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.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
Keywords
EllipseOperator (biology)Simple (philosophy)EigenfunctionMathematicsEigenvalues and eigenvectorsMathematical analysisPhase spaceHermite polynomialsComplex planePlane (geometry)Operator theorySpace (punctuation)Phase (matter)Pure mathematicsComputer scienceGeometryPhysicsQuantum mechanics
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Publication Info
- Year
- 1988
- Type
- article
- Volume
- 34
- Issue
- 4
- Pages
- 605-612
- Citations
- 634
- Access
- Closed
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Cite This
Ingrid Daubechies
(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
Identifiers
- DOI
- 10.1109/18.9761