A method of detection of the correlation function and frequency power spectrum for random noise or vibration with amplitude limitation

A method for determining the linear correlation function and the frequency power spectrum for random noise or vibration of which the amplitude fluctuation is limited by upper and/or lower levels is proposed, for an idealized case of a Gaussian random process. The standard method based on the definition of the linear correlation function and the FFT procedure has frequently been employed for linear correlation and spectrum analyses. These usual methods, however, cannot be adopted for actual noise or vibration signals with the above amplitude limitations. In this paper, a simplified method which can determine the correlation function through the conditional average is used. First, an explicit expression for the probability density function for random noise or vibration signals with amplitude limitations is introduced by using the well known Gaussian distribution and Dirac's delta functions. Next, by use of this expression, an original linear correlation function can be determined through the conditional average calculated by using the first and second order moments of this limited observed data. Then, the power spectrum latent in the actual noise or vibration signals with no amplitude limitations can be determined through Fourier transformation of the linear correlation function based on the well known Wiener-Khintchine theorem. Finally, the effectiveness of the proposed method is confirmed experimentally not only by means of the digital simulation technique but also by applying it to actual noise and vibration signals observed at a hydroelectric plant.