On the clifford short-time fourier transform and its properties

In this paper we investigate how the short-time Fourier transform can be extended in a Clifford setting. We prove some of the main properties of the Clifford short-time Fourier transform such as the orthogonality relation, the reconstruction property and the repro-ducing kernel formula. Moreover, we show the effects of modulating and translating the signal and the window function, respectively. Finally, we demonstrate the Lieb's uncer-tainty principle for the Clifford short-time Fourier transform.(c) 2021 Elsevier Inc. All rights reserved.

Automated summary

In this paper, we investigate how the short-time Fourier transform can be extended in a Clifford setting, proving some of its main properties and demonstrating the effects of modulating and translating the signal and the window function. Finally, we demonstrate Lieb's uncertainty principle for the Clifford short-time Fourier transform.