Zeros of the Spectrogram of Colored Noise

2026-09-16

AI Summary

研究了有色噪声信号的短时傅里叶变换零点数量，并提出一种从零点分布恢复平滑功率谱密度的方法。

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.

Problem

• Short-Time Fourier Transform
• Gaussian window
• colored noise
• power spectral density
• zero distribution

Innovation

• Short-Time Fourier Transform (STFT)
• Gaussian window
• colored noise
• power spectral density (PSD)