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annotate scripts/signal/freqz.m @ 17338:1c89599167a6

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maint: End m-files with 1 blank line. Simplifies automated grammarchecking script. * scripts/@ftp/ascii.m, scripts/@ftp/binary.m, scripts/@ftp/cd.m, scripts/@ftp/close.m, scripts/@ftp/delete.m, scripts/@ftp/dir.m, scripts/@ftp/display.m, scripts/@ftp/ftp.m, scripts/@ftp/loadobj.m, scripts/@ftp/mget.m, scripts/@ftp/mkdir.m, scripts/@ftp/mput.m, scripts/@ftp/rename.m, scripts/@ftp/rmdir.m, scripts/@ftp/saveobj.m, scripts/audio/lin2mu.m, scripts/audio/loadaudio.m, scripts/audio/mu2lin.m, scripts/audio/record.m, scripts/audio/saveaudio.m, scripts/audio/setaudio.m, scripts/deprecated/__error_text__.m, scripts/deprecated/cut.m, scripts/deprecated/error_text.m, scripts/deprecated/isstr.m, scripts/deprecated/polyderiv.m, scripts/deprecated/studentize.m, scripts/deprecated/sylvester_matrix.m, scripts/general/bicubic.m, scripts/general/celldisp.m, scripts/general/colon.m, scripts/general/cplxpair.m, scripts/general/del2.m, scripts/general/display.m, scripts/general/isdir.m, scripts/general/isequaln.m, scripts/general/loadobj.m, 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scripts/signal/arch_test.m, scripts/signal/arma_rnd.m, scripts/signal/durbinlevinson.m, scripts/signal/fractdiff.m, scripts/signal/freqz.m, scripts/signal/freqz_plot.m, scripts/signal/hurst.m, scripts/signal/periodogram.m, scripts/signal/private/rectangle_lw.m, scripts/signal/private/rectangle_sw.m, scripts/signal/private/triangle_sw.m, scripts/signal/spectral_adf.m, scripts/signal/spectral_xdf.m, scripts/signal/stft.m, scripts/signal/synthesis.m, scripts/signal/yulewalker.m, scripts/sparse/colperm.m, scripts/sparse/eigs.m, scripts/sparse/etreeplot.m, scripts/sparse/gmres.m, scripts/sparse/private/__sprand_impl__.m, scripts/sparse/spdiags.m, scripts/sparse/sprandn.m, scripts/specfun/bessel.m, scripts/specfun/betaln.m, scripts/specfun/expint.m, scripts/special-matrix/gallery.m, scripts/startup/__finish__.m, scripts/statistics/base/qqplot.m, scripts/statistics/distributions/tcdf.m, scripts/statistics/distributions/wienrnd.m, scripts/statistics/models/logistic_regression.m, scripts/statistics/models/private/logistic_regression_derivatives.m, scripts/statistics/models/private/logistic_regression_likelihood.m, scripts/statistics/tests/anova.m, scripts/statistics/tests/bartlett_test.m, scripts/statistics/tests/chisquare_test_homogeneity.m, scripts/statistics/tests/chisquare_test_independence.m, scripts/statistics/tests/cor_test.m, scripts/statistics/tests/f_test_regression.m, scripts/statistics/tests/hotelling_test.m, scripts/statistics/tests/hotelling_test_2.m, scripts/statistics/tests/kolmogorov_smirnov_test_2.m, scripts/statistics/tests/kruskal_wallis_test.m, scripts/statistics/tests/manova.m, scripts/statistics/tests/mcnemar_test.m, scripts/statistics/tests/prop_test_2.m, scripts/statistics/tests/run_test.m, scripts/statistics/tests/sign_test.m, scripts/statistics/tests/t_test.m, scripts/statistics/tests/t_test_2.m, scripts/statistics/tests/t_test_regression.m, scripts/statistics/tests/u_test.m, scripts/statistics/tests/var_test.m, scripts/statistics/tests/welch_test.m, scripts/statistics/tests/wilcoxon_test.m, scripts/statistics/tests/z_test.m, scripts/statistics/tests/z_test_2.m, scripts/strings/strcat.m, scripts/strings/strjoin.m, scripts/strings/strsplit.m, scripts/testfun/__have_feature__.m, scripts/testfun/__printf_assert__.m, scripts/testfun/__prog_output_assert__.m, scripts/testfun/__run_test_suite__.m, scripts/time/clock.m, scripts/time/datenum.m, scripts/ui/errordlg.m, scripts/ui/private/message_dialog.m: End m-files with 1 blank line.
author Rik <rik@octave.org>
date Wed, 28 Aug 2013 08:33:02 -0700
parents b81b9d079515
children d63878346099
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72c96de7a403 maint: update copyright notices for 2012
John W. Eaton <jwe@octave.org>
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1 ## Copyright (C) 1994-2012 John W. Eaton
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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} {[@var{h}, @var{w}] =} freqz (@var{b}, @var{a}, @var{n}, "whole")
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21 ## @deftypefnx {Function File} {@var{h} =} freqz (@var{b}, @var{a}, @var{w})
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22 ## @deftypefnx {Function File} {[@dots{}] =} freqz (@dots{}, @var{Fs})
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23 ## @deftypefnx {Function File} {} freqz (@dots{})
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24 ##
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25 ## Return the complex frequency response @var{h} of the rational IIR filter
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26 ## whose numerator and denominator coefficients are @var{b} and @var{a},
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27 ## respectively. The response is evaluated at @var{n} angular frequencies
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28 ## between 0 and
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29 ## @ifnottex
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30 ## 2*pi.
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31 ## @end ifnottex
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32 ## @tex
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33 ## $2\pi$.
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34 ## @end tex
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35 ##
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36 ## @noindent
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37 ## The output value @var{w} is a vector of the frequencies.
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38 ##
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39 ## If @var{a} is omitted, the denominator is assumed to be 1 (this
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40 ## corresponds to a simple FIR filter).
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41 ##
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42 ## If @var{n} is omitted, a value of 512 is assumed.
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43 ##
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44 ## For fastest computation, @var{n} should factor into a small number of
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45 ## small primes.
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46 ##
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47 ## If the fourth argument, @qcode{"whole"}, is omitted the response is
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48 ## evaluated at frequencies between 0 and
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49 ## @ifnottex
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50 ## pi.
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51 ## @end ifnottex
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52 ## @tex
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53 ## $\pi$.
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54 ## @end tex
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55 ##
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56 ## @code{freqz (@var{b}, @var{a}, @var{w})}
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57 ##
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58 ## Evaluate the response at the specific frequencies in the vector @var{w}.
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59 ## The values for @var{w} are measured in radians.
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60 ##
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61 ## @code{[@dots{}] = freqz (@dots{}, @var{Fs})}
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62 ##
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63 ## Return frequencies in Hz instead of radians assuming a sampling rate
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64 ## @var{Fs}. If you are evaluating the response at specific frequencies
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65 ## @var{w}, those frequencies should be requested in Hz rather than radians.
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66 ##
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67 ## @code{freqz (@dots{})}
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68 ##
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69 ## Plot the pass band, stop band and phase response of @var{h} rather
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70 ## than returning them.
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71 ## @end deftypefn
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72
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73 ## Author: jwe ???
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74
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75 function [h_r, f_r] = freqz (b, a, n, region, Fs)
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76
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77 if (nargin < 1 || nargin > 5)
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78 print_usage ();
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79 elseif (nargin == 1)
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80 ## Response of an FIR filter.
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81 a = n = region = Fs = [];
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82 elseif (nargin == 2)
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83 ## Response of an IIR filter
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84 n = region = Fs = [];
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85 elseif (nargin == 3)
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86 region = Fs = [];
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87 elseif (nargin == 4)
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88 Fs = [];
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diff changeset
89 if (! ischar (region) && ! isempty (region))
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diff changeset
90 Fs = region;
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91 region = [];
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92 endif
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93 endif
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94
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95 if (isempty (b))
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diff changeset
96 b = 1;
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97 endif
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98 if (isempty (a))
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99 a = 1;
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100 endif
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101 if (isempty (n))
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102 n = 512;
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103 endif
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104 if (isempty (region))
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105 if (isreal (b) && isreal (a))
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106 region = "half";
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107 else
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108 region = "whole";
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109 endif
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diff changeset
110 endif
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111 if (isempty (Fs))
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112 if (nargout == 0)
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113 Fs = 2;
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114 else
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115 Fs = 2*pi;
3893
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116 endif
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117 endif
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118
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119 a = a(:);
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120 b = b(:);
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121
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122 if (! isscalar (n))
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diff changeset
123 ## Explicit frequency vector given
5377
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124 w = f = n;
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125 if (nargin == 4)
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126 ## Sampling rate Fs was specified
5377
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127 w = 2*pi*f/Fs;
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128 endif
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129 k = max (length (b), length (a));
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130 hb = polyval (postpad (b, k), exp (j*w));
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131 ha = polyval (postpad (a, k), exp (j*w));
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diff changeset
132 else
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133 ## polyval(fliplr(P),exp(jw)) is O(p n) and fft(x) is O(n log(n)),
6653
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134 ## where p is the order of the polynomial P. For small p it
5377
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135 ## would be faster to use polyval but in practice the overhead for
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136 ## polyval is much higher and the little bit of time saved isn't
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137 ## worth the extra code.
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138 k = max (length (b), length (a));
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139 if (k > n/2 && nargout == 0)
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140 ## Ensure a causal phase response.
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141 n = n * 2 .^ ceil (log2 (2*k/n));
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142 endif
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143
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diff changeset
144 if (strcmp (region, "whole"))
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145 N = n;
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146 else
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147 N = 2*n;
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148 endif
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149
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diff changeset
150 f = Fs * (0:n-1).' / N;
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diff changeset
151
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diff changeset
152 pad_sz = N*ceil (k/N);
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diff changeset
153 b = postpad (b, pad_sz);
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diff changeset
154 a = postpad (a, pad_sz);
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diff changeset
155
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diff changeset
156 hb = zeros (n, 1);
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diff changeset
157 ha = zeros (n, 1);
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diff changeset
158
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diff changeset
159 for i = 1:N:pad_sz
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diff changeset
160 hb = hb + fft (postpad (b(i:i+N-1), N))(1:n);
a89198168175 freqz.m: freqz.m: fix for long input
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diff changeset
161 ha = ha + fft (postpad (a(i:i+N-1), N))(1:n);
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diff changeset
162 endfor
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diff changeset
163
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diff changeset
164 endif
8529a21443fa [project @ 1994-07-26 02:07:38 by jwe]
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diff changeset
165
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166 h = hb ./ ha;
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diff changeset
167
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168 if (nargout != 0)
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diff changeset
169 ## Return values and don't plot.
3907
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diff changeset
170 h_r = h;
5377
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171 f_r = f;
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172 else
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173 ## Plot and don't return values.
5377
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diff changeset
174 freqz_plot (f, h);
7151
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diff changeset
175 endif
3907
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diff changeset
176
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diff changeset
177 endfunction
5377
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178
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diff changeset
179
5377
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diff changeset
180 %!test # correct values and fft-polyval consistency
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diff changeset
181 %! ## butterworth filter, order 2, cutoff pi/2 radians
5377
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diff changeset
182 %! b = [0.292893218813452 0.585786437626905 0.292893218813452];
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diff changeset
183 %! a = [1 0 0.171572875253810];
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diff changeset
184 %! [h,w] = freqz (b,a,32);
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diff changeset
185 %! assert (h(1),1,10*eps);
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diff changeset
186 %! assert (abs (h(17)).^2,0.5,10*eps);
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diff changeset
187 %! assert (h,freqz (b,a,w),10*eps); # fft should be consistent with polyval
5377
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diff changeset
188
bd4ee620c38a [project @ 2005-06-02 15:42:39 by jwe]
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diff changeset
189 %!test # whole-half consistency
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diff changeset
190 %! b = [1 1 1]/3; # 3-sample average
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diff changeset
191 %! [h,w] = freqz (b,1,32,"whole");
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diff changeset
192 %! assert (h(2:16),conj (h(32:-1:18)),20*eps);
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diff changeset
193 %! [h2,w2] = freqz (b,1,16,"half");
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diff changeset
194 %! assert (h(1:16),h2,20*eps);
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diff changeset
195 %! assert (w(1:16),w2,20*eps);
5377
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diff changeset
196
bd4ee620c38a [project @ 2005-06-02 15:42:39 by jwe]
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diff changeset
197 %!test # Sampling frequency properly interpreted
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diff changeset
198 %! b = [1 1 1]/3; a = [1 0.2];
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diff changeset
199 %! [h,f] = freqz (b,a,16,320);
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diff changeset
200 %! assert (f,[0:15]'*10,10*eps);
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diff changeset
201 %! [h2,f2] = freqz (b,a,[0:15]*10,320);
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diff changeset
202 %! assert (f2,[0:15]*10,10*eps);
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diff changeset
203 %! assert (h,h2.',20*eps);
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diff changeset
204 %! [h3,f3] = freqz (b,a,32,"whole",320);
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diff changeset
205 %! assert (f3,[0:31]'*10,10*eps);
17338
1c89599167a6 maint: End m-files with 1 blank line.
Rik <rik@octave.org>
parents: 17336
diff changeset
206