Open AccessComposition of wavelet transforms and wave packet transform involving Kontorovich-Lebedev transform
Author(s) -
U. K. Mandal,
Sandeep Verma Kumar,
Akhilesh Prasad
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2101047m
Subject(s) - wavelet transform , wavelet packet decomposition , harmonic wavelet transform , mathematics , stationary wavelet transform , s transform , second generation wavelet transform , wavelet , discrete wavelet transform , constant q transform , continuous wavelet transform , convolution (computer science) , artificial intelligence , computer science , artificial neural network
The main objective of this paper is to study the composition of continuous Kontorovich-Lebedev wavelet transform (KL-wavelet transform) and wave packet transform (WPT) based on the Kontorovich-Lebedev transform (KL-transform). Estimates for KL-wavelet and KL-wavelet transform are obtained, and Plancherel?s relation for composition of KL-wavelet transform and WPT-transform are derived. Reconstruction formula for WPT associated to KL-transform is also deduced and at the end Calderon?s formula related to KL-transform using its convolution property is obtained.