A new method to generate superoscillating functions and supershifts

TL;DR

This paper introduces a novel method for explicitly constructing a broad class of superoscillatory functions, which are band-limited functions capable of oscillating faster than their maximum Fourier component, with applications across various scientific fields.

Contribution

The paper presents a new explicit construction method for superoscillatory functions, expanding the toolkit for generating such functions in science and engineering.

Findings

Enables explicit construction of superoscillatory functions

Allows creation of a large class of superoscillatory functions

Facilitates applications in optics, quantum mechanics, and signal processing

Abstract

Superoscillations are band-limited functions that can oscillate faster than their fastest Fourier component. These functions (or sequences) appear in weak values in quantum mechanics and in many fields of science and technology such as optics, signal processing and antenna theory. In this paper we introduce a new method to generate superoscillatory functions that allows us to construct explicitly a very large class of superoscillatory functions.