The paper presents the use of the autocorrelation function for the description of vibrations and the problems connected with. The proposed method is based on the analysis of vibration signal recorded for machine during its operations using an analytic form of the autocorrelation function. The parameters are obtained using a curve fitting procedure. To keep a quality of parametric representation of considered vibration, only the curve fitting causes a determination coefficient over 0.90 is taken into consideration. Therefore, the autocorrelation functions are submitted for the fast Fourier transform to be helped, in determination of number of the dominant harmonic components. Also, the analytic form and parameters of power spectral density has been also calculated. Finally, the set of parameters has been collected to describe the selected fragment of vibration of the simple rotating machine. The influence of duration of analyzed vibration on the parameters values is also examined in this work.