In signal processing, group delay and phase delay are functions that describe in different ways the delay times experienced by a signal's various sinusoidal frequency components as they pass through a linear time-invariant (LTI) system (such as a microphone, coaxial cable, amplifier, loudspeaker, communications system, ethernet cable, digital filter, or analog filter).

These delays are sometimes frequency dependent,

<math display="block"> \phi(\omega) = -\arctan\left(\frac{\omega}{\omega_o}\right) \, . </math>

Similarly, the phase for a 1st-order RC high-pass filter is:

<math display="block"> \phi(\omega) = \frac{\pi}{2} -\arctan\left(\frac{\omega}{\omega_o}\right) \, . </math>

Taking the negative derivative with respect to <math> \omega </math> for either this low-pass or high-pass filter yields the same group delay of:

  • Phase velocity
  • Wave packet

References

</references>

  • Discussion of Group Delay in Loudspeakers
  • Group Delay Explanations and Applications
  • "Introduction to Digital Filters with Audio Applications", Julius O. Smith III (September 2007 Edition).