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Wigner–Ville Distribution Associated with Clifford Geometric Algebra Cl n,0 , n =3(mod 4) Based on Clifford–Fourier Transform.
- Source :
-
Symmetry (20738994) . Jul2023, Vol. 15 Issue 7, p1421. 16p. - Publication Year :
- 2023
-
Abstract
- In this study, the Wigner–Ville distribution is associated with the one sided Clifford–Fourier transform over R n , n = 3(mod 4). Accordingly, several fundamental properties of the WVD-CFT have been established, including non-linearity, the shift property, dilation, the vector differential, the vector derivative, and the powers of τ ∈ R n . Moreover, powerful results on the WVD-CFT have been derived such as Parseval's theorem, convolution theorem, Moyal's formula, and reconstruction formula. Eventually, we deduce a directional uncertainty principle associated with WVD-CFT. These types of results, as well as methodologies for solving them, have applications in a wide range of fields where symmetry is crucial. [ABSTRACT FROM AUTHOR]
- Subjects :
- *CLIFFORD algebras
*HEISENBERG uncertainty principle
*MATHEMATICAL convolutions
Subjects
Details
- Language :
- English
- ISSN :
- 20738994
- Volume :
- 15
- Issue :
- 7
- Database :
- Academic Search Index
- Journal :
- Symmetry (20738994)
- Publication Type :
- Academic Journal
- Accession number :
- 169700225
- Full Text :
- https://doi.org/10.3390/sym15071421