Helgason Gabor Fourier transform and uncertainty principles

2018/12/06 by Mohammed El Kassimi, Mustapha Boujeddaine, Kassimi, Mohammed El +4
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Fractal and DNA sequence analysis #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #math.CA #msc:42C20 #msc:42C40 #msc:43A30 #msc:43A32

paper · pdf · doi:10.48550/arxiv.1901.01105

arxiv created 2018/12/06 · arxiv updated 2019/01/07

Abstract

Windowing a Fourier transform is a useful tool, which gives us the similarity between the signal and time frequency signal, and it allows to get sense when/where ceratin frequencies occur in the input signal, this method is introduced by Dennis Gabor. In this paper, we generalize the classical Gabor-Fourier transform(GFT) to the Riemannian symmetric space called the Helgason Gabor Fourier transform (HGFT). We continue with proving several important properties of HGFT, like the reconstruction formula, the Plancherel formula, and Parseval formula. Finally we establish some local uncertainty principle such as Benedicks-type uncertainty principle

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