An approach to constructing super oscillatory functions

TL;DR

This paper presents a method for constructing band-limited superoscillating functions capable of exhibiting arbitrarily high frequencies over long intervals, advancing the understanding of superoscillation phenomena.

Contribution

It introduces a novel recipe for creating superoscillating functions with controlled high-frequency behavior over extended intervals.

Findings

Successfully constructs functions with arbitrarily high local frequencies

Demonstrates control over superoscillation duration and amplitude

Provides a framework for further applications in signal processing

Abstract

A recipe is presented for constructing band-limited superoscillating functions that exhibit arbitrarily high frequencies over arbitrarily long intervals.