.. _iirdes-cheby1:

Chebyshev Type-I IIR Filter Design
==================================

:api:`LIQUID_IIRDES_CHEBY1`
is a Chebyshev Type-I filter.
This design uses Chebyshev polynomials to create a filter with a sharper
transition band than the Butterworth design by allowing ripples in the
pass-band.
The analog prototype interface is :api:`cheby1_azpkf()` which
computes the :math:`n` complex roots :math:`p_{ak}` of the :math:`n^{th}`-order
Chebyshev polynomial.

.. 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 cheby1 -n 7 -b LP -r 1 -s 60 -f 0.2 -c 0.25
    :width: 100%
    :name: fig-iirdes-cheby1-0
    :caption: Chebyshev-I 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...