window
======

compute symmetric window of various type



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


::

    win_l=window('re',n)
    win_l=window('tr',n)
    win_l=window('hn',n)
    win_l=window('hm',n)
    win_l=window('kr',n,Beta)
    [win_l,cwp]=window('ch',n,par)




Arguments
~~~~~~~~~

:n window length
: :par parameter 2-vector `par=[dp,df])`, where `dp` ( `0<dp<.5`)
  rules the main lobe width and `df` rules the side lobe height (
  `df>0`). Only one of these two value should be specified the other one
  should set equal to a nonpositive value.
: :Beta Kaiser window parameter `Beta >0`).
: :win window
: :cwp unspecified Chebyshev window parameter
:



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

function which calculates various symmetric window for Digital signal
processing.


+ The Kaiser window is a nearly optimal window function. `Beta` is an
  arbitrary positive real number that determines the shape of the
  window, and the integer `n` is the length of the window. By
  construction, this function peaks at unity for `k = n/2` , i.e. at the
  center of the window, and decays exponentially towards the window
  edges. The larger the value of `Beta`, the narrower the window
  becomes; `Beta = 0` corresponds to a rectangular window. Conversely,
  for larger `Beta` the width of the main lobe increases in the Fourier
  transform, while the side lobes decrease in amplitude. Thus, this
  parameter controls the tradeoff between main-lobe width and side-lobe
  area. Beta window shape 0 Rectangular shape 5 Similar to the Hamming
  window 6 Similar to the Hann window 8.6 Similar to the Blackman window
+ The Chebyshev window minimizes the mainlobe width, given a
  particular sidelobe height. It is characterized by an equiripple
  behavior, that is, its sidelobes all have the same height.
+ The Hann and Hamming windows are quite similar, they only differ in
  the choice of one parameter `alpha`: `w=alpha+(1 -
  alpha)*cos(2*%pi*x/(n-1))` `alpha` is equal to 1/2 in Hann window and
  to 0.54 in Hamming window.




Examples
~~~~~~~~


::

    `clf`_()
    N=24;
    whm=window('hm',N);//Hamming window
    wkr=window('kr',N,6);//Hamming Kaiser window
    wch=window('ch',N,[0.005,-1]);//Chebychev window
    //plot the window profile
    `subplot`_(121);`plot`_(1:N,[whm;wkr;wch]')
    `set`_(`gca`_(),'grid',[1 1]*`color`_('gray'))
    `xlabel`_("n")
    `ylabel`_("w_n")
    `title`_(`gettext`_("Profile plot"))
    //plot the magnitude of the frequency responses
    n=256;
    [Whm,fr]=`frmag`_(whm,n);
    [Wkr,fr]=`frmag`_(wkr,n);
    [Wch,fr]=`frmag`_(wch,n);
    `subplot`_(122);`plot`_(fr,20*`log10`_([Whm;Wkr;Wch]'))
    `set`_(`gca`_(),'grid',[1 1]*`color`_('gray'))
    `xlabel`_(`gettext`_("Pulsation (rd/s)"))
    `ylabel`_(`gettext`_("Magnitude (dB)"))
    `legend`_(["Hamming N=24";"Kaiser N=24, Beta=6";"Chebychev N=24, dp=0.005"]);
    `title`_(`gettext`_("Magnitude plot"))





::

    `clf`_()
    N=140;
    w1=window('kr',N,1);
    w2=window('kr',N,2);
    w4=window('kr',N,4);
    w8=window('kr',N,8);
    w16=window('kr',N,16);
    
    //plot the window profile
    `plot`_(1:N,[w1;w2;w4;w8;w16]')
    `set`_(`gca`_(),'grid',[1 1]*`color`_('gray'))
    `legend`_("$\beta="+`string`_([1;2;4;8;16])+'$',[55,0.3])
    `xlabel`_("n")
    `ylabel`_("w_n")
    `title`_(`gettext`_("Comparison of Kaiser window profiles"))





::

    `clf`_()
    N=140;
    w1=window('ch',N,[0.001,-1]);
    w2=window('ch',N,[0.05,-1]);
    w3=window('ch',N,[-1,0.4]);
    
    //plot the window profile
    `subplot`_(121);`plot`_(1:N,[w1;w2;w3]')
    `set`_(`gca`_(),'grid',[1 1]*`color`_('gray'))
    //legend("$\beta="+string([1;2;4;8;16])+'$',[55,0.3])
    `xlabel`_("n")
    `ylabel`_("w_n")
    `title`_(`gettext`_("Comparison of Chebychev window profiles"))
    //plot the magnitude of the frequency responses
    n=256;
    [W1,fr]=`frmag`_(w1,n);
    [W2,fr]=`frmag`_(w2,n);
    [W3,fr]=`frmag`_(w3,n);
    `subplot`_(122);`plot`_(fr,20*`log10`_([W1;W2;W3]'))
    `set`_(`gca`_(),'grid',[1 1]*`color`_('gray'))
    `xlabel`_(`gettext`_("Pulsation (rd/s)"))
    `ylabel`_(`gettext`_("Magnitude (dB)"))
    `legend`_(["Chebychef dp=0.001";"Chebychef dp=0.05";"Chebychef df=0.4"]);
    `title`_(`gettext`_("Chebychev window Magnitude plot"))






See Also
~~~~~~~~


+ `wfir`_ linear-phase FIR filters
+ `frmag`_ magnitude of FIR and IIR filters
+ `ffilt`_ coefficients of FIR low-pass




Bibliography
~~~~~~~~~~~~

IEEE. Programs for Digital Signal Processing. IEEE Press. New York:
John Wiley and Sons, 1979. Program 5.2.

.. _frmag: frmag.html
.. _wfir: wfir.html
.. _ffilt: ffilt.html