I need help with this question. I am sure this is the right StackExchange forum for this type of question. <br/><br/>
Consider a nonlinear device such that the output is $Y(t) = aX^2(t)$, where the input X(t) consists of a signal plus a noise component, $X(t) = S(t) + N(t)$.<br/>
Determine the **mean** and **autocorrelation** function for $Y(t)$ when the signal $S(t)$ and the noise $N(t)$ are both Gaussian random processes and wide sense stationary (WSS) with zero mean, and $S(t)$ is independent of $N(t)$. <br><br>

I know that for a WSS signal, the mean and autocorrelation depends on the time difference, $\tau$ only. Meaning that the mean of $S(t)$ and $N(t)$ is a constant and their individual autocorrelation is not dependent on $t$. <br>
I've been working only with linear systems. I don't know how to solve this problem since $Y(t)$ a nonlinear system. I will be happy if you can help me with the solution