Objective

Recent work has drawn attention to the valuable information contained in the set of zeros of the short Fourier transform (STFT) of a noisy signal. We contribute to study of the statistics of STFT zeros, the development of numerical algorithms to compute them from finite data, and investigate the extent to which such computations reflect underlying analog models. Special emphasis is put on applications to signal processing.

Method

In addition to writing research articles, we also publish open-source implementations of the proposed algorithms, and of the various numerical experiments that validate theoretical statistics.

Application

The computation of STFT zeros finds applications in signal estimation, for example in filtering procedures that exploit theoretical knowledge of the statistics of zeros. Our recent research supports such practices by showing that empirically computed statistics are faithful.

Figure: Spectrogram of a signal contaminated with noise, and algorithmically computed zeros. Even though the spectrogram is only given on a finite grid, the algorithm succeeds in computing an approximation of the zeros of the underlying analog signal, up to the resolution of the data.

Partners

  • Antti Haimi, University of Vienna

Funding

This is a subproject of the project "Time-Frequency Analysis, Randomness and Sampling", funded by the FWF START award Y 1199 (Austrian Science Fund).

References

  • R. Bardenet, J. Flamant, and P. Chainais. On the zeros of the spectrogram of white noise. Appl. Comput. Harmon. Anal. 2020.
  • R. Bardenet and A. Hardy. Time-frequency transforms of white noises and Gaussian analytic functions. Appl. Comput. Harmon. Anal. 2021.
  • L. A. Escudero, N. Feldheim, G. Koliander, J. L. Romero. Efficient computation of the zeros of the Bargmann transform under additive white noise. Arxiv: 2108.12921.
  • P. Flandrin. Time–frequency filtering based on spectrogram zeros. IEEE Signal Processing Letters, 2015.
  • P. Flandrin. The sound of silence: Recovering signals from time-frequency zeros. In 2016 50th Asilomar Conference on Signals, Systems and Computers, 2016.
  • A. Haimi, G. Koliander, J. L. Romero. Zeros of Gaussian Weyl-Heisenberg functions and hyperuniformity of charge. Arxiv: https:2012.12298.