Editing Group delay and phase delay (section)

== Deviation from Linear Phase ==
Deviation from [[Linear phase|Linear Phase]], <math>\phi_{DLP}(\omega)</math>, sometimes referred to as just, "phase deviation", is the difference between the phase response, <math>\phi(\omega)</math>, and the [[Linearity|linear]] portion of the phase response <math>\phi_L(\omega)</math>,<ref name="Keysight"/> and is a useful measurement to determine the linearity of <math>\phi(\omega)</math>.

A convenient means to measure <math>\phi_{DLP}(\omega)</math> is to take the [[simple linear regression]] of <math>\phi(\omega)</math> sampled over a frequency range of interest, and subtract it from the actual <math>\phi(\omega)</math>. The <math>\phi_{DLP}(\omega)</math> of an ideal linear phase response would be expected to have a value of 0 across the frequency range of interest (such as the pass band of a filter), while the <math>\phi_{DLP}(\omega)</math> of a real-world approximately linear phase response may deviate from 0 by a small finite amount across the frequency range of interest.

=== Advantage over group delay ===
An advantage of measuring or calculating <math>\phi_{DLP}(\omega)</math> over measuring or calculating group delay, <math>gd(\omega)</math>, is <math>\phi_{DLP}(\omega)</math> always converges to 0 as the phase becomes linear, whereas <math>gd(\omega)</math> converges on a finite quantity that may not be known ahead of time. Given this, a linear phase optimizing function may more easily be executed with a <math>\phi_{DLP}(\omega){=}0</math> goal than with a <math>gd(\omega){=}constant</math> goal when the value for <math>constant</math> is not necessarily already known.