Abstract

The statistical distribution of the phase of a quasi-harmonic signal has been theoretically investigated. An analytical expression for the probability density function of this distribution has been obtained for the first time, and the distribution has been shown to be a two-parameter one and to be determined by the following parameters: the signal-to-noise ratio and the deviation of the current phase value from the phase value in the initial noiseless signal. The dependence of the probability density function for the signal phase upon its parameters has been analyzed. This research is meaningful for solving tasks of high-precision phase measurements by means of statistical data processing methods.

中文翻译：

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准谐波信号相位的统计分布特征

摘要

理论上研究了准谐波信号相位的统计分布。首次获得了该分布的概率密度函数的解析表达式，该分布已被证明是一个双参数分布，并由以下参数确定：信噪比和当前相位值与初始无噪声信号中的相位值的偏差。已经分析了信号相位的概率密度函数对其参数的依赖性。该研究对于利用统计数据处理方法解决高精度相位测量任务具有重要意义。