CHAPTER 2
SEGMENTATION METHODS
2.1 Statistical Model of a Signal and Definitions
2.1.1 Random Processes and Time Series
A random variable Xrealizes a mapping from the sample space on the real line. It is
usually described by its probability density function (PDF)fx(x), which can be
represented roughly as a histogramm" of the probability for a realization of the random
variable Xto take the value x, described with respect to all possible values of the random
variable Random variables usually describe systems that are not time dependent. On the
contrary, a random (or stochastic) process can describe a system that changes with time.
It realizes a mapping from the sample space onto an ensemble of time functions: each
realization X(t,p) of a random process X consists in a well-defined function of time (in the
continuous case), or a sequence of values indexed by time (in the discrete case). At a
given time t, the realization of a random process is a random variable represented by its
own PDF.
F(x,t) = P[X(t)