Fourier Transforms of Finite Chirps

Document Type


Publication Date



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.


The "Link to Full Text" button on this page loads the open access article version of record, hosted at SpringerOpen on behalf of Hindawi. The publisher retains permissions to re-use and distribute this article.

This paper predates the "Gold OA" status for the source journal.



Source Publication

EURASIP Journal on Applied Signal Processing