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annotate scripts/signal/detrend.m @ 19840:c5270263d466 gui-release

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author John W. Eaton <jwe@octave.org>
date Fri, 30 Jan 2015 17:41:50 -0500
parents d63878346099
children 4197fc428c7d
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d63878346099 maint: Update copyright notices for release.
John W. Eaton <jwe@octave.org>
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1 ## Copyright (C) 1995-2013 Kurt Hornik
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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 3 of the License, or (at
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8 ## your option) 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, see
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17 ## <http://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {Function File} {} detrend (@var{x}, @var{p})
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21 ## If @var{x} is a vector, @code{detrend (@var{x}, @var{p})} removes the
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22 ## best fit of a polynomial of order @var{p} from the data @var{x}.
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23 ##
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24 ## If @var{x} is a matrix, @code{detrend (@var{x}, @var{p})} does the same
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25 ## for each column in @var{x}.
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26 ##
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27 ## The second argument is optional. If it is not specified, a value of 1
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28 ## is assumed. This corresponds to removing a linear trend.
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29 ##
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30 ## The order of the polynomial can also be given as a string, in which case
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31 ## @var{p} must be either @qcode{"constant"} (corresponds to
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32 ## @code{@var{p}=0}) or
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33 ## @qcode{"linear"} (corresponds to @code{@var{p}=1}).
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34 ## @seealso{polyfit}
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35 ## @end deftypefn
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36
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37 ## Author: KH <Kurt.Hornik@wu-wien.ac.at>
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38 ## Created: 11 October 1994
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39 ## Adapted-By: jwe
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40
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41 function y = detrend (x, p = 1)
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42 ## Check input
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43 if (nargin > 0 && isreal (x) && ndims (x) <= 2)
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44 ## Check p
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45 if (ischar (p) && strcmpi (p, "constant"))
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46 p = 0;
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47 elseif (ischar (p) && strcmpi (p, "linear"))
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48 p = 1;
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49 elseif (!isscalar (p) || p < 0 || p != fix (p))
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50 error ("detrend: second input argument must be 'constant', 'linear' or a positive integer");
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51 endif
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52 else
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53 error ("detrend: first input argument must be a real vector or matrix");
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54 endif
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55
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56 [m, n] = size (x);
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57 if (m == 1)
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58 x = x';
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59 endif
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60
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61 r = rows (x);
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62 b = ((1 : r)' * ones (1, p + 1)) .^ (ones (r, 1) * (0 : p));
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63 y = x - b * (b \ x);
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64
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65 if (m == 1)
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66 y = y';
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67 endif
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68
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69 endfunction
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72 %!test
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73 %! N = 32;
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74 %! x = (0:1:N-1)/N + 2;
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75 %! y = detrend (x);
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76 %! assert (abs (y(:)) < 20*eps);
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77
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78 %!test
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79 %! N = 32;
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80 %! t = (0:1:N-1)/N;
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81 %! x = t .* t + 2;
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82 %! y = detrend (x,2);
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83 %! assert (abs (y(:)) < 30*eps);
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84
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85 %!test
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86 %! N = 32;
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87 %! t = (0:1:N-1)/N;
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88 %! x = [t;4*t-3]';
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89 %! y = detrend (x);
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90 %! assert (abs (y(:)) < 20*eps);
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91