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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 H(ejω), then the group delay is


where θ(ω) is the phase, or argument, of H(ejω). 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.

fs = 2000;
b = fir1(20,200/(fs/2));

ans = logical


The phase delay of a filter is defined as the negative of the phase divided by the frequency:


Use the 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.


Plot the group delay and the phase delay of a fifth-order Butterworth lowpass filter.

[b,a] = butter(5,200/(fs/2));



See Also