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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