Group Delay

Group delay is often used as a criterion to evaluate the phase nonlinearity of a filter.

The following equation defines the group delay:

GD ( f ) = − 1 2 π d d f phase ( f )

where phase(f) is the phase response.

If the phase response is linear, the group delay of the filter is constant, which means each frequency component experiences the same delay. Otherwise, the frequency components have different delays, which cause the smearing phenomenon of the time-domain signal.

The following figure compares the effects of a Kaiser FIR lowpass filter and an Elliptic lowpass filter on the same input signal.

Figure 78. Effects of Kaiser FIR Lowpass Filter and Elliptic Lowpass Filter on Input Signal

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The first waveform, which is the input signal, is a periodic sinc pattern with an order of 12.

The second waveform shows the effects of a Kaiser FIR lowpass filter on the input signal. The Kaiser filter has a linear phase response, so the filter delays the input without distorting the signal. The waveform is similar to the input signal, except for the delay and the attenuation.

The third waveform shows the effects of an Elliptic lowpass filter on the input signal. The phase response of the Elliptic filter is nonlinear, so the frequency components experience different delays. Thus, the shape of the waveform is different from the input signal.