I have the next two signals:(adsbygoogle = window.adsbygoogle || []).push({});

X(t) and G(t) and a random process Y(t)=G(t)X(t) where X(t) and G(t) are wide sense stationary with expectation values: E(X)=0, E(G)=1.

Now, it's also given that ##G(t)=\cos(3t+\psi)## where ##\psi## is uniformly distributed on the interval ##(0,2\pi]## and is statistically independent of X(t).

The signal X(t) is transfered through a low pass filter, given in the frequency domain as ##H(\Omega)=1## when ##\Omega \leq 4\pi## and otherwise zero.

I am given that ##Y(\Omega)=X(\Omega)H(\Omega)##, and I want to calculate:

##\epsilon = E((X(t)-Y(t))^2)##

I guess I can go to the frequency domain, but I also need to use the http://en.wikipedia.org/wiki/Law_of_total_expectation

But I am not sure how exactly to condition this, thanks in advance.

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# Calculation of the error function.

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