An evaluation on the peak value distribution using level crossings for non-Gaussian-type random signals with wide frequency band

Abstract

It is extremely difficult to carry out a rigorous theoretical evaluation of the peak value distribution in the maximum-value statistical analysis of random signals because second derivative information is needed in addition to the instantaneous value and the first derivative. On the other hand, the number of level crossings can be evaluated with only the first derivative information, and hence a theoretical evaluation equation that can be applied regardless of the amplitude distribution and the frequency characteristics is explicitly derived. In this paper, a function is derived to evaluate theoretically the relationship between the expected number of signal crossings of a certain level and the number of peaks exceeding this level under the condition of Gaussian distribution. The non-Gaussian nature of the amplitude distribution is reflected in this function and is coupled to a conventional non-Gaussian level-crossing evaluation equation, allowing the practical peak value distribution analysis of broadband non-Gaussian arbitrary random signals. Finally, the validity of the evaluation equation is confirmed by digital simulation. © 2000 Scripta Technica, Electron Comm Jpn Pt 3, 83(11): 20–31, 2000