Reconstructing superoscillations buried deeply in noise

Derek D. White, Shunxing Zhang, Barbara Šoda, Achim Kempf, Daniele C. Struppa, Andrew N. Jordan, John C. Howell*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Article numberL061502
JournalPhysical Review A
Volume110
Issue number6
DOIs
StatePublished - Dec 2024

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