Bulg. J. Phys. vol.36 no.s1 (2009), pp. 54-59

Applications of the Uncertainty Principle for Finite Abelian Groups to Communications Engineering

F. Krahmer1, G. Pfander2, P. Rashkov2
1Courant Institute of Mathematical Sciences, New York University, 10009 New York NY, USA
2School of Engineering and Science, Jacobs University, 28759 Bremen, Germany
Abstract. We obtain uncertainty principles for finite Abelian groups relating the cardinality of the support of a function to the cardinality of the support of its short-time Fourier transform and discuss their applications. These uncertainty principles are based on well-established uncertainty principles for the Fourier transform. Areas of applications include the existence of a class of equal norm tight Gabor frames that are maximally robust to erasures and implications for to the theory of recovering and storing signals with sparse time-frequency representation.

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