Let $X(t) = Acos(2\pi f_c t)$ be a random process where $A$ is a uniform random variable within $(-1,1)$. I'm trying to prove this is a weakly(i.e. wide sense) stationary process. I need to show two conditions
- Constant mean.
- Autocorrelation $R_X(t_1,t_2)$ only depends on the time difference $t_2-t_1$.
First one is easy. However, I can't prove the second condition. I've tried the following,
$R_X(t_1,t_2) = E[X(t_1)X(t_2)] = E[ Acos(2\pi f_c t_1) * Acos(2\pi f_c t_2)] = cos(2\pi f_c t_1)* cos(2\pi f_c t_2)*E[A^2]$
Using trig identities,
$=1/2(cos(2\pi f_c (t_1+t_2)-cos(2\pi f_c (t_1-t_2))*E[A^2] $
Where $E[.]$ is the expectation operator.
I'm stuck here, how can I do this?