUSA

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