Wave packet systems and connections to spectral analysis of limiting operators

TL;DR

This paper introduces wave packet systems with strong phase space concentration and explores their connection to spectral analysis of limiting operators, with applications in medical imaging, geophysics, and astronomy.

Contribution

It establishes a novel link between wave packet systems and spectral properties of limiting operators, advancing understanding in signal processing.

Findings

Wave packet systems exhibit strong phase space concentration.

Spectral analysis of limiting operators is connected to wave packet design.

Applications demonstrated in medical imaging, geophysics, and astronomy.

Abstract

We discuss the design of ``wave packet systems'' that admit strong concentration properties in phase space. We make a connection between this problem and topics in signal processing related to the spectral behavior of spatial and frequency-limiting operators. The results have engineering applications in medical imaging, geophysics, and astronomy.