firkaiser.m

linear time－frequency toolbox

function g=firkaiser(p1,p2,p3,p4)
%FIRKAISER  Kaiser-Bessel window
%   Usage:  g=firkaiser(M,beta);
%           g=firkaiser(M,beta,centering);
%
%   FIRKAISER(M,beta) computes the Kaiser-Bessel window of length M with
%   parameter beta.
%
%   FIRKAISER(M,beta,'zero') will set the smallest element of the window
%   to zero. This makes it possible to use the window for a Wilson basis.
%
%   FIRKAISER(M,beta,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).
%
%   SEE ALSO: FIRWIN
%
%   REFERENCES:
%     A. V. Oppenheim and R. W. Schafer. Discrete-time signal processing. Prentice
%     Hall, Englewood Cliffs, NJ, 1989.

error(nargchk(2,4,nargin));

if ischar(p1)
  % The user supplied a type argument

  if nargin==2
    error('Two few input arguments.');
  end;

  stype=p1;
  M=p2;
  z=p3;
  
  if nargin==3
    centering=0;
  else
    centering=p4;
  end;

else

  stype='normal';
  M=p1;
  z=p2;
  
  if nargin==2
    centering=0;
  else
    centering=p3;
  end;

end;

switch centering
  case {'zero','Zero','ZERO'}
    centering=0;
    dozero=1;
  otherwise
    dozero=0;
end;

m=2*((0:M-1)+centering).'/M-1;
switch lower(stype)
  case {'n','normal'}
    g=besseli(0,z*sqrt(1-m.^2))/besseli(0,z);
    g=fftshift(g);

  case {'d','deriv','derived'}
    g=besseli(0,z*sqrt(1-m.^2))/besseli(0,z);    
    g1=sqrt(cumsum(g(1:M/2))./sum(g(1:M/2)));

    if centering==0
      g=[flipud(g1);...
	 0;
	 g1(1:M/2-1)];
    else
      g=[flipud(g1);...
	 g1];
    end;
          
  otherwise
    error('Unknown window type.');
end;