yulewalk
========

least-square filter design



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


::

    Hz = yulewalk(N,frq,mag)




Arguments
~~~~~~~~~

:N integer (order of desired filter)
: :frq real row vector (non-decreasing order), frequencies.
: :mag non negative real row vector (same size as frq), desired
  magnitudes.
: :Hz filter `B(z)/A(z)`
:



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

Hz = yulewalk(N,frq,mag) finds the N-th order iir filter


::

    n-1         n-2            
    B(z)   b(1)z     + b(2)z    + .... + b(n)
    H(z)= ---- = ---------------------------------
    n-1       n-2
    A(z)    z   + a(2)z    + .... + a(n)


which matches the magnitude frequency response given by vectors frq
and mag. Vectors frq and mag specify the frequency and magnitude of
the desired frequency response. The frequencies in frq must be between
0.0 and 1.0, with 1.0 corresponding to half the sample rate. They must
be in increasing order and start with 0.0 and end with 1.0.



Examples
~~~~~~~~


::

    f=[0,0.4,0.4,0.6,0.6,1];H=[0,0,1,1,0,0];Hz=yulewalk(8,f,H);
    fs=1000;fhz = f*fs/2;  
    `clf`_(0);`xset`_('window',0);`plot2d`_(fhz',H');
    `xtitle`_('Desired Frequency Response (Magnitude)')
    [frq,repf]=`repfreq`_(Hz,0:0.001:0.5);
    `clf`_(1);`xset`_('window',1);`plot2d`_(fs*frq',`abs`_(repf'));
    `xtitle`_('Obtained Frequency Response (Magnitude)')