Sharper version of uncertainty principles in the framework of quaternion Fourier transform

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Sharper version of uncertainty principles in the framework of quaternion Fourier transform

Year : 2025

Publisher : World Scientific

Source Title : International Journal of Geometric Methods in Modern Physics

Document Type :

Abstract

The quaternion Fourier Transform (QFT) finds extensive applications across various domains, such as signal processing and optics. This paper strengthens two important uncertainty principles for QFT. First, we proposed two different sharper versions of generalized Heisenberg’s uncertainty principle associated with quaternion Fourier transform in Lp(R2, H) space for p ∈ [1, 2]. Also a new version of Donoho–Stark’s uncertainty principle associated with QFT is discussed. Furthermore, in some particular case this new Donoho–Stark’s uncertainty principle is the sharper version than the existing one in quaternion sense.