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Types of Noise
Noise can be classified into several categories. For the description
of noise, one can use three statistical properties which are described
in more detail below.
Stationarity
When the characteristics of a random process do not vary over time, the
process is called stationary. A generalization of stationarity is ergodicity.
A random process is ergodic when its properties are the same for different
samples. Of course, only stationary processes can be ergodic. Ergodic processes
are an important class of processes, since their properties can be determined
from a single sample.
The properties of a non-stationary process vary over time. One special
aspect of non-stationary processes is the changing of the variance in the
process. When the variance of the random process is constant, we speak
of homoscedastic noise. Its opposite is called heteroscedastic noise, i.e.
the variance changes with the height of the signal (often it is simply
proportional to it).
In order to get more information on homo- and heteroscedasticity, please
start an interactive example by clicking at the image above.
Autocorrelation
Usually we assume that the random errors are completely independent of
each other. The error at one specific time does not influence the error
at another time. This is the assumption of independence. However, in practical
signals we often find that this assumption is not true and the random parts
of the signal are (auto)correlated. We speak of autocorrelation
because the correlation occurs within the same signal. The degree of correlation
between random errors at different times can be described by the autocorrelation
function (ACF) or its equivalent, the power spectral density (PSD). Engineers
have given the different shapes of the PSD the names of colors:
-
white noise: the random errors are independent of each other, the
spectrum of white noise is uniform
-
pink noise: the intensity of the noise decreases with the frequency;
it is also called 1/f noise
-
red noise: more of low frequency than the average
-
blue noise: more of high frequency than the average
Distribution
In most cases the noise has normal (Gaussian) distribution. Complex instruments
have many sources of noise that are convolved with each other, resulting
in a normal distribution due to the central
limit theorem. But in certain instruments one process is predominant
and it determines the type of the distribution. When we count electrons
or other particles at a low rate, the noise is Poisson
distributed. When the noise follows a well-known distribution, it can be
described by a set of parameters.
Last Update: 2004-Jul-03
