Is the expectation of a random process $X(t)$ with zero DC component necessarily zero? Or can it be non-zero depending upon the process?
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$\begingroup$ no, the pdf of amplitudes is symmetric around zero. another way of looking at it is the AC electrical power socket produces power but has a mean voltage of zero $\endgroup$ – Stanley Pawlukiewicz Jul 10 at 16:58
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3$\begingroup$ What is the DC component of a random process? How is it defined? $\endgroup$ – Dilip Sarwate Jul 10 at 18:17
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$\begingroup$ $X(t)$ is said to have a DC component of $A$ if $X(t) = Y(t) + A$ , where $Y(t)$ has zero DC component. $\endgroup$ – helloworld1e. Jul 11 at 1:00
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1$\begingroup$ That just begs the question since you still haven’t told us what it means for a process to have a zero DC component. $\endgroup$ – Dilip Sarwate Jul 11 at 1:35
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$\begingroup$ My guess is the OP is assuming a random process to be DC free iff its power spectral density is zero at $\omega = 0$. But that's just guessing really. So far we don't even know if the process is assumed to be stationary? $\endgroup$ – Florian Jul 11 at 7:15
