Short-Time Fourier transform zeros reveal noise characteristics clearly
Zeros of the Spectrogram of Colored Noise
Information Theory
Summary
Signals often get noisy, making it hard to analyze them. This paper looks at a specific way to study signals called the Short-Time Fourier Transform and focuses on where this transform hits zero when noise is added. The authors found an exact formula for how often these zeros appear when the noise has some color (not just random white noise). They also show how these zeros can help recover information about the noise's power, guiding better noise detection even when the noise is not perfectly random.
What this means in practice
- •For signal processing engineers: Design detection algorithms that accurately identify signals in colored noise by using the distribution of transform zeros to estimate noise characteristics.
- •For wireless communication teams: Improve noise characterization in communication channels by extracting smoothed power spectral density information from spectrogram zeros in noisy environments.
Authors
Luis Alberto Escudero, Günther Koliander, José Luis Romero
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.