Environmental Engineering Reference
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and are said to be uncorrelated if A stochastic
process is said to be stationary
in the strict sense
if all of its statistical
properties are time-invariant. It is stationary in the wide sense if its
mean is constant and its autocorrelation function satisfies
where Note that the wide-sense stationarity involves only
the first and second-order moments. Because it is generally difficult
to evaluate the high-order moments of a given stochastic process, the
wide-sense stationarity is widely used in practice. If both the mean
and autocorrelation function of a wide-sense stationary noise signal are
periodic in time, the noise signal is said to be cyclo-stationary in the
wide sense.
In the frequency domain, the power spectral density of a noise signal
denoted by depicts the spectrum of the power of the noise
signal. It is defined as the Fourier transform of the autocorrelation
function of
Eq.(11.71) is also known as Wiener-Khintchine theorem [56]. If
where
A
is a constant, then Processes of such
characteristics are said to be
white.
For a wide-sense process
if
i.e.
then
Eq.(11.72) reveals that the area under
specifies the mean-
square value of
The power spectral density of noise sources encountered in integrated
devices has been investigated extensively and is readily computable.
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