Research PaperNo Access

Free metaplectic wavelet transform in $L^{2} (ℝ^{n})$

Firdous A. Shah

https://orcid.org/0000-0001-8461-869X

Department of Mathematics, University of Kashmir, South Campus, Anantnag 192101, Jammu and Kashmir, India

E-mail Address: [email protected]

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Huzaifa L. Qadri

Department of Mathematics, University of Kashmir, South Campus, Anantnag 192101, Jammu and Kashmir, India

E-mail Address: [email protected]

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, and

Waseem Z. Lone

Department of Mathematics, University of Kashmir, South Campus, Anantnag 192101, Jammu and Kashmir, India

E-mail Address: [email protected]

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https://doi.org/10.1142/S0219691322500059Cited by:5 (Source: Crossref)

Abstract

With the aim to achieve an efficient time-frequency representations of higher dimensional signals, we introduce the notion of free metaplectic wavelet transform in $L^{2} (ℝ^{n})$ by employing the convolution structure of the free-metaplectic transforms. The preliminary analysis encompasses the derivation of fundamental properties of the novel integral transform including the orthogonality and inversion formula. Subsequently, Heisenberg’s and Pitt’s inequalities are also obtained. To extend the scope of the study, a detailed analysis of the double windowed wavelet transform in the free-metaplectic domain is presented at the end.

Keywords:

AMSC: 53D22, 42B10, 42C40, 65R10, 44A35

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