Say I have a PAM signal as $x(t) = \sum_n a_n h(t-nT)$ where $\{a_n\} \in \{\pm 1\}$ are equiprobable random binary bits and $h(t)$ is bandlimited to $[-1/(2T),1/(2T)]$. ($x(t)$ is random process and cyclostationary).
My first question is that can I compute the energy of $x(t)$ as: $$E_x = E\left\{(x(t))^2\right\} = \int_{-\infty}^\infty \lvert X(f)\rvert^2 df$$
If yes, then my next question is where I get stuck in the solution: \begin{align} X(f) &= \int_{-\infty}^{\infty} \sum_n a_n h(t-nT) e^{-j2 \pi ft} dt\\ &= \sum_n a_n \int_{-\infty}^{\infty} h(t-nT)e^{-j2 \pi ft} dt\\ &= \sum_n a_n H(f) e^{-j2 \pi fnT}\\ &= H(f)A(e^{-j2 \pi fT}) \end{align} Therefore, $$E_x = \int_{-\infty}^\infty \lvert H(f)\rvert^2\lvert A(e^{-j2 \pi fT})\rvert^2 df$$
I know the answer is $E_x = \frac{1}{T} E_h E_a$ but I cannot make the connection.