annotate scripts/signal/blackman.m @ 31706:597f3ee61a48 stable

update Octave Project Developers copyright for the new year
author John W. Eaton <jwe@octave.org>
date Fri, 06 Jan 2023 13:11:27 -0500
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1 ########################################################################
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2 ##
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3 ## Copyright (C) 1995-2023 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/>.
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7 ##
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8 ## This file is part of Octave.
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9 ##
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10 ## Octave is free software: you can redistribute it and/or modify it
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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.
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14 ##
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15 ## Octave is distributed in the hope that it will be useful, but
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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.
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19 ##
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20 ## You should have received a copy of the GNU General Public License
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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 ########################################################################
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25
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26 ## -*- texinfo -*-
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27 ## @deftypefn {} {@var{c} =} blackman (@var{m})
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28 ## @deftypefnx {} {@var{c} =} blackman (@var{m}, "periodic")
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29 ## @deftypefnx {} {@var{c} =} blackman (@var{m}, "symmetric")
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30 ## Return the filter coefficients of a @nospell{Blackman} window of length
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31 ## @var{m}.
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32 ##
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33 ## If the optional argument @qcode{"periodic"} is given, the periodic form
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34 ## of the window is returned. This is equivalent to the window of length
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35 ## @var{m}+1 with the last coefficient removed. The optional argument
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36 ## @qcode{"symmetric"} is equivalent to not specifying a second argument.
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37 ##
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38 ## For a definition of the @nospell{Blackman} window, see, e.g.,
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39 ## @nospell{A.V. Oppenheim & R. W. Schafer},
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40 ## @cite{Discrete-Time Signal Processing}.
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41 ## @end deftypefn
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42
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43 function c = blackman (m, opt)
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44
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45 if (nargin < 1)
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46 print_usage ();
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47 endif
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48
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49 if (! (isscalar (m) && m > 0 && m == fix (m)))
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50 error ("blackman: M must be a positive integer");
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51 endif
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52
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53 N = m - 1;
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54 if (nargin == 2)
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55 switch (opt)
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56 case "periodic"
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57 N = m;
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58 case "symmetric"
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59 ## Default option, same as no option specified.
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60 otherwise
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61 error ('blackman: window type must be either "periodic" or "symmetric"');
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62 endswitch
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63 endif
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64
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65 if (m == 1)
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66 c = 1;
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67 else
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68 m -= 1;
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69 k = (0 : m)' / N;
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70 c = 0.42 - 0.5 * cos (2 * pi * k) + 0.08 * cos (4 * pi * k);
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71 endif
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72
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73 endfunction
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74
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75
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76 %!assert (blackman (1), 1)
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77 %!assert (blackman (2), zeros (2,1), 1e-6)
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78 %!assert (blackman (15), flip (blackman (15)), 5*eps)
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79 %!assert (blackman (16), flip (blackman (16)), 5*eps)
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80 %!test
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81 %! N = 9;
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82 %! A = blackman (N);
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83 %! assert (A(ceil (N/2)), 1, 1e-6);
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84 %! assert ([A(1), A(length (A))], zeros (1,2), 1e-6);
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85
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86 %!assert (blackman (15), blackman (15, "symmetric"))
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87 %!assert (blackman (16)(1:15), blackman (15, "periodic"))
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88 %!test
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89 %! N = 16;
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90 %! A = blackman (N, "periodic");
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91 %! assert (A(N/2 + 1), 1, 1e-6);
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92
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93 %!error <Invalid call> blackman ()
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94 %!error blackman (0.5)
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95 %!error blackman (-1)
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96 %!error blackman (ones (1,4))
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97 %!error blackman (1, "invalid")