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.