remezb
======

Minimax approximation of magnitude response



Calling Sequence
~~~~~~~~~~~~~~~~


::

    [an]=remezb(nc,fg,ds,wt)




Arguments
~~~~~~~~~

:nc Number of cosine functions
: :fg Grid of frequency points in [0,.5)
: :ds Desired magnitude on grid `fg`
: :wt Weighting function on error on grid `fg`
: :an Cosine filter coefficients
:



Description
~~~~~~~~~~~

Minimax approximation of a frequency domain magnitude response. The
approximation takes the form `h = sum[a(n)*cos(wn)]` for n=0,1,...,nc.
An FIR, linear-phase filter can be obtained from the output of the
function by using the following commands


::

    hn(1:nc-1)=an(nc:-1:2)/2;
    hn(nc)=an(1);
    hn(nc+1:2*nc-1)=an(2:nc)/2;




Examples
~~~~~~~~


::

    // Choose the number of cosine functions and create a dense grid 
    // in [0,.24) and [.26,.5)
    nc=21;ngrid=nc*16;
    fg=.24*(0:ngrid/2-1)/(ngrid/2-1);
    fg(ngrid/2+1:ngrid)=fg(1:ngrid/2)+.26*`ones`_(1:ngrid/2);
    
    // Specify a low pass filter magnitude for the desired response
    ds(1:ngrid/2)=`ones`_(1:ngrid/2);
    ds(ngrid/2+1:ngrid)=`zeros`_(1:ngrid/2);
    
    // Specify a uniform weighting function
    wt=`ones`_(fg);
    
    // Run remezb
    an=remezb(nc,fg,ds,wt)
    
    // Make a linear phase FIR filter 
    hn(1:nc-1)=an(nc:-1:2)/2;
    hn(nc)=an(1);
    hn(nc+1:2*nc-1)=an(2:nc)/2;
    
    // Plot the filter's magnitude response
    `plot`_(.5*(0:255)/256,`frmag`_(hn,256));
    
    // Choose the number of cosine functions and create a dense grid in [0,.5)
    nc=21; ngrid=nc*16;
    fg=.5*(0:(ngrid-1))/ngrid;
    
    // Specify a triangular shaped magnitude for the desired response
    ds(1:ngrid/2)=(0:ngrid/2-1)/(ngrid/2-1);
    ds(ngrid/2+1:ngrid)=ds(ngrid/2:-1:1);
    
    // Specify a uniform weighting function
    wt=`ones`_(fg);
    
    // Run remezb
    an=remezb(nc,fg,ds,wt)
    
    // Make a linear phase FIR filter 
    hn(1:nc-1)=an(nc:-1:2)/2;
    hn(nc)=an(1);
    hn(nc+1:2*nc-1)=an(2:nc)/2;
    
    // Plot the filter's magnitude response
    `plot`_(.5*(0:255)/256,`frmag`_(hn,256));




See Also
~~~~~~~~


+ `eqfir`_ minimax approximation of FIR filter


.. _eqfir: eqfir.html