Non-Separable Linear Canonical Wavelet Transform

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 L2(Rn). 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.

Characterizations of Continuous Fractional Bessel Wavelet Transforms

“…The theory that we have developed in this article is potentially useful for a variety of applications of the fractional Bessel wavelet transform in signal processing, image processing, quantum mechanics and other areas of engineering and applied sciences. Some instances of applications have been presented in Section 3 (see also several recent developments involving continuous and discrete wavelet transforms in [5,[18][19][20][21][22][23][24][25][26][27], each of which will presumably motivate further researches involving the continuous and discrete fractional Bessel wavelet transforms).…”

Filtering of Audio Signals Using Discrete Wavelet Transforms

“…Readers may consult the works of [10][11][12][13][14] for further details on wavelet decomposition and related topics. Readers may also consult the most recent works of [15][16][17][18] for further details on the direction of present work.…”

Wavelet transform of multiplicators and convolutors for ultradistributions

“…8 Further, they introduced the application of wavelet transform to efficiently localize any nontransient signal in the time-frequency plane with more degrees of freedom in the linear canonical domain. 9 The other basic properties and results of the transform were discussed in previous works. [10][11][12] Definitions and properties of test functions and ultradistribution spaces are given in previous studies.…”

“…Srivastava et al discussed the wavelet collocation method based on Fibonacci wavelets 8 . Further, they introduced the application of wavelet transform to efficiently localize any nontransient signal in the time‐frequency plane with more degrees of freedom in the linear canonical domain 9 . The other basic properties and results of the transform were discussed in previous works 10–12 .…”