Non-separable linear canonical wavelet transform

Date

2021

Authors

Srivastava, H.M.
Shah, Firdous A.
Garg, Tarun K.
Lone, Waseem Z.
Qadri, Huzaifa L.

Journal Title

Journal ISSN

Volume Title

Publisher

Symmetry

Abstract

This study aims to achieve an efficient time-frequency representation of higher-dimensional signals by introducing the notion of a non-separable linear canonical wavelet transform in L^2(R^n). The preliminary analysis encompasses the derivation of fundamental properties of the novel integral transform including the orthogonality relation, inversion formula, and the range theorem. To extend the scope of the study, we formulate several uncertainty inequalities, including the Heisenberg’s, logarithmic, and Nazorav’s inequalities for the proposed transform in the linear canonical domain. The obtained results are reinforced with illustrative examples.

Description

Keywords

non-separable linear canonical wavelet, symplectic matrix, non-separable linear canonical transform, uncertainty principle

Citation

Srivastava, H. M., Shah, F. A., Garg, T. K., Lone, W. Z., & Qadri, H. L. (2021). “Non-separable linear canonical wavelet transform.” Symmetry, 13(11), 2182. https://doi.org/10.3390/sym13112182