0
$\begingroup$

Anybody give me an advice how to find the auto-covariance of the product of deterministic and wide-sense stationary signal. I couldn't find how to solve this, I have looked and searched the internet, I found just 1 similar topic here so I think someone in here may solve it.

The mean and autocorrelation of $X(t)$ are $m$ and $R$, respectively, and the $X(t)$ process is wide-sense stationary. $g(t)$ is a deterministic function, $Y(t)=X(t)\cdot g(t)$ is defined.

  • A. Find the mean, autocovariance and autocorrelation functions of the $Y(t)$ process.
  • B. Is the $Y(t)$ process wide-sense stationary ? Explain your answer.
$\endgroup$
  • 1
    $\begingroup$ Should we assume you already tried to apply the definition of mean and autocorrelation to Y? What did you get? $\endgroup$ – Juancho Jun 13 '17 at 20:08
  • $\begingroup$ I don't know how to relate deterministic and wide-sense signal, so I couldn't try with respect to any rule, just tried some of formulas but I did not sure about that because couldnt find even some example or theory about this. $\endgroup$ – Ofe Jun 13 '17 at 20:35
  • $\begingroup$ Look for the definition of a wide-sense stationary (WSS) process. Be careful that you do not confuse it with a strict-stationary process as they are different. You'll see that many deterministic processes also have WSS properties; constant mean across all time is one of them. $\endgroup$ – Envidia Jun 13 '17 at 21:35
  • $\begingroup$ Thank you, so I could use g(t) as an WSS ? $\endgroup$ – Ofe Jun 14 '17 at 3:48
  • $\begingroup$ The term "deterministic process" is peculiar. All moments in a WSS are constant. Your deterministic process would be a flat line. Not very interesting . I believe that you just confused the person who asked the question $\endgroup$ – Stanley Pawlukiewicz Jun 14 '17 at 6:58
2
$\begingroup$

Let me give a clue $$ E\{ y \} = E\{ x g \} = E\{ x \} g $$

$\endgroup$
  • $\begingroup$ Is g(t) behave like constant in mean operator ? Could you be more spesific and please write also autocorrelation equation ? $\endgroup$ – Ofe Jun 14 '17 at 3:46
  • $\begingroup$ g(t) is deterministic. E{g(t)} is g(t). Expectations of anything deterministic is just itself. It's just like E{1} g(t). $\endgroup$ – Stanley Pawlukiewicz Jun 14 '17 at 5:23
  • $\begingroup$ If I had any confidence that you would understand what I wrote, I would but since you don't understand the clue I have you, I don't. I think your confusion is rooted in not understanding the difference between an ensemble average and time average. $\endgroup$ – Stanley Pawlukiewicz Jun 14 '17 at 6:45
  • $\begingroup$ Could you also tell me how to find autocovariance and autocorrelation of y(t) ? $\endgroup$ – Ofe Jun 14 '17 at 17:00

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.