Level-Crossing Problem of a Gaussian Process Having Gaussian Power Spectrum Density

The distribution density of the level-crossing interval lengths is experimentally studied for a Gaussian random process having Gaussian power spectrum density. The multi-peak property of the density does not appear for a Gaussian-lowpass spectrum, although it does for a Gaussian-bandpass spectrum. This situation is different from the cases of Butterworth spectra, in which the multi-peak property always appears both for lowpass and bandpass processes. In addition to the disappearance of the multi-peak property, the result of the fluctuation of the number of the crossings leads to a conclusion that a Gaussian process having Gaussian-lowpass spectrum is highly random.