In a recent paper, Flandrin [16] proposed filtering based on the zeros of a spectrogram with Gaussian window. His results are based on empirical observations on the distribution of the zeros of the spectrogram of white Gaussian noise. These zeros tend to be uniformly spread over the time–frequency plane, and not to clutter. Our contributions are threefold: we rigorously define the zeros of the spectrogram of continuous white Gaussian noise, we explicitly characterize their statistical distribution, and we investigate the computational and statistical underpinnings of the practical implementation of signal detection based on the statistics of the zeros of the spectrogram. The crux of our analysis is that the zeros of the spectrogram of white Gaussian noise correspond to the zeros of a Gaussian analytic function, a topic of recent independent mathematical interest [24].

在最近的一篇论文中，Flandrin [16]提出了一种基于具有高斯窗的频谱图零点的滤波方法。他的结果基于对白高斯噪声频谱图的零点分布的经验观察。这些零趋向于均匀分布在时频平面上，而不混乱。我们的贡献是三方面的：我们严格定义连续高斯白噪声频谱图的零点，明确表征其统计分布，并基于信号零点的统计数据研究信号检测实际实施的计算和统计基础。频谱图。我们分析的症结在于，高斯白噪声频谱图的零点对应于高斯分析函数的零点，