Quadratic-Phase Hilbert Transform and the Associated Bedrosian Theorem

被引:1
作者
Srivastava, Hari M. M. [1 ,2 ,3 ,6 ]
Shah, Firdous A. A. [4 ]
Qadri, Huzaifa L. L. [5 ]
Lone, Waseem Z. Z. [4 ]
Gojree, Musadiq S. S. [4 ]
机构
[1] China Med Univ, China Med Univ Hosp, Dept Med Res, Taichung 40402, Taiwan
[2] Azerbaijan Univ, Dept Math & Informat, 71 Jeyhun Hajibeyli St, AZ-1007 Baku, Azerbaijan
[3] Kyung Hee Univ, Ctr Converging Humanities, 26 Kyungheedae Ro, Seoul 02447, South Korea
[4] Univ Kashmir, Dept Math, South Campus, Anantnag 192101, India
[5] Islamic Univ Sci & Technol, Dept Math Sci, Kashmir 192122, India
[6] Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3R4, Canada
关键词
quadratic-phase Fourier transform; Hilbert transform; analytical signal; Bedrosian theorem;
D O I
10.3390/axioms12020218
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The Hilbert transform is a commonly used linear operator that separates the real and imaginary parts of an analytic signal and is employed in various fields, such as filter design, signal processing, and communication theory. However, it falls short in representing signals in generalized domains. To address this limitation, we propose a novel integral transform, coined the quadratic-phase Hilbert transform. The preliminary study encompasses the formulation of all the fundamental properties of the generalized Hilbert transform. Additionally, we examine the relationship between the quadratic-phase Fourier transform and the proposed transform, and delve into the convolution theorem for the quadratic-phase Hilbert transform. The Bedrosian theorem associated with the quadratic-phase Hilbert transform is explored in detail. The validity and accuracy of the obtained results were verified through simulations.
引用
收藏
页数:15
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