.. _iirdes-bessel:

Bessel IIR Filter Design
========================

:api:`LIQUID_IIRDES_BESSEL`
is a Bessel filter.
This is an all-pole analog design that has a maximally flat group delay
response (maximally linear phase response).
The solution to the design happens to be the roots to the Bessel
polynomials of equal order.
Computing the roots to the polynomial is, again, somewhat complex.
For a more detailed description we refer the interested reader to
:cite:`Orchard:1965`.
The analog prototype interface is :api:`bessel_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 the figure below.

.. qplot:: iirdes iirdes/iirdes.c
    :args: -t bessel -n 7 -f 0.2
    :width: 100%
    :name: fig-iirdes-bessel-0
    :caption: Bessel filter design, :math:`7^{th}`, :math:`f_c=0.2 F_s`

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