Mean and correlation of product of two random processes

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP











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












    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

























          active

          oldest

          votes











          Your Answer




          StackExchange.ifUsing("editor", function ()
          return StackExchange.using("mathjaxEditing", function ()
          StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
          StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
          );
          );
          , "mathjax-editing");

          StackExchange.ready(function()
          var channelOptions =
          tags: "".split(" "),
          id: "69"
          ;
          initTagRenderer("".split(" "), "".split(" "), channelOptions);

          StackExchange.using("externalEditor", function()
          // Have to fire editor after snippets, if snippets enabled
          if (StackExchange.settings.snippets.snippetsEnabled)
          StackExchange.using("snippets", function()
          createEditor();
          );

          else
          createEditor();

          );

          function createEditor()
          StackExchange.prepareEditor(
          heartbeatType: 'answer',
          convertImagesToLinks: true,
          noModals: false,
          showLowRepImageUploadWarning: true,
          reputationToPostImages: 10,
          bindNavPrevention: true,
          postfix: "",
          noCode: true, onDemand: true,
          discardSelector: ".discard-answer"
          ,immediatelyShowMarkdownHelp:true
          );



          );








           

          draft saved


          draft discarded


















          StackExchange.ready(
          function ()
          StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2887529%2fmean-and-correlation-of-product-of-two-random-processes%23new-answer', 'question_page');

          );

          Post as a guest



































          active

          oldest

          votes













          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes










           

          draft saved


          draft discarded


























           


          draft saved


          draft discarded














          StackExchange.ready(
          function ()
          StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2887529%2fmean-and-correlation-of-product-of-two-random-processes%23new-answer', 'question_page');

          );

          Post as a guest













































































          這個網誌中的熱門文章

          How to combine Bézier curves to a surface?

          Mutual Information Always Non-negative

          Why am i infinitely getting the same tweet with the Twitter Search API?