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Time-frequency concentration operators restrict the integralanalysis-synthesis formula for the short-time Fourier transform to a givencompact domain. We estimate how much the corresponding eigenvalue countingfunction deviates from the Lebesgue measure of the time-frequency domain. Forwindow functions in the Gelfand-Shilov class, the bounds almost match knownasymptotics, with the advantage of being effective for concrete domains andspectral thresholds. As such our estimates allow for applications where thespectral threshold depends on the geometry of the time-frequency concentrationdomain. We also consider window functions that decay only polynomially in timeand frequency.

Spectral deviation of concentration operators for the short-time Fourier transform