On the characterization of dynamic properties of random processes by spectral parameters

This paper deals with the general problem of directly relating the distribution of ranges of wide hand random processes to the power spectral density (PSD) by means of closed-form expressions. Various attempts to relate the statistical distribution of ranges to the PSD by means of the irregularity factor or similar parameters have been done by several authors but, unfortunately, they have not been fully successful. In the present study, introducing the so-called analytic processes, the reasons for which these parameters are insufficient to an unambiguous determination of the range distribution and the fact that parameters regarding the time-derivative processes are needed have been explained. Furthermore, numerical simulations have shown that the range distributions depend on the irregularity factor and bandwidth parameter of both the process and its derivative. These observations are the basis for the determination of accurate relationships between range distributions and PSDs.