Year: 2025
Type: article
Abstract: Among the class of generalized Fourier transformations, the linear canonical transform is of crucial importance, mainly due to its higher degrees of freedom compared to the conventional Fourier and fractional Fourier transforms. In this paper, we will introduce and study two versions of wavelet transforms associated with the linear canonical Dunkl transform. More precisely, we investigate some applications for Dunkl linear canonical wavelet transforms. Next we will introduce and develop the harmonic analysis associated with the Dunkl linear canonical wavelet packets transform. We introduce and study three types of wavelet packets along with their associated wavelet transforms. For each of these transforms, we establish a Plancherel and a reconstruction formula, and we analyze the associated scale-discrete scaling functions.
Source: Mathematics
DOI: 10.3390/math13193225
Authors: Saifallah Ghobber, Hatem Mejjaoli
Institutions: King Faisal University, Taibah University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
Funder: King Faisal University
OpenAlex ID: W4414959455