firwin.m

linear time－frequency toolbox

function g=firwin(name,M,centering);
%FIRWIN  FIR window
%   Usage:  g=firwin(name,M);
%           g=firwin(name,M,centering);
%
%   FIRWIN(name,M) will compute a two overlapping window of
%   length M of type name.
%
%   FIRWIN(name,M,centering) will create a window centered as 
%   specified by centering. The default (centering=0) is to return
%   a whole-point centered window, while a value of .5 will produce a
%   half-point even function (traditional signal processing style).
%
%   The windows are normalized, such that if used for Gabor systems
%   with parameters a=M/2 and M, they will generate Gabor frames
%   with framebounds close to 1.
%
%   All windows are symmetric and can be used for Wilson bases, except
%   when noted otherwise. 
%
%   The windows available are:
%
%-      hanning - Hanning window. Forms a PU.
%
%-      sqrthan - Square root of a Hanning window. Normalized so it
%                 generates a normalized tight Gabor system with parameters
%                 a=M/2 and M
%
%-      hamming - Hamming window. Forms a PU. This window cannot
%                 be used for a Wilson basis.
%
%-      sqrtham - Square root of a Hamming window. As sqrthan.
%
%-      blackman - Blackman window
%
%-      vorbis  - Iterated sine window. This is a tight window.
%-
%   SEE ALSO:  PGAUSS, PBSPLINE, FIRKAISER
%
%   REFERENCES:
%     A. V. Oppenheim and R. W. Schafer. Discrete-time signal processing. Prentice
%     Hall, Englewood Cliffs, NJ, 1989.

error(nargchk(2,3,nargin));

if nargin==2
  centering=0;
end;

name=lower(name);

% This is the normally used sampling vector.
x=((0:M-1)'+centering)/M;
switch name
  case {'hanning'}
    g=(0.5+0.5*cos(2*pi*x));

  case {'sqrthan'}
    g=sqrt(firwin('hanning',M,centering))/sqrt(M);

  case {'hamming'}
    g=0.54-0.46*cos(2*pi*(x-.5));

  case {'sqrtham'}
    g=sqrt(firwin('hamming',M,centering)/1.08)/sqrt(M);

  case {'blackman'}
    g=0.42-0.5*cos(2*pi*(x-.5))+0.08*cos(4*pi*(x-.5));

  case {'vorbis'}
    g=sin(pi/2*sin(pi*(x-.5).^2))/sqrt(M);

  otherwise
    error('Unknown window.');
end;