IIR Filter Group Delay

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The group delay of a filter is the frequency-dependent delay imparted by its process. This is calculated by taking the derivative of the phase of the frequency response of the filter with respect to radial frequency, viz.

(30)\[g_d(\omega) = \frac{\partial}{\partial \omega} \arg\left\{ H(\omega) \right\}\]

Here is a simple example:

Figure 11 Example group delay