The Eigenvalue Distribution of Discrete Periodic Time-Frequency Limiting Operators

TL;DR

This paper investigates the eigenvalue distribution of a discrete time-frequency limiting operator, providing new nonasymptotic results and insights into the eigenvalues of DFT submatrices, relevant for signal analysis.

Contribution

It introduces novel nonasymptotic bounds on the eigenvalue distribution of the discrete time-frequency limiting operator and characterizes eigenvalues of DFT submatrices.

Findings

Established new bounds on eigenvalue distribution.

Characterized eigenvalues of DFT submatrices.

Provided insights into signal analysis applications.

Abstract

Bandlimiting and timelimiting operators play a fundamental role in analyzing bandlimited signals that are approximately timelimited (or vice versa). In this paper, we consider a time-frequency (in the discrete Fourier transform (DFT) domain) limiting operator whose eigenvectors are known as the periodic discrete prolate spheroidal sequences (PDPSSs). We establish new nonasymptotic results on the eigenvalue distribution of this operator. As a byproduct, we also characterize the eigenvalue distribution of a set of submatrices of the DFT matrix, which is of independent interest.