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The group delay and phase delay properties of a linear time-invariant (LTI) system are functions of frequency, giving the time from when a frequency component of a time varying physical quantity—for example a voltage signal—appears at the LTI system input, to the time when a copy of that same frequency component—perhaps of a different physical phenomenon—appears at the LTI system output.
A closely related yet independent quantity is the group-delay dispersion (GDD), defined such that group-velocity dispersion is the group-delay dispersion per unit length. GDD is commonly used as a parameter in characterizing layered mirrors, where the group-velocity dispersion is not particularly well-defined, yet the chirp induced after ...
In a dispersive prism, material dispersion (a wavelength-dependent refractive index) causes different colors to refract at different angles, splitting white light into a spectrum. A compact fluorescent lamp seen through an Amici prism. Dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency. [1]
Frequency dispersion in groups of gravity waves on the surface of deep water. The red square moves with the phase velocity, and the green circles propagate with the group velocity. In this deep-water case, the phase velocity is twice the group velocity. The red square overtakes two green circles when moving from the left to the right of the figure.
For a sufficiently large delay (from 10 to 1000 times the Fourier transform limited [FTL] pulse duration), the interference of the two time-delayed fields results in a cosine modulation with a nominal spacing of /; and any dispersion of the pulse results in minor deviations in the nominal fringe spacing. Effectively it is these deviations in ...
The introduced dispersion by such a compressor is often described in dispersion orders: the group delay dispersion (GGD), third order of dispersion (TOD) etc. Figure 2 shows the dispersion orders for a grating compressor with a groove density of = /, an incidence angle of =, and a normal grating separation of =, as described in the original ...
Frequency dispersion in groups of gravity waves on the surface of deep water. The red square moves with the phase velocity, and the green circles propagate with the group velocity. In this deep-water case, the phase velocity is twice the group velocity. The red square overtakes two green circles when moving from the left to the right of the figure.
For loudspeakers, group delay is a metric for smearing in time of the input signal, as dictated by the integration time, or rather, the smearing is observed when group delay isn't constant and can be expressed, for example, by the first-order derivative of group delay (named dispersion). Group delay can be different at different frequencies (as ...