The windowed quadratic phase Fourier transform: structure, convolution theorem and application
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909678526529536 |
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| author | Varghese, Sarga Kundu, Manab |
| author_facet | Varghese, Sarga Kundu, Manab |
| contents | The windowed quadratic phase Fourier transform (WQPFT) combines the localization capabilities of windowed transforms with the phase modulation structure of the quadratic phase Fourier transform (QPFT). This paper investigates fundamental properties of the WQPFT, including linearity, shifting, modulation, conjugation, and symmetry. In addition, we derive the reproducing kernel, establish a reconstruction formula, and characterize the range of the transform. Convolution theorems in both the spectral and spatial domains are developed, along with the existence results and norm estimates for the convolution operation associated with the WQPFT. Finally, as an application, the solution of a convolution equation is given using the convolution theorem of the WQPFT. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_03911 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The windowed quadratic phase Fourier transform: structure, convolution theorem and application Varghese, Sarga Kundu, Manab Functional Analysis Mathematical Physics Operator Algebras The windowed quadratic phase Fourier transform (WQPFT) combines the localization capabilities of windowed transforms with the phase modulation structure of the quadratic phase Fourier transform (QPFT). This paper investigates fundamental properties of the WQPFT, including linearity, shifting, modulation, conjugation, and symmetry. In addition, we derive the reproducing kernel, establish a reconstruction formula, and characterize the range of the transform. Convolution theorems in both the spectral and spatial domains are developed, along with the existence results and norm estimates for the convolution operation associated with the WQPFT. Finally, as an application, the solution of a convolution equation is given using the convolution theorem of the WQPFT. |
| title | The windowed quadratic phase Fourier transform: structure, convolution theorem and application |
| topic | Functional Analysis Mathematical Physics Operator Algebras |
| url | https://arxiv.org/abs/2507.03911 |