Stability estimates for adaptive focused time-frequency transforms
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916788061601792 |
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| author | Warion, Pierre Torrésani, Bruno |
| author_facet | Warion, Pierre Torrésani, Bruno |
| contents | This contribution is a follow-up of a recent paper by the authors on adaptive, non-linear time-frequency transforms, focusing on the STFT based transforms. The adaptivity is provided by a focus function, that depends on the analyzed function or signal, and that adapts dynamically the time-frequency resolution of the analysis. Sticking to the continuous case setting, this work provides new stability results for the transform (stability with respect with the focus function). It also investigates in some details focus functions based upon regularized R{é}nyi entropies and show corresponding continuity results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_08637 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stability estimates for adaptive focused time-frequency transforms Warion, Pierre Torrésani, Bruno Classical Analysis and ODEs Signal Processing This contribution is a follow-up of a recent paper by the authors on adaptive, non-linear time-frequency transforms, focusing on the STFT based transforms. The adaptivity is provided by a focus function, that depends on the analyzed function or signal, and that adapts dynamically the time-frequency resolution of the analysis. Sticking to the continuous case setting, this work provides new stability results for the transform (stability with respect with the focus function). It also investigates in some details focus functions based upon regularized R{é}nyi entropies and show corresponding continuity results. |
| title | Stability estimates for adaptive focused time-frequency transforms |
| topic | Classical Analysis and ODEs Signal Processing |
| url | https://arxiv.org/abs/2506.08637 |