Short time quaternion quadratic phase Fourier transform and its uncertainty principles

2022/04/03 by Bivek Gupta, Amit Verma, Gupta, Bivek +1 · 3 citations
Mathematics · #11R52 #42A05 #42B10 #FOS: Electrical engineering #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Signal Processing (eess.SP) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.2204.09017

openalex publication_date 2022/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we extend the quadratic phase Fourier transform of a complex valued functions to that of the quaternion valued functions of two variables. We call it the quaternion quadratic phase Fourier transform (QQPFT). Based on the relation between the QQPFT and the quaternion Fourier transform (QFT) we obtain the sharp Hausdorff-Young inequality for QQPFT. We define the short time quaternion quadratic phase Fourier transform (STQQPFT) and explore some of its properties including inner product relation and inversion formula. We find its relation with that of the 2D quaternion ambiguity function and the quaternion Wigner-Ville distribution associated with QQPFT and obtain the Lieb's uncertainty and entropy uncertainty principles for these three transforms.

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