Time-Frequency Localization Operators: A Geometric Phase Space Approach
Publication
, Journal Article
Daubechies, I
Published in: IEEE Transactions on Information Theory
January 1, 1988
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
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Published In
IEEE Transactions on Information Theory
DOI
EISSN
1557-9654
ISSN
0018-9448
Publication Date
January 1, 1988
Volume
34
Issue
4
Start / End Page
605 / 612
Related Subject Headings
- Networking & Telecommunications
- 4613 Theory of computation
- 4006 Communications engineering
- 1005 Communications Technologies
- 0906 Electrical and Electronic Engineering
- 0801 Artificial Intelligence and Image Processing
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Daubechies, I. (1988). Time-Frequency Localization Operators: A Geometric Phase Space Approach. IEEE Transactions on Information Theory, 34(4), 605–612. https://doi.org/10.1109/18.9761
Daubechies, I. “Time-Frequency Localization Operators: A Geometric Phase Space Approach.” IEEE Transactions on Information Theory 34, no. 4 (January 1, 1988): 605–12. https://doi.org/10.1109/18.9761.
Daubechies I. Time-Frequency Localization Operators: A Geometric Phase Space Approach. IEEE Transactions on Information Theory. 1988 Jan 1;34(4):605–12.
Daubechies, I. “Time-Frequency Localization Operators: A Geometric Phase Space Approach.” IEEE Transactions on Information Theory, vol. 34, no. 4, Jan. 1988, pp. 605–12. Scopus, doi:10.1109/18.9761.
Daubechies I. Time-Frequency Localization Operators: A Geometric Phase Space Approach. IEEE Transactions on Information Theory. 1988 Jan 1;34(4):605–612.
Published In
IEEE Transactions on Information Theory
DOI
EISSN
1557-9654
ISSN
0018-9448
Publication Date
January 1, 1988
Volume
34
Issue
4
Start / End Page
605 / 612
Related Subject Headings
- Networking & Telecommunications
- 4613 Theory of computation
- 4006 Communications engineering
- 1005 Communications Technologies
- 0906 Electrical and Electronic Engineering
- 0801 Artificial Intelligence and Image Processing