Mean and correlation of product of two random processes

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I have two random process:
$$A(at)$$
$$cos(2pi f_0t+Phi)$$ with these hypothesis:



  1. $a$ and $f_0$ are constant

  2. $Phi$ is uniformly distributed in $[0,pi)$

  3. $A(at)$ is WSS

I must calculate the statistical averages and autocorrelation of the random process:
$$X(t)=A(at)cos(2pi f_0t+Phi)$$
I started to define the integral
$$E[X(t)]=frac1piint_0^pi A(at)cos(2pi f_0t+phi)dphi$$ but I think is wrong because i don't know how to consider the process $A(at)$







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    up vote
    1
    down vote

    favorite












    I have two random process:
    $$A(at)$$
    $$cos(2pi f_0t+Phi)$$ with these hypothesis:



    1. $a$ and $f_0$ are constant

    2. $Phi$ is uniformly distributed in $[0,pi)$

    3. $A(at)$ is WSS

    I must calculate the statistical averages and autocorrelation of the random process:
    $$X(t)=A(at)cos(2pi f_0t+Phi)$$
    I started to define the integral
    $$E[X(t)]=frac1piint_0^pi A(at)cos(2pi f_0t+phi)dphi$$ but I think is wrong because i don't know how to consider the process $A(at)$







    share|cite|improve this question
























      up vote
      1
      down vote

      favorite









      up vote
      1
      down vote

      favorite











      I have two random process:
      $$A(at)$$
      $$cos(2pi f_0t+Phi)$$ with these hypothesis:



      1. $a$ and $f_0$ are constant

      2. $Phi$ is uniformly distributed in $[0,pi)$

      3. $A(at)$ is WSS

      I must calculate the statistical averages and autocorrelation of the random process:
      $$X(t)=A(at)cos(2pi f_0t+Phi)$$
      I started to define the integral
      $$E[X(t)]=frac1piint_0^pi A(at)cos(2pi f_0t+phi)dphi$$ but I think is wrong because i don't know how to consider the process $A(at)$







      share|cite|improve this question














      I have two random process:
      $$A(at)$$
      $$cos(2pi f_0t+Phi)$$ with these hypothesis:



      1. $a$ and $f_0$ are constant

      2. $Phi$ is uniformly distributed in $[0,pi)$

      3. $A(at)$ is WSS

      I must calculate the statistical averages and autocorrelation of the random process:
      $$X(t)=A(at)cos(2pi f_0t+Phi)$$
      I started to define the integral
      $$E[X(t)]=frac1piint_0^pi A(at)cos(2pi f_0t+phi)dphi$$ but I think is wrong because i don't know how to consider the process $A(at)$









      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited Aug 19 at 9:44

























      asked Aug 19 at 9:26









      Andrea Bellizzi

      1064




      1064

























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