Time-frequency localization operators: a geometric phase space approach

Author

Daubechies, Ingrid

Author_Institution

Courant Inst., New York Univ., NY, USA

Volume

34

Issue

4

fYear

1988

fDate

7/1/1988 12:00:00 AM

Firstpage

605

Lastpage

612

Abstract

The author defines a set of operators which localize in both time and frequency. These operators are similar to but different from the low-pass time-limiting operator, the singular functions of which are the prolate spheroidal wave functions. The author´s construction differs from the usual approach in that she treats the time-frequency plane as one geometric whole (phase space) rather than as two separate spaces. For disk-shaped or ellipse-shaped domains in time-frequency plane, the associated localization operators are remarkably simple. Their eigenfunctions are Hermite functions, and the corresponding eigenvalues are given by simple explicit formulas involving the incomplete gamma functions

Keywords

eigenvalues and eigenfunctions; information theory; phase space methods; signal processing; Hermite functions; disk-shaped domains; eigenfunctions; eigenvalues; ellipse-shaped domains; geometric phase space approach; incomplete gamma functions; prolate spheroidal wave functions; signal analysis; time-frequency localisation operators; time-frequency plane; Eigenvalues and eigenfunctions; Filtering; Lighting; Optical filters; Optical sensors; Phase noise; Quantum mechanics; Signal analysis; Time frequency analysis; Wave functions;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.9761

Filename

9761