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Correlation confused on integration

  1. Mar 14, 2014 #1
    x(n)=exp(i(x*n+theta1)) +exp(i(y*n+theta2)) x and y are constants , theta1, theta2 are uniform random on [0,2*pi]

    R(f) =E[{ exp(i(x*n+theta1)) +exp(i(y*n+theta2)) }exp(-i(x*(n-f)+theta1)) +exp(-i(y*(n-f)+theta2)) }]
    = 4 products 2 of which will be similar but with the opposite constants

    E[exp(i*x*n+i*theta1 -i*x*n+i*n*f0i*theta1] = E[exp(i*x*f)] =integral exp(i*x*f) dtheta1 0 to 2 pi = 2*pi*exp(i(x*f)
    Or am I suppose to integral over both theta1 and theta 2 to get 4*pi*exp(i*x*f) ?


    E[exp(i*n*n+i*theta1 -i*y*n +i*y*f- i*theta2 ] = double integral of the inside but it equals zero since we can separate the exponential and get exp(i*theta1) and the integral of this over 0 2pi = 0.
    Right?
     
  2. jcsd
  3. Mar 15, 2014 #2

    micromass

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    You're gonna get much more responses if you learn LaTeX. It'll make your posts way more readable. Read this: https://www.physicsforums.com/showpost.php?p=3977517&postcount=3

    Anyway, because jbunniii asked me to:

     
    Last edited: Mar 15, 2014
  4. Mar 15, 2014 #3

    mathman

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    There seem to be some typos in the formulas, which make it difficult to understand what is being presented.
     
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