The novel quadratic phase Fourier S-transform and associated uncertainty principles in the quaternion setting
In this article, we propose a novel integral transform coined as quaternion quadratic phase S-transform (Q-QPST), which is an extension of the quadratic phase S-transform and study the uncertainty principles associated with the Q-QPST. The Q-QPST possesses some desirable characteristics that are abs...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2024-11-01
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| Series: | Demonstratio Mathematica |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/dema-2024-0077 |
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| Summary: | In this article, we propose a novel integral transform coined as quaternion quadratic phase S-transform (Q-QPST), which is an extension of the quadratic phase S-transform and study the uncertainty principles associated with the Q-QPST. The Q-QPST possesses some desirable characteristics that are absent in conventional time-frequency transforms, especially for dealing with the time-varying quaternion-valued signals. First, we propose the definition of Q-QPST and then we explore some mathematical properties of the of quaternion Q-QPST, including the linearity, modulation, shift, orthogonality relation, and reconstruction formula. Second, we derive the associated Heisenberg’s uncertainty inequality and the corresponding logarithmic version for Q-QPST. Finally, an illustrative example and some potential applications of the Q-QPST are introduced. |
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| ISSN: | 2391-4661 |