Reconstructing Superoscillations Buried Deeply in Noise

TL;DR

This paper presents a method using frequency combs to construct and reconstruct superoscillating waves that are robust against noise, enabling sub-bandlimit resolution and accurate recovery of signals buried in noise.

Contribution

It introduces a novel frequency comb-based technique for creating and reconstructing superoscillations with high accuracy even in noisy environments.

Findings

Superoscillations can be accurately reconstructed in noisy conditions.

The method enables sub-bandlimit resolution of signals.

Superoscillating waves mimic arbitrary analytic functions.

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.