Two-Dimensional Clifford Windowed Fourier Transform
作者： Mawardi Bahri , Eckhard M. S. Hitzer , Sriwulan Adji
DOI: 10.1007/978-1-84996-108-0_5
关键词:
摘要: Recently several generalizations to higher dimension of the classical Fourier transform (FT) using Clifford geometric algebra have been introduced, including two-dimensional (2D) Clifford–Fourier (CFT). Based on 2D CFT, we establish windowed (CWFT). Using spectral representation derive important properties such as shift, modulation, a reproducing kernel, isometry, and an orthogonality relation. Finally, discuss examples CWFT compare CFT CWFT.
harvard.edu
springer.com
rxiv.org参考文章(7)
Ferenc Weisz, Multiplier Theorems for the Short-Time Fourier Transform Integral Equations and Operator Theory. ,vol. 60, pp. 133- 149 ,(2008) , 10.1007/S00020-007-1546-5
Eckhard M. S. Hitzer, Bahri Mawardi, Clifford Fourier Transform on Multivector Fields and Uncertainty Principles for Dimensions n = 2 (mod 4) and n = 3 (mod 4) Advances in Applied Clifford Algebras. ,vol. 18, pp. 715- 736 ,(2008) , 10.1007/S00006-008-0098-3
Fred Brackx, Nele De Schepper, Frank Sommen, The Two-Dimensional Clifford-Fourier Transform Journal of Mathematical Imaging and Vision. ,vol. 26, pp. 5- 18 ,(2006) , 10.1007/S10851-006-3605-Y
Qian Kemao, Two-dimensional windowed Fourier transform for fringe pattern analysis: Principles, applications and implementations Optics and Lasers in Engineering. ,vol. 45, pp. 304- 317 ,(2007) , 10.1016/J.OPTLASENG.2005.10.012
Jingang Zhong, Huiping Zeng, Multiscale windowed Fourier transform for phase extraction of fringe patterns Applied Optics. ,vol. 46, pp. 2670- 2675 ,(2007) , 10.1364/AO.46.002670
Karlheinz Gröchenig, Georg Zimmermann, Hardy's Theorem and the Short‐Time Fourier Transform of Schwartz Functions Journal of The London Mathematical Society-second Series. ,vol. 63, pp. 205- 214 ,(2001) , 10.1112/S0024610700001800
Thomas Bülow, Michael Felsberg, Gerald Sommer, Non-commutative hypercomplex Fourier tranforms of multidimensional signals Geometric computing with Clifford algebras. pp. 187- 207 ,(2001) , 10.1007/978-3-662-04621-0_8