Mercurial > octave
annotate scripts/signal/diffpara.m @ 29358:0a5b15007766 stable
update Octave Project Developers copyright for the new year
In files that have the "Octave Project Developers" copyright notice,
update for 2021.
author | John W. Eaton <jwe@octave.org> |
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date | Wed, 10 Feb 2021 09:52:15 -0500 |
parents | b09432b20a84 |
children | 7854d5752dd2 |
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1 ######################################################################## |
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2 ## |
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3 ## Copyright (C) 1995-2021 The Octave Project Developers |
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4 ## |
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5 ## See the file COPYRIGHT.md in the top-level directory of this |
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6 ## distribution or <https://octave.org/copyright/>. |
3426 | 7 ## |
3922 | 8 ## This file is part of Octave. |
9 ## | |
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10 ## Octave is free software: you can redistribute it and/or modify it |
3922 | 11 ## under the terms of the GNU General Public License as published by |
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12 ## the Free Software Foundation, either version 3 of the License, or |
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13 ## (at your option) any later version. |
3426 | 14 ## |
3922 | 15 ## Octave is distributed in the hope that it will be useful, but |
3191 | 16 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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17 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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18 ## GNU General Public License for more details. |
3426 | 19 ## |
3191 | 20 ## You should have received a copy of the GNU General Public License |
7016 | 21 ## along with Octave; see the file COPYING. If not, see |
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22 ## <https://www.gnu.org/licenses/>. |
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23 ## |
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24 ######################################################################## |
3191 | 25 |
3449 | 26 ## -*- texinfo -*- |
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27 ## @deftypefn {} {[@var{d}, @var{dd}] =} diffpara (@var{x}, @var{a}, @var{b}) |
3449 | 28 ## Return the estimator @var{d} for the differencing parameter of an |
3191 | 29 ## integrated time series. |
30 ## | |
3499 | 31 ## The frequencies from @math{[2*pi*a/t, 2*pi*b/T]} are used for the |
32 ## estimation. If @var{b} is omitted, the interval | |
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33 ## @math{[2*pi/T, 2*pi*a/T]} is used. If both @var{b} and @var{a} are omitted |
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34 ## then @math{a = 0.5 * sqrt (T)} and @math{b = 1.5 * sqrt (T)} is used, where |
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35 ## @math{T} is the sample size. If @var{x} is a matrix, the differencing |
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36 ## parameter of each column is estimated. |
3191 | 37 ## |
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38 ## The estimators for all frequencies in the intervals described above is |
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39 ## returned in @var{dd}. |
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40 ## |
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41 ## The value of @var{d} is simply the mean of @var{dd}. |
3191 | 42 ## |
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43 ## Reference: @nospell{P.J. Brockwell & R.A. Davis}. @cite{Time Series: |
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44 ## Theory and Methods}. @nospell{Springer} 1987. |
3449 | 45 ## @end deftypefn |
3426 | 46 |
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47 function [d, dd] = diffpara (x, a, b) |
3426 | 48 |
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49 if (nargin < 1 || nargin > 3) |
6046 | 50 print_usage (); |
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51 endif |
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52 |
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53 if (isvector (x)) |
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54 n = length (x); |
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55 k = 1; |
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56 x = reshape (x, n, 1); |
3191 | 57 else |
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58 [n, k] = size (x); |
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59 endif |
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60 if (nargin == 1) |
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61 a = 0.5 * sqrt (n); |
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62 b = 1.5 * sqrt (n); |
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63 elseif (nargin == 2) |
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64 b = a; |
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65 a = 1; |
3191 | 66 endif |
3426 | 67 |
4030 | 68 if (! (isscalar (a) && isscalar (b))) |
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69 error ("diffpara: A and B must be scalars"); |
3191 | 70 endif |
3426 | 71 |
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72 dd = zeros (b - a + 1, k); |
3426 | 73 |
3191 | 74 for l = 1:k |
3426 | 75 |
3191 | 76 w = 2 * pi * (1 : n-1) / n; |
3426 | 77 |
3457 | 78 x = 2 * log (abs (1 - exp (-i*w))); |
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79 y = log (periodogram (x(2:n,l))); |
3426 | 80 |
3191 | 81 x = center (x); |
82 y = center (y); | |
3426 | 83 |
3191 | 84 for m = a:b |
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85 dd(m-a+1) = - x(1:m) * y(1:m) / sumsq (x(1:m)); |
3191 | 86 endfor |
3426 | 87 |
3191 | 88 endfor |
3426 | 89 |
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90 d = mean (dd); |
3426 | 91 |
3191 | 92 endfunction |