DocumentCode
1505657
Title
The optimal transform for the discrete Hirschman uncertainty principle
Author
Przebinda, Tomasz ; DeBrunner, Victor ; Özaydin, Murad
Author_Institution
Dept. of Math., Oklahoma Univ., Norman, OK, USA
Volume
47
Issue
5
fYear
2001
fDate
7/1/2001 12:00:00 AM
Firstpage
2086
Lastpage
2090
Abstract
We determine all signals giving equality for the discrete Hirschman uncertainty principle. We single out the case where the entropies of the time signal and its Fourier transform are equal. These signals (up to scalar multiples) form an orthonormal basis giving an orthogonal transform that optimally packs a finite-duration discrete-time signal. The transform may be computed via a fast algorithm due to its relationship to the discrete Fourier transform
Keywords
discrete Fourier transforms; discrete transforms; entropy; information theory; signal representation; Fourier transform; discrete Fourier transform; discrete Hirschman uncertainty principle; entropy; finite-duration discrete-time signal; optimal transform; orthogonal transform; orthonormal basis; time signal; Compaction; Discrete Fourier transforms; Discrete transforms; Entropy; Fast Fourier transforms; Fourier transforms; Mathematics; Phase measurement; Signal representations; Uncertainty;
fLanguage
English
Journal_Title
Information Theory, IEEE Transactions on
Publisher
ieee
ISSN
0018-9448
Type
jour
DOI
10.1109/18.930948
Filename
930948
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