System and method for statistically separating and characterizing noise which is added to a signal of a machine or a system

Abstract

Method for finding the probability density function type and the variance properties of the noise component N of a raw signal S of a machine or a system, said raw signal S being combined of a pure signal component P and said noise component N, the method comprising: (a) defining a window within said raw signal; (b) recording the raw signal S; (c) numerically differentiating the raw signal S within the range of said window at least a number of times m to obtain an m order differentiated signal; (d) finding a histogram that best fits the m order differentiated signal; (e) finding a probability density function type that fits the distribution of the histogram; (f) determining the variance of the histogram, said histogram variance being essentially the m order variance σof the noise component N; and (g) knowing the histogram distribution type, and the m order variance σof the histogram, transforming the m order variance σto the zero order variance σ, said σbeing the variance of the pdf of the noise component N, and wherein the histogram type as found in step (e) being the probability density function type of the noise component N.