Let a wide-sense stationary random process $X(t)$ pass through a stable LTI system with frequency response $H(f)$.

If the input has power spectral density $S_X(f)$, the output PSD is

$$S_Y(f)=|H(f)|^2S_X(f).$$

The filter therefore scales random-signal power at each frequency by its squared magnitude response, just as it scales sinusoidal components of deterministic signals.

The total output power is

$$P_Y=\int_{-\infty}^{\infty}S_Y(f),df =\int_{-\infty}^{\infty}|H(f)|^2S_X(f),df.$$

A filter can therefore reduce unwanted random-signal power by attenuating frequency ranges in which that disturbance is present.

This relation connects deterministic frequency response with stochastic signal analysis: $H(f)$ describes the system, while $S_X(f)$ describes how input power is distributed across frequency.