Mercurial > octave
annotate scripts/signal/arma_rnd.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 {} {} arma_rnd (@var{a}, @var{b}, @var{v}, @var{t}, @var{n}) |
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28 ## Return a simulation of the ARMA model. |
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29 ## |
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30 ## The ARMA model is defined by |
3449 | 31 ## |
32 ## @example | |
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33 ## @group |
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34 ## x(n) = a(1) * x(n-1) + @dots{} + a(k) * x(n-k) |
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35 ## + e(n) + b(1) * e(n-1) + @dots{} + b(l) * e(n-l) |
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36 ## @end group |
3449 | 37 ## @end example |
3191 | 38 ## |
3449 | 39 ## @noindent |
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40 ## in which @var{k} is the length of vector @var{a}, @var{l} is the length of |
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41 ## vector @var{b} and @var{e} is Gaussian white noise with variance @var{v}. |
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42 ## The function returns a vector of length @var{t}. |
3191 | 43 ## |
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44 ## The optional parameter @var{n} gives the number of dummy @var{x}(@var{i}) |
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45 ## used for initialization, i.e., a sequence of length @var{t}+@var{n} is |
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46 ## generated and @var{x}(@var{n}+1:@var{t}+@var{n}) is returned. If @var{n} |
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47 ## is omitted, @var{n} = 100 is used. |
3449 | 48 ## @end deftypefn |
3426 | 49 |
3191 | 50 function x = arma_rnd (a, b, v, t, n) |
51 | |
5568 | 52 if (nargin == 4) |
53 n = 100; | |
54 elseif (nargin == 5) | |
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55 if (! isscalar (n)) |
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56 error ("arma_rnd: N must be a scalar"); |
3191 | 57 endif |
5568 | 58 else |
6046 | 59 print_usage (); |
5568 | 60 endif |
3191 | 61 |
5568 | 62 if ((min (size (a)) > 1) || (min (size (b)) > 1)) |
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63 error ("arma_rnd: A and B must not be matrices"); |
5568 | 64 endif |
3426 | 65 |
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66 if (! isscalar (t)) |
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67 error ("arma_rnd: T must be a scalar"); |
5568 | 68 endif |
3426 | 69 |
5568 | 70 ar = length (a); |
71 br = length (b); | |
3426 | 72 |
5568 | 73 a = reshape (a, ar, 1); |
74 b = reshape (b, br, 1); | |
3426 | 75 |
8506 | 76 ## Apply our notational convention. |
77 a = [1; -a]; | |
5568 | 78 b = [1; b]; |
79 | |
80 n = min (n, ar + br); | |
3191 | 81 |
5568 | 82 e = sqrt (v) * randn (t + n, 1); |
83 | |
84 x = filter (b, a, e); | |
85 x = x(n + 1 : t + n); | |
3191 | 86 |
87 endfunction |