The distribution of level-crossing time-intervals of Gaussian random signals

With Gaussian random signals approximative formulas are derived for the distribution density P(a, t) of time intervals of lengths t between two successive crossings of the level a. The derivation is based on some assumptions about the statistical dependence between successive time intervals. Solutions are given for signals with low-pass spectra and band-pass spectra, respectively. Accuracy and range of validity of the approximations are determined experimentally. In nearly all cases, the measured values agree closely with the approximations in a range of time intervals which contains more than 97% of all time intervals occurring. It is discussed how far the assumptions used are admissible.