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Support size restrictions on time‐frequency representations of functions on finite abelian groups
Author(s) -
Krahmer Felix,
Pfander Götz,
Rashkov Peter
Publication year - 2008
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200810825
Subject(s) - abelian group , fourier transform , fourier transform on finite groups , gabor transform , cardinality (data modeling) , short time fourier transform , fourier inversion theorem , mathematics , fractional fourier transform , uncertainty principle , class (philosophy) , pure mathematics , discrete mathematics , fourier analysis , mathematical analysis , time–frequency analysis , computer science , physics , telecommunications , artificial intelligence , data mining , radar , quantum mechanics , quantum
We obtain uncertainty principles for finite abelian groups that relate the cardinality of the support of a function to the cardinality of the support of its short–time Fourier transform. These uncertainty principles are based on well–established uncertainty principles for the Fourier transform. In terms of applications, the uncertainty principle for the short–time Fourier transform implies the existence of a class of equal norm tight Gabor frames that are maximally robust to erasures. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)