A stationary Gaussian random process $x(t)$ with zero mean and power spectral density $S_x(f)$ is applied to a linear filter hay frequency response

$H(f)=\{\begin{array}{cc}\frac{1}{T},& |f|\frac{T}{2}\\ 0,& \text{e}\text{l}\text{s}\text{e}\text{w}\text{h}\text{e}\text{r}\text{e}& \end{array}$

Let $Y(t)$ denote the random process at the filter output. The power spectral density of $Y(t)$ is given by:

$$

$S_Y(f)=\{\begin{array}{cc}\frac{S_x(f)}{T},& |f|\frac{T}{2}\\ 0,& \text{e}\text{l}\text{s}\text{e}\text{w}\text{h}\text{e}\text{r}\text{e}& \end{array}$

Dum

$S_Y(f)=\{\begin{array}{cc}\frac{S_x(f)}{2T},& |f|T\\ 0,& \text{e}\text{l}\text{s}\text{e}\text{w}\text{h}\text{e}\text{r}\text{e}& \end{array}$