标题： 关于噪声信号谱图零点的两个基本性质 显示英文标题

标题： On two fundamental properties of the zeros of spectrograms of noisy signals

摘要： 当信号被添加到白高斯噪声中时，频谱图零点的空间分布会发生显著变化。 零点倾向于勾勒出信号的支撑区域，在干扰存在的情况下会形成确定性结构，仿佛零点被困住了一样。 虽然已经提出了复杂的方法来检测频谱图零点模式中的信号作为孔洞，但很少有正式的论证来支持勾勒和被困效应。 通过针对简单玩具信号的详细计算，我们表明两个基本的数学论证，即零点的强度和儒歇定理，可以用来讨论勾勒和被困现象，以及信噪比等参数的影响。 特别是，干扰的线性调频信号，即使几乎叠加在一起，也会在零点之间产生易于检测的确定性结构。 显示英文摘要

摘要： The spatial distribution of the zeros of the spectrogram is significantly altered when a signal is added to white Gaussian noise. The zeros tend to delineate the support of the signal, and deterministic structures form in the presence of interference, as if the zeros were trapped. While sophisticated methods have been proposed to detect signals as holes in the pattern of spectrogram zeros, few formal arguments have been made to support the delineation and trapping effects. Through detailed computations for simple toy signals, we show that two basic mathematical arguments, the intensity of zeros and Rouch\'e's theorem, allow discussing delineation and trapping, and the influence of parameters like the signal-to-noise ratio. In particular, interfering chirps, even nearly superimposed, yield an easy-to-detect deterministic structure among zeros.