I have white Gaussian noise $F[n]$ with zero mean and autocorrelation $R_F[n_1,n_2]=\delta[n_1-n_2]$.
If now I consider the random process defined as
$$X[n]=u[n]e^{-kn}F[n]$$ Is $X[n]$ a wide-ense stationary random process for all values of $k$?
I tried to solve the autocorrelation function to check if it depended only on the lag but my result was that $X$ is WSS only for $k=0$, but I think that since it's a sort of a linear filtering it should be that it is WSS for all $k$.