IIR Filter Group Delay
======================

.. author   jgaeddert Joseph D. Gaeddert <joseph@liquidsdr.org>
.. date     January 1, 1975
.. location Boston, MA
.. header   /doc/iirdes/banner.png
.. keywords infinite impulse response, IIR, filter design, iirdes, bilinear z-transform

.. attention:: This page is a work in progress.

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.

.. math::
    g_d(\omega) = \frac{\partial}{\partial \omega}
        \arg\left\{ H(\omega) \right\}
    :label: eqn-iir-group-delay

Here is a simple example:

.. qplot:: series iirdes/groupdelay.c
    :kwargs: {
        "format":
        {
            "xlabel" : "Time [samples]",
            "ylabel" : "Signal",
            "xrange" : [0, 480],
            "yrange" : [-1.5, 1.5],
            "legend" : true
        },
        "plots":
        [
            {
                "series" : [
                    ["x",{"color":"#aaaaaa","label":"Input"}],
                    ["y",{"color":"#004080","label":"Filtered"}]
                ]
            }
        ]}
    :width: 75%
    :name: fig-iirdes-groupdelay
    :caption: Example group delay