# Discrete Random Process

• May 6th 2009, 08:34 PM
krispiekream
Discrete Random Process
I don't know how to do this problem.
I really need help because I think this problem will be on my midterms coming up as my professor mentioned to study for it.

http://i709.photobucket.com/albums/w...m/Untitled.jpg
• May 7th 2009, 07:37 AM
cl85
(a) $E[X(k,\theta)] = \int_0^{\pi} A\cos(\omega k + \theta)\frac{1}{\pi} d\theta = 0$

Similarly with the autocorrelation, first apply the trig identity for product of cosines, then evaluate the integral. You'll get a function of (m-k).

Plug in k=m into the autocorrelation to get the third expectation.

(b) Both mean and autocorrelation only depend on m-k, and so X is a WSS process.
• May 7th 2009, 12:02 PM
rayhld
sorry if this is a dumb question, but what would the autocorrelation integral equation look like in this case? I'm curious. Thanks
• May 7th 2009, 08:58 PM
cl85
The only random variable is $\Theta$. So
$E[X(k, \theta)X(m, \theta)] = A^2 \int_0^{\pi} \cos(\omega k +\theta)\cos(\omega m +\theta) \frac{1}{\pi} d\theta$
• May 7th 2009, 09:44 PM
rayhld
Thanks, I got it now.