1. correlation function describes the statistical characteristics of random process in time domain, and power spectrum describes the statistical characteristics of random process in frequency domain.

2. The information provided by them is completely consistent, the power spectrum is easy to obtain, and it is widely used.

Second, mathematically:

Power spectrum is equal to Fourier transform of correlation function, and correlation function is equal to inverse Fourier transform of power spectrum.

1. Power spectral density spectrum is a probability statistical method and a measure of the mean square value of random variables. Generally used for random vibration analysis, continuous transient response can only be described by probability distribution function, that is, the probability corresponding to a certain response level.

2. The definition of power spectral density is "power" (mean square value) in unit frequency band.

3. Power spectral density is the statistical result of the response of the structure under random dynamic load excitation, and it is a curve of power spectral density-frequency value, in which power spectral density can be in the form of displacement power spectral density, velocity power spectral density, acceleration power spectral density, force power spectral density and so on.

4. Autocorrelation (English: Autocorrelation), also called sequence correlation, is the cross-correlation between a signal and itself at different time points. Unofficially, it is a function of the similarity of the time difference between two observations. It is a mathematical tool to find repetitive patterns (such as periodic signals covered by noise) or identify the fundamental frequency hidden in the harmonic frequency of signals. It is often used in signal processing to analyze functions or a series of values, such as time domain signals.