## Copyright (C) 2001 Paul Kienzle
##
## 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, write to the Free Software
## Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA

## y = interpft (x, n)
## Resample x with n points using Fourier interpolation.
## The data x must be equally spaced and n >= length(x).

## Author: Paul Kienzle
## 2001-02-11
##    * initial version

function z = interpft (x, n)
  if (nargin < 2 || nargin > 3)
    usage ("y=interpft (x, n)");
  endif

  transpose = ( rows (x) == 1 ); 
  if (transpose) x = x (:); endif
  [nr, nc] = size (x);
  if n > nr
    y = fft (x) / nr;
    k = floor (nr / 2);
    z = n * ifft ( [ y(1:k,:); zeros(n-nr,nc); y(k+1:nr) ] );
    if isreal (x), z = real (z); endif
  elseif n < nr
    error ("interpft: n must be bigger than x");
    ## XXX FIXME XXX the following doesn't work so well
    y = fft (x) / nr;
    k = ceil (n / 2);
    z = n * ifft ( [ y(1:k,:); y(nr-k+2:nr) ] );
    if isreal (x), z = real (z); endif
  else
    z = x;
  endif
  if transpose, z = z.'; endif
endfunction

%!demo
%! t = 0 : 0.3 : pi; dt = t(2)-t(1);
%! n = length (t); k = 100;
%! ti = t(1) + [0 : k-1]*dt*n/k;
%! y = sin (4*t + 0.3) .* cos (3*t - 0.1);
%! yp = sin (4*ti + 0.3) .* cos (3*ti - 0.1);
%! plot (ti, yp, 'g;sin(4t+0.3)cos(3t-0.1);', ...
%!       ti, interp1 (t, y, ti, 'spline'), 'b;spline;', ...
%!       ti, interpft (y, k), 'c;interpft;', ...
%!       t, y, 'r+;data;');

%!#demo
%! t = 0:0.3:pi; dt = t(2)-t(1);
%! n = length(t); k = 100;
%! ti = t(1)+[0:k-1]*dt*n/k;
%! y = sin (4*t+0.3).*cos(3*t-0.1);
%! yp = sin (4*ti+0.3).*cos(3*ti-0.1);
%! plot (ti, yp, 'g;sin(4t+0.3)cos(3t-0.1);', ...
%!       t, interp1(ti,yp,t,'spline'), 'bx;spline;', ...
%!       t, interpft(yp,n), 'co;interpft;', ...
%!       t, y, 'r+;data;');