No abstract

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.

No abstract

No abstract

Theoretical results concerning the level crossings of the phase -π≤θ(t)≤π of the process consisting of a sine wave disturbed by additive Gaussian noise are presented, along with the experimental results supporting the theory. The average number of crossings of the phase angle θ(t), as well as the conditional probability densities for R(t), the envelope of the considered process, and for θ′(t), the time derivative of θ(t), are derived for an arbitrary crossing level θ. These derivations are a generalization of the existing theory to the case of a nonsymmetric (about the sine wave frequency) noise spectrum and an arbitrary crossing level -π≤θ≤π. To verify the derivations, experimental measurement of the considered quantities is performed for the case of a Gaussian noise having the 7th-order Butterworth spectrum. The experimental results are compared with the corresponding theoretical ones, and are found to be in good agreement.