Finite Impulse Response (FIR) Design using Parks-McClellan Algorithm
====================================================================

FIR filter design using the Parks-McClellan algorithm is implemented in
liquid with the :api:`firdespm` interface.
The Parks-McClellan algorithm uses the Remez exchange algorithm to solve
the minimax problem (minimize the maximum error) for filter design.
The interface accepts a description of :math:`N_b` disjoint and
non-overlapping frequency bands with a desired response and relative
error weighting for each, and computes the resulting filter
coefficients.

.. code-block:: c

    int firdespm_run(unsigned int            _h_len,
                     unsigned int            _num_bands,
                     float *                 _bands,
                     float *                 _des,
                     float *                 _weights,
                     liquid_firdespm_wtype * _wtype,
                     liquid_firdespm_btype   _btype,
                     float *                 _h);


* :c:`_bands`
  is a :math:`[N_b \times 2]` matrix of the band edge descriptions.
  Each row corresponds to an upper and lower band edge for each region
  of interest.
  These regions cannot be overlapping.
* :c:`_des`
  is an array of size :math:`N_b` with the desired response (linear) for
  each band.
* :c:`_weights`
  is an array of size :math:`N_b` with the relative error weighting for each
  band.
* :c:`_num_bands`
  represents :math:`N_b`, the number of bands in the design.
* :c:`_btype`
  gives the filter type for the design.
  This is typically :api:`LIQUID_FIRDESPM_BANDPASS` for the majority
  of filters.
* :c:`_wtype`
  is an array of length :math:`N_b` which specifies the weighting function
  for each band (flat, exponential, or linear).

Example
~~~~~~~

Listed below is an example of the :api:`firdespm` interface.

.. literalinclude:: firdespm.c
   :language: c

.. qplot:: window firdes/firdespm.c
    :width: 80%
    :kwargs: {"figsize":[12,12], "layout":"rows", "onesided":true, "ylim":[-70,10]}
    :name: fig-firdespm
    :caption: Example of :api:`firdespm`