A Generalized Windowed Fourier Transform in Real Clifford Algebra Cl 0,n

Abstract

Abstract. The Clifford Fourier transform in Cl 0,n (CFT) can be regarded as a generalization of the two-dimensional quaternionic Fourier transform (QFT), which is introduced from the mathematical aspect by Brackx at first. In this research paper, we propose the Clifford windowed Fourier transform using the kernel of the CFT. Some important properties of the transform are investigated.

On Two-Dimensional Quaternion Wigner-Ville Distribution

“…In [10,11], special properties of the asymptotic behaviour of the right-sided QFT are discussed and generalization of the classical Bohner-Millos theorems to the framework of quaternion analysis is established. Many generalized transforms are closely related to the QFTs, for example, the quaternion wavelet transform, fractional quaternion Fourier transform, quaternion linear canonical transform, and quaternionic windowed Fourier transform [12][13][14][15][16][17][18]. Based on the QFTs, one also may extend the WVD to the quaternion algebra while enjoying similar properties as in the classical case.…”