The 2-D Hyper-complex Gabor quadratic-phase Fourier transform and uncertainty principles

被引：0
|
作者：
M. Younus Bhat
Aamir H. Dar
机构：
[1] Islamic University of Science and Technology,Department of Mathematical Sciences
来源：
The Journal of Analysis | 2023年 / 31卷
关键词：
2-D Hyper-complex quadratic-phase Fourier transform; 2-D Hyper-complex Gabor quadratic-phase Fourier transform; Isometry; Uncertainty principle; Primary 42C40; Secondary 42C15; 47G10; 42A38; 42B10;
D O I：
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中图分类号：
学科分类号：
摘要：
In this paper, we present a novel integral transform known as the 2-D Hyper-complex(quaternion) Gabor quadratic-phase Fourier transform (Q-GQPFT), which is embodiment of several well known signal processing tools. We first define the 2-D Hyper-complex(quaternion) quadratic-phase Fourier transform (Q-QPFT) and then we propose the definition of novel Q-GQPFT, which is a modified version of the classical windowed quadratic-phase Fourier transform to quaternion-valued signals and we study various properties of the proposed Q-GQPFT, including Moyal’s formula, reconstruction formula, isometry and reproducing kernel formula. We also establish the Heisenberg and logarithmic uncertainty inequalities for the Q-GQPFT.
引用
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页码：243 / 260
页数：17
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