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Math Help - Discrete Random Process

  1. #1
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    Discrete Random Process

    Can someone please help me with this.
    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.

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  2. #2
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    (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.
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  3. #3
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    sorry if this is a dumb question, but what would the autocorrelation integral equation look like in this case? I'm curious. Thanks
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  4. #4
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    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
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  5. #5
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    Thanks, I got it now.
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