Sharp rates of convergence for accumulated spectrograms

Abstract

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.

14 pages, 2 figures

References in corpus (2)

• ConceFT: Concentration of Frequency and Time via a multitapered synchrosqueezed transform
• Uncertainty principles for orthonormal sequences

Cited by in corpus (4)

• The Faber-Krahn inequality for the Short-time Fourier transform
• Harmonic analysis in phase space and finite Weyl-Heisenberg ensembles
• Entanglement entropy and hyperuniformity of Ginibre and Weyl-Heisenberg ensembles
• On accumulated spectrograms for Gabor frames