Fractal characteristics of characteristic parameter statistical distributions of typical random signals

Abstract

A two-parameter statistical model of the pulsed signals which can be used to describe the basic structural characteristics of the random signals is established in this paper. As a result, the random signal counting distributions of amplitude q(lV) and width p(l), as well as the different signal subset counting distributions under given width l(lV) and amplitude lV(l), all match well with the form of the lognormal distribution with a natural numberused as an independent variable. Besides, it is also found that there are internal relations between the counting distribution statistical characteristic parameters lnV, ln, lnV, ln and the corresponding signal characteristic parameters lV and l. In essence, these relations are the representations of random signal fractal characteristics. In a word, two characteristic parameter statistical distributions of the random signals each have a non-integral dimensional fractal feature.