# Sharp rates of convergence for accumulated spectrograms

## TL;DR

This paper studies how quickly accumulated spectrograms can approximate the symbol of a time-frequency localization operator, providing improved bounds on convergence rates for this inverse problem.

## Contribution

It introduces a sharper bound for the convergence rate of accumulated spectrograms, advancing the understanding of spectral approximation in time-frequency analysis.

## Key findings

- Derived a sharp convergence rate bound for accumulated spectrograms
- Improved upon previous results in spectral approximation accuracy
- Enhanced understanding of inverse problems in time-frequency localization

## 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.