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: | , , , , |
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| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
MDPI AG
2021
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| Materias: | |
| Acceso en línea: | https://doaj.org/article/dbc97f6417a7477383a211fe21723e0a |
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| Sumario: | 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. |
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