Math @ Duke

Publications [#287130] of Ingrid Daubechies
Papers Published
 Daubechies, I, TimeFrequency Localization Operators: A Geometric Phase Space Approach,
Ieee Transactions on Information Theory, vol. 34 no. 4
(January, 1988),
pp. 605612, Institute of Electrical and Electronics Engineers (IEEE) [doi]
(last updated on 2019/08/21)
Abstract: We define a set of operators which localize in both time and frequency. These operators are similar to but different from the lowpass timelimiting operators, the singular functions of which are the prolate spheroidal wave functions. Our construction differs from the usual approach in that we treat the timefrequency plane as one geometric whole (phase space) rather than as two separate spaces. For diskshaped or ellipseshaped domains in the timefrequency 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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