# Auto-covariance of the product of deterministic and wide-sense stationary signal

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.
• Should we assume you already tried to apply the definition of mean and autocorrelation to Y? What did you get? – Juancho Jun 13 '17 at 20:08
• 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. – Ofe Jun 13 '17 at 20:35
• 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. – Envidia Jun 13 '17 at 21:35
• Thank you, so I could use g(t) as an WSS ? – Ofe Jun 14 '17 at 3:48
• 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 – user28715 Jun 14 '17 at 6:58

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