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.
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}
}