Time-frequency analysis associated with the k-Hankel wavelet transform on ℝ^d

Abstract

The k-Hankel wavelet transform (k-HWT) is a novel addition to the class of wavelet transforms, which has gained a respectable status in the realm of time-frequency signal analysis within a short span of time. Knowing the fact that the study of the time-frequency analysis is both theoretically interesting and practically useful, the aim of this article is to explore two more aspects of the time-frequency analysis associated with the k-HWT including the spectral analysis associated with the concentration operators and the scalogram.

Keywords:

• k-Hankel transform on ${\mathbb{R}}^d$
• k-Hankel wavelet transform on ${\mathbb{R}}^d$
• localization operators
• scalogram

AMS CLASSIFICATIONS:

• 42B10
• 47G10
• 94A12

Acknowledgments

The author is deeply indebted to the referees for providing constructive comments. The author thanks professors K. Trimèche, Firdous A. Shah and MW. Wong for their helps.

Data availability statement

The data used to support the findings of this study are included within the article.

Disclosure statement

No potential conflict of interest was reported by the author.