Two-Dimensional Quaternion Fourier Transform Method in Probability Modeling

被引：3

作者：

Nurwahidah, Nurwahidah ^{[1
,2
]}

Bahri, Mawardi ^{[1
]}

Rahim, Amran ^{[1
]}

机构：

[1] Hasanuddin Univ, Dept Math, Makassar 90245, Indonesia

[2] Univ Islam Negeri Alauddin Makassar, Dept Math, Gowa 92113, Indonesia

来源：

SYMMETRY-BASEL | 2024年 / 16卷 / 03期

关键词：

two-dimensional quaternion Fourier transform; quaternion characteristic function; quaternion probability density function; quaternion covariance; REPRESENTATION;

D O I：

10.3390/sym16030257

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

The Fourier transform plays a crucial role in statistics, applied mathematics, and engineering sciences. In this study, we give a definition of the two-dimensional quaternion Fourier transform, which is an extension of the two-dimensional Fourier transform. We present a new convolution theorem including this transformation. We study the characteristic function in the setting of quaternion algebra and obtain the essential properties. Based on this, we seek the expected value, variance, covariance, and their basic relations to the two-dimensional quaternion Fourier transform. We illustrate the results by giving examples to see how the obtained results differ from the classical case.

引用

页数：15

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