.. _iirdes-ellip:

Elliptical IIR Filter Design
============================

:api:`LIQUID_IIRDES_ELLIP`
is an elliptic (Cauer) filter.
This design allows ripples in both the pass-band and stop-bands to create a
filter with a very sharp transition band.
The design process is somewhat more involved than the Butterworth and
Chebyshev prototypes and requires solving the elliptic integral of
different moduli.
For a more detailed description we refer the interested reader to
:cite:`Orfanidis:2006`.
The analog prototype interface is :api:`ellip_azpkf()`.

.. attention:: talk about analog prototype

An example elliptic design can be seen in the code listing here:

.. code-block:: c

    #include <liquid/liquid.h>
    int main()
    {
        return 0;
    }

An example of a digital filter response can be found in
[fig-filter-ellip].

.. qplot:: iirdes iirdes/iirdes.c
    :args: -t ellip -n 7 -b LP -r 1 -s 60 -f 0.2 -c 0.25
    :width: 100%
    :name: fig-iirdes-ellip-0
    :caption: Elliptic filter design, :math:`n=7`, :math:`f_c=0.2 F_s`,
        :math:`A_p=1` dB, and :math:`A_s=60` dB.

Notice how the performance changes as the order increases to 15...