The uncertainty principle for the two-sided quaternion Fourier transform

TL;DR

This paper extends classical uncertainty principles, like Heisenberg's inequality and Hardy's theorem, to the context of the two-sided quaternion Fourier transform, broadening their applicability in quaternion analysis.

Contribution

It introduces the Heisenberg's inequality and Hardy's theorem specifically for the two-sided quaternion Fourier transform, a novel extension in quaternion analysis.

Findings

Heisenberg's inequality established for the two-sided quaternion Fourier transform

Hardy's theorem proved in the quaternion Fourier transform context

Provides foundational results for quaternion signal processing

Abstract

In this paper, we provide the Heisenberg's inequality and the Hardy's theorem for the two-sided quaternion Fourier transform.