The finite harmonic oscillator and its associated sequences
Shamgar Gurevich, Ronny Hadani, Nir Sochen
TL;DR
This paper introduces the finite harmonic oscillator system, explores its mathematical properties, and discusses its applications in discrete radar and digital communication, highlighting its deterministic construction and eigenfunction behavior.
Contribution
It presents a new finite harmonic oscillator system with applications in radar and communication, connecting Weil representation and eigenfunctions.
Findings
The oscillator system exhibits specific eigenfunction properties.
Applications in discrete radar and digital communication are demonstrated.
The system's deterministic construction is detailed.
Abstract
A system of functions (signals) on the finite line, called the oscillator system, is described and studied. Applications of this system for discrete radar and digital communication theory are explained. Keywords: Weil representation, commutative subgroups, eigenfunctions, random behavior, deterministic construction
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Taxonomy
TopicsCoding theory and cryptography · Advanced Algebra and Geometry · Mathematical Analysis and Transform Methods