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arXiv · 2410.05399

Reconstructing Superoscillations Buried Deeply in Noise

Derek D. White·Shunxing Zhang·Barbara Soda·Achim Kempf·Daniele C. Struppa·Andrew N. Jordan·John C. Howell
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Abstract

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.

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Derek D. White, Shunxing Zhang, Barbara Soda, Achim Kempf, Daniele C. Struppa, Andrew N. Jordan, John C. Howell. 2024-10-07. Reconstructing Superoscillations Buried Deeply in Noise. https://arxiv.org/abs/2410.05399

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