Uncertainty in time–frequency representations on finite Abelian groups and applications
نویسندگان
چکیده
منابع مشابه
Uncertainty in time–frequency representations on finite Abelian groups and applications
Classical and recent results on uncertainty principles for functions on finite Abelian groups relate the cardinality of the support of a function to the cardinality of the support of its Fourier transforms. We obtain corresponding results relating the support sizes of functions and their short–time Fourier transforms. We use our findings to construct a class of equal norm tight Gabor frames tha...
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Let G be a finite abelian group of order n. For a complex valued function f on G let f̂ denote the Fourier transform of f . The classical uncertainty inequality asserts that if f 6= 0 then |supp(f)| · |supp(f̂)| ≥ |G| . (1) Answering a question of Terence Tao, the following improvement of (1) is shown: Theorem: Let d1 < d2 be two consecutive divisors of n. If d1 ≤ k = |supp(f)| ≤ d2 then |supp(f̂)...
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ژورنال
عنوان ژورنال: Applied and Computational Harmonic Analysis
سال: 2008
ISSN: 1063-5203
DOI: 10.1016/j.acha.2007.09.008