Time-Frequency Localization Operators: A Geometric Phase Space Approach

Journal Article (Journal Article)

We define a set of operators which localize in both time and frequency. These operators are similar to but different from the low-pass time-limiting operators, the singular functions of which are the prolate spheroidal wave functions. Our construction differs from the usual approach in that we treat the time-frequency plane as one geometric whole (phase space) rather than as two separate spaces. For disk-shaped or ellipse-shaped domains in the 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. © 1988 IEEE

Full Text

Duke Authors

Cited Authors

  • Daubechies, I

Published Date

  • January 1, 1988

Published In

Volume / Issue

  • 34 / 4

Start / End Page

  • 605 - 612

Electronic International Standard Serial Number (EISSN)

  • 1557-9654

International Standard Serial Number (ISSN)

  • 0018-9448

Digital Object Identifier (DOI)

  • 10.1109/18.9761

Citation Source

  • Scopus