.. _iirdes-cheby2:

Chebyshev Type-II IIR Filter Design
===================================

:api:`LIQUID_IIRDES_CHEBY2`
is a Chebyshev Type-II filter.
This design is similar to that of Chebyshev Type-I, except that the
Chebyshev polynomial is inverted.
This inverts the magnitude response of the filter and exhibits an
equiripple behavior in the stop-band, rather than the pass-band.
The analog prototype interface is :api:`cheby2_azpkf()`.

.. attention:: talk about analog prototype

An example Chebyshev-I 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 cheby2 -n 7 -b LP -r 1 -s 60 -f 0.2 -c 0.25
    :width: 100%
    :name: fig-iirdes-cheby2-0
    :caption: Chebyshev-II 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...