A Generalization of the Fractional Stockwell Transform
This paper presents a generalized fractional Stockwell transform (GFST), extending the classical Stockwell transform and fractional Stockwell transform, which are widely used tools in time–frequency analysis. The GFST on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML&q...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-03-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/9/3/166 |
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| Summary: | This paper presents a generalized fractional Stockwell transform (GFST), extending the classical Stockwell transform and fractional Stockwell transform, which are widely used tools in time–frequency analysis. The GFST on <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><mi mathvariant="double-struck">R</mi><mo>,</mo><mi mathvariant="double-struck">C</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> is defined as a convolution consistent with the classical Stockwell transform, and the fundamental properties of GFST such as linearity, translation, scaling, etc., are discussed. We focus on establishing an orthogonality relation and derive an inversion formula as a direct application of this relation. Additionally, we characterize the range of the GFST on <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><mi mathvariant="double-struck">R</mi><mo>,</mo><mi mathvariant="double-struck">C</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>. Finally, we prove an uncertainty principle of the Heisenberg type for the proposed GFST. |
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| ISSN: | 2504-3110 |