Uncertainty principles associated with the short time quaternion coupled fractional Fourier transform

TL;DR

This paper extends the coupled fractional Fourier transform to quaternion-valued functions, establishing new uncertainty principles and inequalities for the quaternion short time fractional Fourier transform.

Contribution

It introduces the quaternion coupled fractional Fourier transform and its short time version, deriving key inequalities and uncertainty principles for these transforms.

Findings

Established the sharp Hausdorff-Young inequality for QCFrFT

Derived the R\

R\

Abstract

In this paper, we extend the coupled fractional Fourier transform of a complex valued functions to that of the quaternion valued functions on $\mathbb{R}^4$ and call it the quaternion coupled fractional Fourier transform (QCFrFT). We obtain the sharp Hausdorff-Young inequality for QCFrFT and obtain the associated R\`enyi uncertainty principle. We also define the short time quaternion coupled fractional Fourier transform (STQCFrFT) and explore its important properties followed by the Lieb's and entropy uncertainty principles.