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Fourier Transforms of Finite Chirps

EURASIP Journal on Advances in Signal Processing volume 2006, Article number: 070204 (2006) Cite this article

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.

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Authors and Affiliations

  1. Department of Mathematics, University of Missouri, Columbia, MO, 65211, USA

    Peter G. Casazza

  2. Department of Mathematics and Statistics, Air Force Institute of Technology, Wright-Patterson AFB, OH, 45433, USA

    Matthew Fickus

Authors
  1. Peter G. Casazza
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  2. Matthew Fickus
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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Casazza, P.G., Fickus, M. Fourier Transforms of Finite Chirps. EURASIP J. Adv. Signal Process. 2006, 070204 (2006). https://doi.org/10.1155/ASP/2006/70204

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  • DOI: https://doi.org/10.1155/ASP/2006/70204

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