Spectral density of an ARMA process ($f_X=\frac{{\sigma }^2}{\pi }\frac{|\Theta (e^{i\omega }){|}^2}{|\Phi (e^{i\omega }){|}^2}$)

With the convention $\Phi (B)X_t=\Theta (B){\epsilon }_t$, the one-sided spectral density is ${\sigma }^2|\Theta (e^{i\omega }){|}^2/(\pi |\Phi (e^{i\omega }){|}^2)$ whenever the stationary filter is well defined. Stable autoregressive roots give the causal representation; moving-average invertibility is a separate property.