Many communication channels can be approximated over an operating range as linear time-invariant systems followed by additive noise.

A continuous-time model is

$$y(t)=h(t)*x(t)+n(t),$$

where $x(t)$ is the transmitted waveform, $h(t)$ is the channel impulse response and $n(t)$ is additive disturbance.

In frequency domain,

$$Y(f)=H(f)X(f)+N(f).$$

If $H(f)$ is nearly constant over the signal bandwidth, the channel mainly scales and delays the waveform. If $H(f)$ varies strongly with frequency, different spectral components experience different gain or phase and the waveform is distorted.

An impulse response containing several delayed components can model propagation along multiple paths. Its time spread can cause one transmitted symbol to overlap later symbol intervals.

This model separates two impairments: deterministic linear distortion is described by $h$ or $H$, while additive noise is represented by $n$.