Mercurial > hg > octave-lyh
annotate scripts/signal/freqz.m @ 10297:ed88ea036716
improve docs of fzero/fminbnd
| author | Jaroslav Hajek <highegg@gmail.com> |
|---|---|
| date | Wed, 10 Feb 2010 16:15:30 +0100 |
| parents | f0c3d3fc4903 |
| children | fd0a3ac60b0e |
| rev | line source |
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| 7017 | 1 ## Copyright (C) 1994, 1995, 1996, 1997, 1999, 2000, 2002, 2005, 2006, |
| 8920 | 2 ## 2007, 2009 John W. Eaton |
| 2313 | 3 ## |
| 4 ## This file is part of Octave. | |
| 5 ## | |
| 6 ## Octave is free software; you can redistribute it and/or modify it | |
| 7 ## under the terms of the GNU General Public License as published by | |
| 7016 | 8 ## the Free Software Foundation; either version 3 of the License, or (at |
| 9 ## your option) any later version. | |
| 2313 | 10 ## |
| 11 ## Octave is distributed in the hope that it will be useful, but | |
| 12 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
| 13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 14 ## General Public License for more details. | |
| 15 ## | |
| 16 ## You should have received a copy of the GNU General Public License | |
| 7016 | 17 ## along with Octave; see the file COPYING. If not, see |
| 18 ## <http://www.gnu.org/licenses/>. | |
| 2303 | 19 |
| 3367 | 20 ## -*- texinfo -*- |
| 21 ## @deftypefn {Function File} {[@var{h}, @var{w}] =} freqz (@var{b}, @var{a}, @var{n}, "whole") | |
| 22 ## Return the complex frequency response @var{h} of the rational IIR filter | |
| 23 ## whose numerator and denominator coefficients are @var{b} and @var{a}, | |
| 24 ## respectively. The response is evaluated at @var{n} angular frequencies | |
| 25 ## between 0 and | |
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26 ## @ifnottex |
| 3367 | 27 ## 2*pi. |
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28 ## @end ifnottex |
| 3367 | 29 ## @tex |
| 30 ## $2\pi$. | |
| 31 ## @end tex | |
| 3426 | 32 ## |
| 3367 | 33 ## @noindent |
| 34 ## The output value @var{w} is a vector of the frequencies. | |
| 3426 | 35 ## |
| 3367 | 36 ## If the fourth argument is omitted, the response is evaluated at |
| 37 ## frequencies between 0 and | |
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38 ## @ifnottex |
| 3367 | 39 ## pi. |
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40 ## @end ifnottex |
| 3367 | 41 ## @tex |
| 42 ## $\pi$. | |
| 43 ## @end tex | |
| 3426 | 44 ## |
| 3367 | 45 ## If @var{n} is omitted, a value of 512 is assumed. |
| 3426 | 46 ## |
| 3367 | 47 ## If @var{a} is omitted, the denominator is assumed to be 1 (this |
| 48 ## corresponds to a simple FIR filter). | |
| 3426 | 49 ## |
| 3367 | 50 ## For fastest computation, @var{n} should factor into a small number of |
| 51 ## small primes. | |
| 3893 | 52 ## |
| 53 ## @deftypefnx {Function File} {@var{h} =} freqz (@var{b}, @var{a}, @var{w}) | |
| 54 ## Evaluate the response at the specific frequencies in the vector @var{w}. | |
| 55 ## The values for @var{w} are measured in radians. | |
| 56 ## | |
| 57 ## @deftypefnx {Function File} {[@dots{}] =} freqz (@dots{}, @var{Fs}) | |
| 58 ## Return frequencies in Hz instead of radians assuming a sampling rate | |
| 59 ## @var{Fs}. If you are evaluating the response at specific frequencies | |
| 60 ## @var{w}, those frequencies should be requested in Hz rather than radians. | |
| 61 ## | |
| 3920 | 62 ## @deftypefnx {Function File} {} freqz (@dots{}) |
| 3907 | 63 ## Plot the pass band, stop band and phase response of @var{h} rather |
| 64 ## than returning them. | |
| 3367 | 65 ## @end deftypefn |
| 904 | 66 |
| 3367 | 67 ## Author: jwe ??? |
| 2314 | 68 |
| 5377 | 69 function [h_r, f_r] = freqz (b, a, n, region, Fs) |
| 566 | 70 |
| 3893 | 71 if (nargin < 1 || nargin > 5) |
| 6046 | 72 print_usage (); |
| 3893 | 73 elseif (nargin == 1) |
| 2303 | 74 ## Response of an FIR filter. |
| 3893 | 75 a = n = region = Fs = []; |
| 566 | 76 elseif (nargin == 2) |
| 2303 | 77 ## Response of an IIR filter |
| 3893 | 78 n = region = Fs = []; |
| 566 | 79 elseif (nargin == 3) |
| 3893 | 80 region = Fs = []; |
| 566 | 81 elseif (nargin == 4) |
| 3893 | 82 Fs = []; |
| 5443 | 83 if (! ischar (region) && ! isempty (region)) |
| 3893 | 84 Fs = region; |
| 85 region = []; | |
| 86 endif | |
| 87 endif | |
| 88 | |
| 5377 | 89 if (isempty (b)) |
| 90 b = 1; | |
| 91 endif | |
| 3893 | 92 if (isempty (a)) |
| 93 a = 1; | |
| 94 endif | |
| 95 if (isempty (n)) | |
| 96 n = 512; | |
| 97 endif | |
| 98 if (isempty (region)) | |
| 99 if (isreal (b) && isreal (a)) | |
| 100 region = "half"; | |
| 101 else | |
| 102 region = "whole"; | |
| 103 endif | |
| 104 endif | |
| 105 if (isempty (Fs)) | |
| 106 if (nargout == 0) | |
| 107 Fs = 2; | |
| 108 else | |
| 109 Fs = 2*pi; | |
| 110 endif | |
| 566 | 111 endif |
| 112 | |
| 5583 | 113 a = a(:); |
| 114 b = b(:); | |
| 566 | 115 |
| 8506 | 116 if (! isscalar (n)) |
| 117 ## Explicit frequency vector given | |
| 5377 | 118 w = f = n; |
| 8506 | 119 if (nargin == 4) |
| 120 ## Sampling rate Fs was specified | |
| 5377 | 121 w = 2*pi*f/Fs; |
| 566 | 122 endif |
| 5986 | 123 k = max (length (b), length (a)); |
| 124 hb = polyval (postpad (b, k), exp (j*w)); | |
| 125 ha = polyval (postpad (a, k), exp (j*w)); | |
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126 else |
| 5583 | 127 ## polyval(fliplr(P),exp(jw)) is O(p n) and fft(x) is O(n log(n)), |
| 6653 | 128 ## where p is the order of the polynomial P. For small p it |
| 5377 | 129 ## would be faster to use polyval but in practice the overhead for |
| 130 ## polyval is much higher and the little bit of time saved isn't | |
| 131 ## worth the extra code. | |
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132 k = max (length (b), length (a)); |
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133 if (k > n/2 && nargout == 0) |
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134 ## Ensure a causal phase response. |
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135 n = n * 2 .^ ceil (log2 (2*k/n)); |
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136 endif |
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137 |
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138 if (strcmp (region, "whole")) |
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139 N = n; |
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140 else |
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141 N = 2*n; |
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142 endif |
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143 |
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144 f = Fs * (0:n-1).' / N; |
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145 |
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146 pad_sz = N*ceil (k/N); |
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147 b = postpad (b, pad_sz); |
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148 a = postpad (a, pad_sz); |
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149 |
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150 hb = zeros (n, 1); |
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151 ha = zeros (n, 1); |
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152 |
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153 for i = 1:N:pad_sz |
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154 hb = hb + fft (postpad (b(i:i+N-1), N))(1:n); |
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155 ha = ha + fft (postpad (a(i:i+N-1), N))(1:n); |
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156 endfor |
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157 |
| 566 | 158 endif |
| 159 | |
| 3893 | 160 h = hb ./ ha; |
| 161 | |
| 8506 | 162 if (nargout != 0) |
| 163 ## Return values and don't plot. | |
| 3907 | 164 h_r = h; |
| 5377 | 165 f_r = f; |
| 8506 | 166 else |
| 167 ## Plot and don't return values. | |
| 5377 | 168 freqz_plot (f, h); |
| 7151 | 169 endif |
| 3907 | 170 |
| 566 | 171 endfunction |
| 5377 | 172 |
| 173 %!test # correct values and fft-polyval consistency | |
| 174 %! # butterworth filter, order 2, cutoff pi/2 radians | |
| 175 %! b = [0.292893218813452 0.585786437626905 0.292893218813452]; | |
| 176 %! a = [1 0 0.171572875253810]; | |
| 177 %! [h,w] = freqz(b,a,32); | |
| 178 %! assert(h(1),1,10*eps); | |
| 179 %! assert(abs(h(17)).^2,0.5,10*eps); | |
| 180 %! assert(h,freqz(b,a,w),10*eps); # fft should be consistent with polyval | |
| 181 | |
| 182 %!test # whole-half consistency | |
| 183 %! b = [1 1 1]/3; # 3-sample average | |
| 184 %! [h,w] = freqz(b,1,32,'whole'); | |
| 185 %! assert(h(2:16),conj(h(32:-1:18)),20*eps); | |
| 186 %! [h2,w2] = freqz(b,1,16,'half'); | |
| 187 %! assert(h(1:16),h2,20*eps); | |
| 188 %! assert(w(1:16),w2,20*eps); | |
| 189 | |
| 190 %!test # Sampling frequency properly interpreted | |
| 5986 | 191 %! b = [1 1 1]/3; a = [1 0.2]; |
| 192 %! [h,f] = freqz(b,a,16,320); | |
| 5583 | 193 %! assert(f,[0:15]'*10,10*eps); |
| 5986 | 194 %! [h2,f2] = freqz(b,a,[0:15]*10,320); |
| 5377 | 195 %! assert(f2,[0:15]*10,10*eps); |
| 5986 | 196 %! assert(h,h2.',20*eps); |
| 197 %! [h3,f3] = freqz(b,a,32,'whole',320); | |
| 5583 | 198 %! assert(f3,[0:31]'*10,10*eps); |