Empirical plunge profiles of time-frequency localization operators
Simon Halvdansson · Applied and Computational Harmonic Analysis · 2025
For time-frequency localization operators, related to the short-time Fourier transform, with symbol R Ω, we work out the exact large R eigenvalue behavior for rotationally invariant Ω and conjecture that the same relation holds for all scaled symbols R Ω as long as the window is the standard Gaussian. Specifically, we conjecture that the k -th eigenvalue of the localization operator with symbol R Ω converges to 1 2 erfc ( 2 π k − R 2 | Ω | R | ∂ Ω | ) as R → ∞. To support the conjecture, we compute the eigenvalues of discrete frame multipliers with various symbols using LTFAT and find that they agree with the behavior of the conjecture to a large degree.