Quadratic-phase Hilbert transform and the associated Bedrosian theorem

Date

2023

Authors

Srivastava, Hari M.
Shah, Firdous A.
Qadri, Huzaifa L.
Lone, Waseem Z.
Musadiq, Gojree S.

Journal Title

Journal ISSN

Volume Title

Publisher

Axioms

Abstract

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.

Description

Keywords

quadratic-phase Fourier transform, Hilbert transform, analytical signal, Bedrosian theorem

Citation

Srivastava, H. M., Shah, F. A., Qadri, H. L., Lone, W. Z., & Gojree, M. S. (2023). Quadratic-phase Hilbert transform and the associated Bedrosian theorem. Axioms, 12(2), 218. https://doi.org/10.3390/axioms12020218