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1 ## Copyright (C) 2001 Paul Kienzle |
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2 ## |
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3 ## This file is part of Octave. |
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4 ## |
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5 ## Octave is free software; you can redistribute it and/or modify it |
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6 ## under the terms of the GNU General Public License as published by |
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7 ## the Free Software Foundation; either version 2, or (at your option) |
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8 ## any later version. |
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9 ## |
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10 ## Octave is distributed in the hope that it will be useful, but |
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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13 ## General Public License for more details. |
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14 ## |
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15 ## You should have received a copy of the GNU General Public License |
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16 ## along with Octave; see the file COPYING. If not, write to the Free |
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17 ## Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA |
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18 ## 02110-1301, USA. |
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19 |
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20 ## -*- texinfo -*- |
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21 ## @deftypefn {Function File} {} interpft (@var{x}, @var{n}) |
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22 ## @deftypefnx {Function File} {} interpft (@var{x}, @var{n}, @var{dim}) |
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23 ## |
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24 ## Fourier interpolation. If @var{x} is a vector, then @var{x} is |
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25 ## resampled with @var{n} points. The data in @var{x} is assumed to be |
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26 ## equispaced. If @var{x} is an array, then operate along each column of |
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27 ## the array seperately. If @var{dim} is specified, then interpolate |
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28 ## along the dimension @var{dim}. |
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29 ## |
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30 ## @code{interpft} assumes that the interpolated function is periodic, |
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31 ## and so assumption are made about the end points of the inetrpolation. |
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32 ## |
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33 ## @seealso{interp1} |
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34 ## @end deftypefn |
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35 |
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36 ## Author: Paul Kienzle |
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37 ## 2001-02-11 |
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38 ## * initial version |
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39 ## 2002-03-17 aadler |
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40 ## * added code to work on matrices as well |
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41 ## 2006-05-25 dbateman |
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42 ## * Make it matlab compatiable, cutting out the 2-D interpolation |
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43 |
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44 function z = interpft (x, n, dim) |
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45 |
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46 if (nargin < 2 || nargin > 3) |
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47 print_usage (); |
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48 endif |
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49 |
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50 if (nargin == 2) |
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51 if (isvector(x) && size(x,1) == 1) |
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52 dim = 2; |
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53 else |
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54 dim = 1; |
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55 endif |
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56 endif |
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57 |
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58 if (!isscalar (n)) |
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59 error ("interpft: n must be an integer scalar"); |
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60 endif |
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61 |
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62 nd = ndims(x); |
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63 |
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64 if (dim < 1 || dim > nd) |
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65 error ("interpft: integrating over invalid dimension"); |
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66 endif |
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67 |
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68 perm = [dim:nd,1:(dim-1)]; |
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69 x = permute(x, perm); |
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70 m = size (x, 1); |
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71 |
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72 inc = 1; |
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73 while (inc * n < m) |
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74 inc++; |
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75 endwhile |
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76 y = fft (x) / m; |
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77 k = floor (m / 2); |
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78 sz = size(x); |
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79 sz(1) = n * inc - m; |
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80 idx = cell(nd,1); |
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81 for i = 2:nd |
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82 idx{i} = 1:sz(i); |
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83 endfor |
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84 idx{1} = 1:k; |
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85 z = cat (1, y(idx{:}), zeros(sz)); |
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86 idx{1} = k+1:m; |
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87 z = cat (1, z, y(idx{:})); |
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88 z = n * ifft (z); |
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89 |
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90 if (inc != 1) |
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91 sz(1) = n; |
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92 z = inc * reshape(z(1:inc:end),sz); |
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93 endif |
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94 |
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95 z = ipermute (z, perm); |
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96 endfunction |
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97 |
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98 %!demo |
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99 %! t = 0 : 0.3 : pi; dt = t(2)-t(1); |
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100 %! n = length (t); k = 100; |
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101 %! ti = t(1) + [0 : k-1]*dt*n/k; |
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102 %! y = sin (4*t + 0.3) .* cos (3*t - 0.1); |
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103 %! yp = sin (4*ti + 0.3) .* cos (3*ti - 0.1); |
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104 %! plot (ti, yp, 'g;sin(4t+0.3)cos(3t-0.1);', ... |
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105 %! ti, interp1 (t, y, ti, 'spline'), 'b;spline;', ... |
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106 %! ti, interpft (y ,k), 'c;interpft;', ... |
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107 %! t, y, 'r+;data;'); |
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108 |
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109 %!shared n,y |
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110 %! x = [0:10]'; y = sin(x); n = length (x); |
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111 %!assert (interpft(y, n), y, eps); |
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112 %!assert (interpft(y', n), y', eps); |
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113 %!assert (interpft([y,y],n), [y,y], eps); |
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114 |
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115 %!error (interpft(y,n,0)) |
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116 %!error (interpft(y,[n,n])) |
