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PreprintarXiv licencearXiv

Zeros of the Spectrogram of Colored Noise

  • Luis Alberto Escudero
  • Günther Koliander
  • José Luis Romero
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Abstract

We study the expected number of zeros of the Short-Time Fourier Transform (STFT) with a Gaussian window for signals degraded by complex Gaussian colored noise. We provide an exact formula for this quantity and investigate its asymptotic behavior. From a computational perspective, we propose an algorithmic method to recover a smoothed power spectral density (PSD) directly from the spatial distribution of the transform's zeros. Our results formalize the commonly-held heuristic that detection algorithms based on spectrogram zeros, though designed for white noise, also perform adequately under moderately colored noise.

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Cite

BibTeXRIS
BibTeX
@misc{escudero2026zeros,
  title = {{Zeros of the Spectrogram of Colored Noise}},
  author = {Luis Alberto Escudero and Günther Koliander and José Luis Romero},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.18689},
  eprint = {2609.18689},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.18689},
}
RIS
TY  - UNPB
TI  - Zeros of the Spectrogram of Colored Noise
AU  - Luis Alberto Escudero
AU  - Günther Koliander
AU  - José Luis Romero
PY  - 2026
DA  - 2026/09/18
PB  - arXiv
DO  - 10.48550/arxiv.2609.18689
UR  - https://arxiv.org/abs/2609.18689
AB  - We study the expected number of zeros of the Short-Time Fourier Transform (STFT) with a Gaussian window for signals degraded by complex Gaussian colored noise. We provide an exact formula for this quantity and investigate its asymptotic behavior. From a computational perspective, we propose an algorithmic method to recover a smoothed power spectral density (PSD) directly from the spatial distribution of the transform's zeros. Our results formalize the commonly-held heuristic that detection algorithms based on spectrogram zeros, though designed for white noise, also perform adequately under moderately colored noise.
ER  -