Sharp rates of convergence for accumulated spectrograms

We investigate an inverse problem in time-frequency localization: the approximation of the symbol of a time-frequency localization operator from partial spectral information by the method of accumulated spectrograms (the sum of the spectrograms corresponding to large eigenvalues). We derive a sharp...

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Bibliographic Details
Published in:Inverse problems 2017-11, Vol.33 (11), p.115008
Main Authors: Abreu, Luís Daniel, Pereira, João M, Romero, José Luis
Format: Article
Language:English
Subjects:
Gabor
localization operator
phase-space
spectrogram
time-frequency analysis
uncertainty principle
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Summary:We investigate an inverse problem in time-frequency localization: the approximation of the symbol of a time-frequency localization operator from partial spectral information by the method of accumulated spectrograms (the sum of the spectrograms corresponding to large eigenvalues). We derive a sharp bound for the rate of convergence of the accumulated spectrogram, improving on recent results.
ISSN:0266-5611
1361-6420
DOI:10.1088/1361-6420/aa8d79