Work

Gabor Transform Associated with the Dunkl–Bessel Transform and Spectrograms

Year: 2024

Type: article

Abstract: Time–frequency (or space–phase) analysis plays a key role in signal analysis. In particular, signals that have a very concentrated time–frequency content are of great importance. However, the uncertainty principle sets a limitation to the possible simultaneous concentration of a function and its Dunkl–Bessel transform. For this purpose, we introduce and study a new transformation called Dunkl–Bessel Gabor transform. For this transformation, we define the Toeplitz-type (or time–frequency localization) operators, in order to localize signals on the time–frequency plane. We study these operators; in particular, we give criteria for their boundedness and Schatten class properties. Then, using the special class of concentration operators, which are compact and self-adjoint, we show that their eigenfunctions are maximally time–frequency-concentrated in the region of interest.

Source: Symmetry

DOI: 10.3390/sym16111410

Authors: Saifallah Ghobber, Hatem Mejjaoli, Nadia Sraieb

Institutions: King Faisal University, Taibah University, Tunis University, Tunis El Manar University, University of Gabès

Language: English

Topic: Mathematical Analysis and Transform Methods

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,728

Funder: Deanship of Scientific Research, King Faisal University