Four Aspects of Superoscillations

TL;DR

This paper explores four key aspects of superoscillations, including their generation, potential applications like superabsorption, implications for information theory, and their generalization beyond bandlimited functions.

Contribution

It introduces new methods for generating superoscillations, discusses their practical uses, and extends the theoretical understanding of their role in information and signal processing.

Findings

Superoscillations can be generated efficiently via multiplication.

They can be used for superabsorption, enhancing low-frequency signals.

Superoscillations generalize beyond bandlimited functions.

Abstract

A function f is said to possess superoscillations if, in a finite region, f oscillates faster than the shortest wavelength that occurs in the Fourier transform of f. I will discuss four aspects of superoscillations: 1. Superoscillations can be generated efficiently and stably through multiplication. 2. There is a win-win situation in the sense that even in circumstances where superoscillations cannot be used for superresolution, they can be useful for what may be called superabsorption, an effective up-conversion of low frequencies 3. The study of superoscillations may be useful for generalizing the Shannon Hartley noisy channel capacity theorem. 4. The phenomenon of superoscillations naturally generalizes beyond bandlimited functions.