diff scripts/general/interpft.m @ 5837:55404f3b0da1

[project @ 2006-06-01 19:05:31 by jwe]
author jwe
date Thu, 01 Jun 2006 19:05:32 +0000
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+## Copyright (C) 2001 Paul Kienzle
+##
+## This file is part of Octave.
+##
+## Octave 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, or (at your option)
+## any later version.
+##
+## Octave 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 Octave; see the file COPYING.  If not, write to the Free
+## Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
+## 02110-1301, USA.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {} interpft (@var{x}, @var{n})
+## @deftypefnx {Function File} {} interpft (@var{x}, @var{n}, @var{dim})
+##
+## Fourier interpolation. If @var{x} is a vector, then @var{x} is
+## resampled with @var{n} points. The data in @var{x} is assumed to be
+## equispaced. If @var{x} is an array, then operate along each column of
+## the array seperately. If @var{dim} is specified, then interpolate
+## along the dimension @var{dim}.
+##
+## @code{interpft} assumes that the interpolated function is periodic,
+## and so assumption are made about the end points of the inetrpolation.
+##
+## @seealso{interp1}
+## @end deftypefn
+
+## Author: Paul Kienzle
+## 2001-02-11
+##    * initial version
+## 2002-03-17 aadler
+##    * added code to work on matrices as well 
+## 2006-05-25 dbateman
+##    * Make it matlab compatiable, cutting out the 2-D interpolation
+
+function z = interpft (x, n, dim)
+
+  if (nargin < 2 || nargin > 3)
+    print_usage ();
+  endif
+
+  if (nargin == 2)
+    if (isvector(x) && size(x,1) == 1)
+      dim = 2;
+    else
+      dim = 1;
+    endif
+  endif
+
+  if (!isscalar (n))
+    error ("interpft: n must be an integer scalar");
+  endif
+
+  nd = ndims(x);
+
+  if (dim < 1 || dim > nd)
+    error ("interpft: integrating over invalid dimension");
+  endif
+
+  perm = [dim:nd,1:(dim-1)];
+  x = permute(x, perm);
+  m = size (x, 1);
+
+  inc = 1;
+  while (inc * n < m)
+    inc++;
+  endwhile
+  y = fft (x) / m;
+  k = floor (m / 2);
+  sz = size(x);
+  sz(1) = n * inc - m;
+  idx = cell(nd,1);
+  for i = 2:nd
+    idx{i} = 1:sz(i);
+  endfor
+  idx{1} = 1:k;
+  z = cat (1, y(idx{:}), zeros(sz));
+  idx{1} = k+1:m;
+  z = cat (1, z, y(idx{:}));
+  z = n * ifft (z);
+
+  if (inc != 1)
+    sz(1) = n;
+    z = inc * reshape(z(1:inc:end),sz);
+  endif
+
+  z = ipermute (z, perm);
+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;');
+
+%!shared n,y
+%! x = [0:10]'; y = sin(x); n = length (x);
+%!assert (interpft(y, n), y, eps);
+%!assert (interpft(y', n), y', eps);
+%!assert (interpft([y,y],n), [y,y], eps);
+
+%!error (interpft(y,n,0))
+%!error (interpft(y,[n,n]))