November 2012
Intermediate to advanced
794 pages
22h 9m
English
book
Probability, Random Variables, and Random Processes: Theory and Signal Processing Applications
by John J. Shynk
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8.6 POWER SPECTRAL DISTRIBUTION
In Chapter 3 on random variables, we defined the cdf FX(x) and pdf FX(x) for random variable X, which are related as follows:
(8.93) 
provided FX(x) is differentiable. In Chapter 5 on expectation and moments, we defined the expectation of function g(X) of random variable X as follows:
(8.94) 
which is a Riemann–Stieltjes integral with integrator FX(x). The cdf 
denotes a particular probability whereas FX(x) is a density function that is integrated in order to obtain a probability:
(8.95) 
The PSD is also a density function that is integrated to obtain the average power of wide-sense stationary process X(t). For example, the overall average power is
(8.96) 
and the average power in some frequency range 
is
(8.97) 
Similar to the cdf, we can describe a power ...
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