Non-Separable Linear Canonical Wavelet Transform

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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><...

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Autores principales:	Hari M. Srivastava, Firdous A. Shah, Tarun K. Garg, Waseem Z. Lone, Huzaifa L. Qadri
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	non-separable linear canonical wavelet symplectic matrix non-separable linear canonical transform uncertainty principle Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/dbc97f6417a7477383a211fe21723e0a
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spelling	oai:doaj.org-article:dbc97f6417a7477383a211fe21723e0a2021-11-25T19:07:24ZNon-Separable Linear Canonical Wavelet Transform10.3390/sym131121822073-8994https://doaj.org/article/dbc97f6417a7477383a211fe21723e0a2021-11-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2182https://doaj.org/toc/2073-8994This 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>L</mi><mn>2</mn></msup><mrow><mo>(</mo><msup><mi mathvariant="double-struck">R</mi><mi>n</mi></msup><mo>)</mo></mrow></mrow></semantics></math></inline-formula>. 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.Hari M. SrivastavaFirdous A. ShahTarun K. GargWaseem Z. LoneHuzaifa L. QadriMDPI AGarticlenon-separable linear canonical waveletsymplectic matrixnon-separable linear canonical transformuncertainty principleMathematicsQA1-939ENSymmetry, Vol 13, Iss 2182, p 2182 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	non-separable linear canonical wavelet symplectic matrix non-separable linear canonical transform uncertainty principle Mathematics QA1-939
spellingShingle	non-separable linear canonical wavelet symplectic matrix non-separable linear canonical transform uncertainty principle Mathematics QA1-939 Hari M. Srivastava Firdous A. Shah Tarun K. Garg Waseem Z. Lone Huzaifa L. Qadri Non-Separable Linear Canonical Wavelet Transform
description	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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>L</mi><mn>2</mn></msup><mrow><mo>(</mo><msup><mi mathvariant="double-struck">R</mi><mi>n</mi></msup><mo>)</mo></mrow></mrow></semantics></math></inline-formula>. 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.
format	article
author	Hari M. Srivastava Firdous A. Shah Tarun K. Garg Waseem Z. Lone Huzaifa L. Qadri
author_facet	Hari M. Srivastava Firdous A. Shah Tarun K. Garg Waseem Z. Lone Huzaifa L. Qadri
author_sort	Hari M. Srivastava
title	Non-Separable Linear Canonical Wavelet Transform
title_short	Non-Separable Linear Canonical Wavelet Transform
title_full	Non-Separable Linear Canonical Wavelet Transform
title_fullStr	Non-Separable Linear Canonical Wavelet Transform
title_full_unstemmed	Non-Separable Linear Canonical Wavelet Transform
title_sort	non-separable linear canonical wavelet transform
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/dbc97f6417a7477383a211fe21723e0a
work_keys_str_mv	AT harimsrivastava nonseparablelinearcanonicalwavelettransform AT firdousashah nonseparablelinearcanonicalwavelettransform AT tarunkgarg nonseparablelinearcanonicalwavelettransform AT waseemzlone nonseparablelinearcanonicalwavelettransform AT huzaifalqadri nonseparablelinearcanonicalwavelettransform
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Non-Separable Linear Canonical Wavelet Transform

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