Year: 2019
Type: preprint
Abstract: Gabor transform is one of the performed tools for time-frequency signal analysis. The principal aim of this paper is to generalize the Gabor Fourier transform to the quaternion linear canonical transform. Actually, this transform gives us more flexibility to studied nonstationary and local signals associated with the quaternion linear canonical transform. Some useful properties are derived, such as Plancherel and inversion formulas. And we prove some uncertainty principles: those including Heisenberg's, Lieb's and logarithmic inequalities. We finish by analogs of concentration and Benedick's type theorems.
Source: arXiv (Cornell University)
Authors: Kassimi, Mohammed El, Fahlaoui, Said
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2948403176