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Expectation of terms in double summation

  1. May 10, 2010 #1
    Does any body help me how to find the average (expectation) of terms involving double summation? Here is the equation which I'm trying solve.

    [\tex]E\Big[2\sum_{k=0}^{N-2}\sum_{j=k+1}^{N-1}f(k,j)\cos[2\pi(j-k)t-\theta_{k,j}]\Big][\tex]
    where f(k,j) and [\tex]\theta_{k,j}[\tex] are some function of k and j.
     
  2. jcsd
  3. May 10, 2010 #2
    [ latex ] expresion [ /latex ]
     
  4. May 10, 2010 #3

    Redbelly98

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    Are you wanting to take the time-average? Have you been given the equation for doing that -- it involves doing an integral with respect to time...
     
  5. May 10, 2010 #4
    Yes I want to take the time average of the said expression. Its not part of any assignment. I came accross this equation while deriving PAPR for the QAM OFDM signal. It does not involve any integral.
     
  6. May 10, 2010 #5

    Redbelly98

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    The cosine terms all have a time-average of 0, except when j=k. As long as the f's and θ's are time-independent, this simplifies things greatly.

    When j=k, the time-average of cos[2π(j-k)t - θk,j]=cos(θk,j). However, it appears that j is never equal to k in this summation, so we are left with 0 for the average.
     
    Last edited: May 10, 2010
  7. May 10, 2010 #6
    Dear Sir
    Thanks a lot for your prompt response. After your comment now I've got the confirmation of my answer. Thanks a lot once again.
     
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