45 citations · 117 across the 13 of their papers we have counts for
13 papers
General One-dimensional Clifford Fourier Transform and Application to Probability Theory
Said Fahlaoui, Hakim Monaim
In this paper, we present the general one-dimensional Clifford Fourier Transform. We derive fundamental properties: Plancherel theorem, reconstruction and convolution formulas. Add…
Titchmarsh theorem associated with QFT
Hakim Monaim, Said Fahlaoui
In this paper, we prove both of the Titchmarsh theorems associated with Two-Sided Quaternionic Fourier Transform and we conclude about Short-Time Two-Sided Quaternionic Fourier Tra…
Uncertainty Principles For the continuous Gabor quaternion linear canonical transform
Mohammed El Kassimi, Said Fahlaoui
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 lin…
Local uncertainty principles for the two-sided Gabor quaternion Fourier transform
M. El Kassimi, S. Fahlaoui
By the important applications of Gabor transform in time-frequency analysis and signal analysis, in this paper, we consider the Gabor quaternion Fourier transform (GQFT), and we pr…
Donoho-Stark's Uncertainty Principles in Real Clifford Algebras
Youssef El Haoui, Said Fahlaoui
The Clifford Fourier transform (CFT) has been shown to be a powerful tool in the Clifford analysis. In this work, several uncertainty inequalities are established in the real Cliff…
The two-sided Gabor quaternion Fourier transform and some uncertainty principles
Mohammed El Kassimi, Said Fahlaoui
In this paper, we define a new transform called the Gabor quaternionic Fourier transform (GQFT), which generalizes the classical windowed Fourier transform to quaternion valued-sig…
Wigner-Ville distribution associated with the quaternion offset linear canonical transforms
Mohammed El Kassimi, Youssef El haoui, Said Fahlaoui
The Wigner-Ville distribution (WVD) and quaternion offset linear canonical transform (QOLCT) are a useful tools in signal analysis and image processing. The purpose of this paper i…
Helgason Gabor Fourier transform and uncertainty principles
Mohammed El Kassimi, Mustapha Boujeddaine, Said Fahlaoui
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 frequencie…
A heat kernel version of Miyachi's Theorem for the Laguerre hypergroup
Mohammed El Kassimi, Said Fahlaoui
Let the Laguerre Hypergroup. In this paper, we are going to formulate and prove an analogue of Miyachi's uncertainty principle for the Lagu…
Benedicks-Amrein-Berthier type theorem related to the two-sided Quaternion Fourier transform
Youssef El Haoui, Said Fahlaoui
The main objective of the present paper is to establish a new uncertainty principle (UP) for the two-sided quaternion Fourier transform (QFT). This result is an extension of a resu…
Beurling's Theorem for the Two-sided Quaternion Fourier Transform
Youssef El Haoui, Said Fahlaoui
The two-sided quaternion Fourier transform satisfies some uncertainty principles similar to the Euclidean Fourier transform. A generalization of Beurling's theorem, Hardy, Cowling-…
Miyachi's Theorem for the Quaternion Fourier Transform
Youssef El Haoui, Said Fahlaoui
The quaternion Fourier transform (QFT) satisfies some uncertainty principles similar to the Euclidean Fourier transform. In this paper, we establish Miyachi's theorem for this tran…
The uncertainty principle for the two-sided quaternion Fourier transform
Youssef El Haoui, Said Fahlaoui
In this paper, we provide the Heisenberg's inequality and the Hardy's theorem for the two-sided quaternion Fourier transform.