On the statistical distribution of the maxima of sine on random process

This study addresses the issue of statistics of maxima for a sine wave superimposed to a Gaussian noise, with particular focus on the maxima probability density function. Starting from the analysis of the well-known Rician Distribution, and of the hypotheses under which it was obtained, it is observed that this represents a valid solution only when the sine frequency is very close to that of random. However there are application of interest, especially in structural dynamics, where sine waves are, in the sense of frequency, before or after the random noise. For this reason the solution for the two cases mentioned above was calculated in terms of Probability Density Function, moving the very first step for application of spectral methods for structural analysis in case of Sine on Random excitation.