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Fourier Transforms of Finite Chirps

  • Peter G. Casazza
  • Matthew Fickus
Open Access
Research Article
Part of the following topical collections:
  1. Frames and Overcomplete Representations in Signal Processing, Communications, and Information Theory

Abstract

Chirps arise in many signal processing applications. While chirps have been extensively studied as functions over both the real line and the integers, less attention has been paid to the study of chirps over finite groups. We study the existence and properties of chirps over finite cyclic groups of integers. In particular, we introduce a new definition of a finite chirp which is slightly more general than those that have been previously used. We explicitly compute the discrete Fourier transforms of these chirps, yielding results that are number-theoretic in nature. As a consequence of these results, we determine the degree to which the elements of certain finite tight frames are well distributed.

Keywords

Fourier Fourier Transform Information Technology Signal Processing Quantum Information 

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Copyright information

© Casazza and Fickus 2006

Authors and Affiliations

  • Peter G. Casazza
    • 1
  • Matthew Fickus
    • 2
  1. 1.Department of MathematicsUniversity of MissouriColumbiaUSA
  2. 2.Department of Mathematics and StatisticsAir Force Institute of TechnologyWright-Patterson AFBUSA

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