Yield--Optimized Superoscillations

TL;DR

This paper presents a method to optimize superoscillating signals by maximizing their energy ratio within the superoscillations, enabling better practical applications through numerical solutions and trade-offs between distortion and yield.

Contribution

It introduces a numerical optimization approach for superoscillation yield, including a generalized eigenvalue problem and methods for higher dimensions and non-trivial domains.

Findings

Superoscillation yield can be increased by slight signal deformation.

Optimization leads to a generalized eigenvalue problem solved numerically.

Trade-off between signal distortion and superoscillation yield is achievable.

Abstract

Superoscillating signals are band--limited signals that oscillate in some region faster their largest Fourier component. While such signals have many scientific and technological applications, their actual use is hampered by the fact that an overwhelming proportion of the energy goes into that part of the signal, which is not superoscillating. In the present article we consider the problem of optimization of such signals. The optimization that we describe here is that of the superoscillation yield, the ratio of the energy in the superoscillations to the total energy of the signal, given the range and frequency of the superoscillations. The constrained optimization leads to a generalized eigenvalue problem, which is solved numerically. It is noteworthy that it is possible to increase further the superoscillation yield at the cost of slightly deforming the oscillatory part of the signal, while keeping the average frequency. We show, how this can be done gradually, which enables a trade-off between the distortion and the yield. We show how to apply this approach to non-trivial domains, and explain how to generalize this to higher dimensions.