Publications [#287130] of Ingrid Daubechies

Papers Published

1. Daubechies, I, Time-Frequency Localization Operators: A Geometric Phase Space Approach, IEEE Transactions on Information Theory, vol. 34 no. 4 (January, 1988), pp. 605-612, Institute of Electrical and Electronics Engineers (IEEE) [doi]
   (last updated on 2025/04/04)

   Abstract:
   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