Find the mean and autocorrelation

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I have this problem. Consider a random process X(t) defined by $X(t) = 2cos(2 pi t+ phi)$.
$phi$ is a random variable with probability density function $f_phi (varphi ) = left{beginmatrix
frac4pi, quad |varphi | leq fracpi8
\
0, quad mathrmotherwise.
endmatrixright.$



Find the mean and autocorrelation functions.



  • Normally when I have a problem like this, the information about the values for which the phase is changing randomly, e.g., from $-pi$ to $pi$. And then i use the formula (the random process is $cos(..)$ in this example) $int_-pi^pi cos(...) frac12 pi dx$ and afterward i calculate the autocorrelation by calculating $E[cos(t_1...)cos(t_2dots)]$. In this problem, the density function is given instead. I know that i should check for if the mean is constant for all $t$. Can I say the mean is $frac12 pi$ for all $t$? And if that is correct, how should I calculate the autocrorrealtion?






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    I have this problem. Consider a random process X(t) defined by $X(t) = 2cos(2 pi t+ phi)$.
    $phi$ is a random variable with probability density function $f_phi (varphi ) = left{beginmatrix
    frac4pi, quad |varphi | leq fracpi8
    \
    0, quad mathrmotherwise.
    endmatrixright.$



    Find the mean and autocorrelation functions.



    • Normally when I have a problem like this, the information about the values for which the phase is changing randomly, e.g., from $-pi$ to $pi$. And then i use the formula (the random process is $cos(..)$ in this example) $int_-pi^pi cos(...) frac12 pi dx$ and afterward i calculate the autocorrelation by calculating $E[cos(t_1...)cos(t_2dots)]$. In this problem, the density function is given instead. I know that i should check for if the mean is constant for all $t$. Can I say the mean is $frac12 pi$ for all $t$? And if that is correct, how should I calculate the autocrorrealtion?






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      I have this problem. Consider a random process X(t) defined by $X(t) = 2cos(2 pi t+ phi)$.
      $phi$ is a random variable with probability density function $f_phi (varphi ) = left{beginmatrix
      frac4pi, quad |varphi | leq fracpi8
      \
      0, quad mathrmotherwise.
      endmatrixright.$



      Find the mean and autocorrelation functions.



      • Normally when I have a problem like this, the information about the values for which the phase is changing randomly, e.g., from $-pi$ to $pi$. And then i use the formula (the random process is $cos(..)$ in this example) $int_-pi^pi cos(...) frac12 pi dx$ and afterward i calculate the autocorrelation by calculating $E[cos(t_1...)cos(t_2dots)]$. In this problem, the density function is given instead. I know that i should check for if the mean is constant for all $t$. Can I say the mean is $frac12 pi$ for all $t$? And if that is correct, how should I calculate the autocrorrealtion?






      share|cite|improve this question














      I have this problem. Consider a random process X(t) defined by $X(t) = 2cos(2 pi t+ phi)$.
      $phi$ is a random variable with probability density function $f_phi (varphi ) = left{beginmatrix
      frac4pi, quad |varphi | leq fracpi8
      \
      0, quad mathrmotherwise.
      endmatrixright.$



      Find the mean and autocorrelation functions.



      • Normally when I have a problem like this, the information about the values for which the phase is changing randomly, e.g., from $-pi$ to $pi$. And then i use the formula (the random process is $cos(..)$ in this example) $int_-pi^pi cos(...) frac12 pi dx$ and afterward i calculate the autocorrelation by calculating $E[cos(t_1...)cos(t_2dots)]$. In this problem, the density function is given instead. I know that i should check for if the mean is constant for all $t$. Can I say the mean is $frac12 pi$ for all $t$? And if that is correct, how should I calculate the autocrorrealtion?








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      edited Aug 21 at 12:34









      Davide Giraudo

      121k15147250




      121k15147250










      asked Dec 28 '17 at 16:24









      Xraycat922

      154




      154

























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