论文标题
高斯噪声的幅度调制模式是高斯性的指纹
The amplitude modulation pattern of Gaussian noise is a fingerprint of Gaussianity
论文作者
论文摘要
我们引入了一种使用信号及其变化系数的信封的高斯测试的新方法。高斯信号的包膜遵循瑞利分布，鉴于瑞利分布的变化系数是不变的，因此高斯噪声变化系数的包络是一个通用常数，并且可以用作歧视统计量。这种方法的主要应用是检测时间序列的高斯性。但是，包膜变化系数也是振幅调制模式的度量，可捕获傅立叶相位剖面的结构，使其成为区分非高斯性类型和信号分类的有用参数。
We introduce a new approach for Gaussianity testing using the envelope of a signal and its coefficient of variation. The envelope of a Gaussian signal follows the Rayleigh distribution, and given that the coefficient of variation of the Rayleigh distribution is invariant, the envelope of Gaussian noise's coefficient of variation is a universal constant and can be exploited as a discriminating statistic. The main application of this approach is to detect the Gaussianity of time series. However, the coefficient of variation of the envelope is also a measure of amplitude modulation patterns that captures the structure of the Fourier phase profile, making it a useful parameter to differentiate types of non-Gaussianity and for signal classification.
