基于方差一致的随机信号功率谱密度修正

由于分析频率间隔与频率分辨率的不同以及窗函数的使用,通常的功率谱密度数值计算可能会损失时域信号的方差信息,分析频率和信号长度选取不同时,得到的功率谱密度幅值不能够保证唯一性。为使得到的功率谱密度能够保持原始时域信号的方差信息,基于时域信号方差和功率谱密度的积分值的一致性,对功率谱密度进行了修正,得到的功率谱密度能够保持时域信号的方差信息,适用于更一般的分析频率要求。

Modification of power spectral density of random signals based on variance consistence

Due to the difference between analysis frequency intervals and frequency resolution, and the introduction of window functions, general numerical calculation of power spectral density (PSD) may cause a loss in variance information. With different selection of sampling length and time step, Different amplitudes of PSD are obtained using the calculation. To deal with this problem, PSD is modified in this paper based on the consistence of the variance of the original signal in time domain and integration of PSD in frequency domain. A PSD result that preserves variance information is obtained, so that the PSD analysis can be applied to more general demands, where frequency interval for analysis differs from frequency resolution, and/or highest analysis frequency differs from the reciprocal of time step.