Group delay (${\tau }_g=\partial \varphi /\partial \omega$)

The group delay is the frequency derivative of an unwrapped transfer wave phase, using the $e^{-i\omega t}$ convention. It predicts the leading delay of a narrow wave envelope when the transfer wave amplitude and the delay vary little across its band; it is not generally a signal-front arrival time.

The second derivative of spectral phase with respect to angular frequency; it measures variation of group delay with angular frequency.

The cubic term in a component's spectral phase, conventionally written ${\varphi }_3{\Omega }^3/6$, where $\Omega$ is an angular frequency offset.