B. Mawardi, E.S.M. Hitzer, S. Adji
Two-Dimensional Clifford Windowed Fourier Transform
in G. Scheuermann, E. Bayro-Corrochano (eds.), Geometric Algebra Computing, Springer, New York, 2010, pp. 93-106.

Abstract: Recently several generalizations to higher dimension of the classical Fourier transform (FT) using Clifford geometric algebra have been introduced, including the two-dimensional (2D) Clifford Fourier transform (CFT). Based on the 2D CFT, we establish the two-dimensional Clifford windowed Fourier transform (CWFT). Using the spectral representation of the CFT, we derive several important properties such as shift, modulation, a reproducing kernel, isometry and an orthogonality relation. Finally, we discuss examples of the CWFT and compare the CFT and the CWFT.


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