Two-Dimensional Quaternionic Windowed Fourier Transform

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 CWFT. © 2010 Springer-Verlag London Limited.