A Systematic Analysis of a Novel Hankel Transform Wavelet Framework and Its Complexity Implications

Abstract

In this paper, a comprehensive analysis attempted to study the application of classical wavelets in Hankel Transform's numerical computation by systematically reviewing the previous studies on this subject, which have been published in recent years, and identifying areas of research for future development. We discussed the mathematical foundations of the Hankel transform, the wavelet
transforms, and their integration to form a Hankel transform wavelet framework. We provide numerical examples to validate the efficiency of the recommended framework in signal and image processing. Finally, we discuss the potential future implications of this framework in various fields, including medical imaging, acoustic and electromagnetic wave propagation, and more. The research employed the systematic review approach. The results for Hankel Transform digital calculation using various classical wavelets have been explored, several research gaps have been pointed out, and possible implications for this topic including chaotic time series prediction are recommended.