Support size restrictions on time-frequency representations of functions on finite abelian groups |
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| Authors: | Felix Krahmer Götz Pfander Peter Rashkov |
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| Institution: | 1. Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY, 10009, USA;2. School of Engineering and Science, Jacobs University, College Ring 1, 28759 Bremen, Germany |
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| Abstract: | 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) |
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