Self-study material - Analysis of Linear Stochastic Systems

The lecture follows Åströms book Chapter 3.6 + Chapter 4

gives some more details on the basics of power spectral density functions and how they relate to the expected value of the absolute value of the Fourier transform of the signal. Note the result

$S_{x} (f) = lim_{T \to \infty} \frac{1}{T} E [| X_{T} (f) |^{2}] (13)$ $\begin{equation} S_x(f) = \lim\limits_{T\to \infty} \frac{1}{T} E[|X_T(f)|^2] \qquad (13) \end{equation}$

and its unit (SU)^2/Hz where "SU" stands for "signal unit", where

$X_{T} (f) = \int_{- T / 2}^{T / 2} x (t) e^{- 2 π i f t} d t$ $\begin{equation} X_T(f) = \int\limits_{-T/2}^{T/2} x(t) e^{-2\pi i f t}dt \end{equation}$