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tukeywin.m

## Copyright (C) 2007 Laurent Mazet
##
## This program is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 2 of the License, or
## (at your option) any later version.
##
## This program is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
## GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with this program; If not, see <http://www.gnu.org/licenses/>.

## -*- texinfo -*-
## @deftypefn {Function File} {@var{w} =} tukeywin (@var{m}, @var{r})
## Return the filter coefficients of a Tukey window (also known as the
## cosine-tapered window) of length @var{m}. @var{r} defines the ratio
## between the constant section and and the cosine section. It has to be
## between 0 and 1. The function returns a Hanning window for @var{r}
## egals 0 and a full box for @var{r} egals 1. By default @var{r} is set
## to 1/2.
##
## For a definition of the Tukey window, see e.g. Fredric J. Harris,
## "On the Use of Windows for Harmonic Analysis with the Discrete Fourier
## Transform, Proceedings of the IEEE", Vol. 66, No. 1, January 1978,
## Page 67, Equation 38.
## @end deftypefn

function w = tukeywin(m,r)

  ## check arguments
  switch nargin
      
    case 1,
      ## default r value
      r = 1/2;
      
    case 2,
      ## check that 0 < r < 1
      if r > 1
        r = 1;
      elseif r < 0
        r = 0;
      endif
      
    otherwise
      ## usage message
      usage ("y = tukeywin(m, [r])");
  endswitch


  ## generate window
  switch r
      
    case 0,
      ## full box
      w = ones (m, 1);
      
    case 1,
      ## Hanning window
      w = hanning (m);

    otherwise
      ## cosine-tapered window
      t = linspace(0,1,m)(1:end/2)';
      w = (1 + cos(pi*(2*t/r-1)))/2;
      w(floor(r*(m-1)/2)+2:end) = 1;
      w = [w; ones(mod(m,2)); flipud(w)];

  endswitch
      
endfunction

%!demo
%! m = 100;
%! r = 1/3;
%! w = tukeywin (m, r);
%! title(sprintf("%d-point Tukey window, R = %d/%d", m, [p, q] = rat(r), q));
%! plot(w);

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