Group Delay and Phase Delay
The group delay of a filter is a measure of the average time delay of the filter as a function of frequency. The group delay is defined as the negative first derivative of the filter's phase response. If the complex frequency response of a filter is , then the group delay is
where is the phase, or argument, of . Use the
grpdelay function to compute group delay of a filter. For example, verify that, for a linear-phase FIR filter, the group delay is one-half the filter order.
d = designfilt('lowpassfir','FilterOrder',20,'CutoffFrequency',200,'SampleRate',2000); islinphase(d)
ans = logical 1
The phase delay of a filter is defined as the negative of the phase divided by the frequency:
phasedelay function to compute the phase delay of a filter. For the linear-phase FIR filter of the previous example, the phase delay is equal to the group delay.
Use FVTool to plot both the group delay and the phase delay of a system on the same graph. For example, plot the delays of a fifth-order Butterworth lowpass filter.
d = designfilt('lowpassiir','FilterOrder',5,'HalfPowerFrequency',200,'SampleRate',2000); fvtool(d,'Analysis','grpdelay','OverlayedAnalysis','phasedelay','Legend','on')