Geodesic
Finite Gabor systems and uncertainty principle for block sliding discrete Fourier transform
Filomat, Tome 37 (2023) no. 8, p. 2361

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DOI

In this paper, we study the finite Gabor system for oversampling schemes. A characterization of dual finite Gabor tight frame using discrete time Zak transform is given. Also, a method to calculate the coefficients of the finite Gabor system expansion in the case of oversampling and a necessary and sufficient condition for the existence of biorthogonal pair of Riesz basis in l 2 (Z L) is given. Further, we introduce the notion of block sliding discrete Fourier transform (BSDFT) which reduces the computational complexity and give uncertainty principle for BSDFT. An uncertainty principle for two finite Parseval Gabor frames in terms of sparse representations is given. Finally, using the notion of numerical sparsity, an uncertainty principle for finite Gabor frames is given.
DOI : 10.2298/FIL2308361P
Classification : 42A38, 42C15, 42C40, 94A12
Keywords: Oversampling, uncertainty principle, finite Gabor frames, block sliding discrete Fourier transform 
Khole Timothy Poumai; Nikhil Khanna; S K Kaushik. Finite Gabor systems and uncertainty principle for block sliding discrete Fourier transform. Filomat, Tome 37 (2023) no. 8, p. 2361 . doi: 10.2298/FIL2308361P
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     title = {Finite {Gabor} systems and uncertainty principle for block sliding discrete {Fourier} transform},
     journal = {Filomat},
     pages = {2361 },
     year = {2023},
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     number = {8},
     doi = {10.2298/FIL2308361P},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2308361P/}
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