Mercurial > hg > octave-nkf
diff scripts/general/interpft.m @ 5837:55404f3b0da1
[project @ 2006-06-01 19:05:31 by jwe]
author | jwe |
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date | Thu, 01 Jun 2006 19:05:32 +0000 |
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children | 376e02b2ce70 |
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new file mode 100644 --- /dev/null +++ b/scripts/general/interpft.m @@ -0,0 +1,116 @@ +## 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]))