English

Reconstructing Superoscillations Buried Deeply in Noise

Optics 2024-10-11 v2

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.

Keywords

Cite

@article{arxiv.2410.05399,
  title  = {Reconstructing Superoscillations Buried Deeply in Noise},
  author = {Derek D. White and Shunxing Zhang and Barbara Soda and Achim Kempf and Daniele C. Struppa and Andrew N. Jordan and John C. Howell},
  journal= {arXiv preprint arXiv:2410.05399},
  year   = {2024}
}
R2 v1 2026-06-28T19:11:58.568Z