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Luis Alberto Escudero

Publications and source records attributed to Luis Alberto Escudero.

3 recordsLinked to original sources
arXiv2026

Zeros of the Spectrogram of Colored Noise

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.

math.PR↗
arXiv2022

Efficient computation of the zeros of the Bargmann transform under additive white noise

We study the computation of the zero set of the Bargmann transform of a signal contaminated with complex white noise, or, equivalently, the computation of the zeros of its short-time Fourier transform with Gaussian window. We introduce the adaptive minimal grid neighbors algorithm (AMN), a variant of a method that has recently appeared in the signal processing literature, and prove that with high probability it computes the desired zero set. More precisely, given samples of the Bargmann transform of a signal on a finite grid with spacing $δ$, AMN is shown to compute the desired zero set up to a factor of $δ$ in the Wasserstein error metric, with failure probability $O(δ^4 \log^2(1/δ))$. We also provide numerical tests and comparison with other algorithms.

math.NA↗