Reconstructing Superoscillations Buried Deeply in Noise
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arXiv
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| Auteurs principaux: | , , , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916431090679808 |
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| author | White, Derek D. Zhang, Shunxing Soda, Barbara Kempf, Achim Struppa, Daniele C. Jordan, Andrew N. Howell, John C. |
| author_facet | White, Derek D. Zhang, Shunxing Soda, Barbara Kempf, Achim Struppa, Daniele C. Jordan, Andrew N. Howell, John C. |
| contents | We utilize a method using frequency combs to construct waves that feature superoscillations - local regions of the wave that exhibit a change in phase that the bandlimits of the wave should not otherwise allow. This method has been shown to create superoscillating regions that mimic any analytic function - even ones well outside the bandlimits - to an arbitrary degree of accuracy. We experimentally demonstrate that these waves are extremely robust against noise, allowing for accurate reconstruction of a superoscillating target function thoroughly buried in noise. We additionally show that such a construction can be easily used to range-resolve a signal well below the commonly accepted fundamental limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_05399 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Reconstructing Superoscillations Buried Deeply in Noise White, Derek D. Zhang, Shunxing Soda, Barbara Kempf, Achim Struppa, Daniele C. Jordan, Andrew N. Howell, John C. Optics We utilize a method using frequency combs to construct waves that feature superoscillations - local regions of the wave that exhibit a change in phase that the bandlimits of the wave should not otherwise allow. This method has been shown to create superoscillating regions that mimic any analytic function - even ones well outside the bandlimits - to an arbitrary degree of accuracy. We experimentally demonstrate that these waves are extremely robust against noise, allowing for accurate reconstruction of a superoscillating target function thoroughly buried in noise. We additionally show that such a construction can be easily used to range-resolve a signal well below the commonly accepted fundamental limit. |
| title | Reconstructing Superoscillations Buried Deeply in Noise |
| topic | Optics |
| url | https://arxiv.org/abs/2410.05399 |