The finite harmonic oscillator and its applications to sequences, communication and radar

TL;DR

This paper introduces a new finite oscillator system with p^3 functions over finite fields, exhibiting excellent correlation properties and Fourier invariance, with applications in radar and digital communications, along with an explicit construction algorithm.

Contribution

It presents a novel oscillator system with specific correlation and Fourier properties, and provides an explicit construction method for the system.

Findings

Good auto-correlation and cross-correlation properties

Low peak-to-average power ratio

Closed under discrete Fourier transform

Abstract

A novel system, called the oscillator system, consisting of order of p^3 functions (signals) on the finite field F_p; with p an odd prime, is described and studied. The new functions are proved to satisfy good auto-correlation, cross-correlation and low peak-to-average power ratio properties. Moreover, the oscillator system is closed under the operation of discrete Fourier transform. Applications of the oscillator system for discrete radar and digital communication theory are explained. Finally, an explicit algorithm to construct the oscillator system is presented.