Mercurial > octave-nkf
annotate scripts/signal/freqz.m @ 14138:72c96de7a403 stable
maint: update copyright notices for 2012
| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Mon, 02 Jan 2012 14:25:41 -0500 |
| parents | c792872f8942 |
| children | f3d52523cde1 |
| rev | line source |
|---|---|
|
14138
72c96de7a403
maint: update copyright notices for 2012
John W. Eaton <jwe@octave.org>
parents:
11587
diff
changeset
|
1 ## Copyright (C) 1994-2012 John W. Eaton |
| 2313 | 2 ## |
| 3 ## This file is part of Octave. | |
| 4 ## | |
| 5 ## Octave is free software; you can redistribute it and/or modify it | |
| 6 ## under the terms of the GNU General Public License as published by | |
| 7016 | 7 ## the Free Software Foundation; either version 3 of the License, or (at |
| 8 ## your option) any later version. | |
| 2313 | 9 ## |
| 10 ## Octave is distributed in the hope that it will be useful, but | |
| 11 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
| 12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 13 ## General Public License for more details. | |
| 14 ## | |
| 15 ## You should have received a copy of the GNU General Public License | |
| 7016 | 16 ## along with Octave; see the file COPYING. If not, see |
| 17 ## <http://www.gnu.org/licenses/>. | |
| 2303 | 18 |
| 3367 | 19 ## -*- texinfo -*- |
| 20 ## @deftypefn {Function File} {[@var{h}, @var{w}] =} freqz (@var{b}, @var{a}, @var{n}, "whole") | |
| 21 ## Return the complex frequency response @var{h} of the rational IIR filter | |
| 22 ## whose numerator and denominator coefficients are @var{b} and @var{a}, | |
| 23 ## respectively. The response is evaluated at @var{n} angular frequencies | |
| 24 ## between 0 and | |
|
8517
81d6ab3ac93c
Allow documentation tobe built for other formats than tex and info
sh@sh-laptop
parents:
8506
diff
changeset
|
25 ## @ifnottex |
| 3367 | 26 ## 2*pi. |
|
8517
81d6ab3ac93c
Allow documentation tobe built for other formats than tex and info
sh@sh-laptop
parents:
8506
diff
changeset
|
27 ## @end ifnottex |
| 3367 | 28 ## @tex |
| 29 ## $2\pi$. | |
| 30 ## @end tex | |
| 3426 | 31 ## |
| 3367 | 32 ## @noindent |
| 33 ## The output value @var{w} is a vector of the frequencies. | |
| 3426 | 34 ## |
| 3367 | 35 ## If the fourth argument is omitted, the response is evaluated at |
| 36 ## frequencies between 0 and | |
|
8517
81d6ab3ac93c
Allow documentation tobe built for other formats than tex and info
sh@sh-laptop
parents:
8506
diff
changeset
|
37 ## @ifnottex |
| 3367 | 38 ## pi. |
|
8517
81d6ab3ac93c
Allow documentation tobe built for other formats than tex and info
sh@sh-laptop
parents:
8506
diff
changeset
|
39 ## @end ifnottex |
| 3367 | 40 ## @tex |
| 41 ## $\pi$. | |
| 42 ## @end tex | |
| 3426 | 43 ## |
| 3367 | 44 ## If @var{n} is omitted, a value of 512 is assumed. |
| 3426 | 45 ## |
| 3367 | 46 ## If @var{a} is omitted, the denominator is assumed to be 1 (this |
| 47 ## corresponds to a simple FIR filter). | |
| 3426 | 48 ## |
| 3367 | 49 ## For fastest computation, @var{n} should factor into a small number of |
| 50 ## small primes. | |
| 3893 | 51 ## |
| 52 ## @deftypefnx {Function File} {@var{h} =} freqz (@var{b}, @var{a}, @var{w}) | |
| 53 ## Evaluate the response at the specific frequencies in the vector @var{w}. | |
| 54 ## The values for @var{w} are measured in radians. | |
| 55 ## | |
| 56 ## @deftypefnx {Function File} {[@dots{}] =} freqz (@dots{}, @var{Fs}) | |
| 57 ## Return frequencies in Hz instead of radians assuming a sampling rate | |
|
11587
c792872f8942
all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents:
11523
diff
changeset
|
58 ## @var{Fs}. If you are evaluating the response at specific frequencies |
| 3893 | 59 ## @var{w}, those frequencies should be requested in Hz rather than radians. |
| 60 ## | |
| 3920 | 61 ## @deftypefnx {Function File} {} freqz (@dots{}) |
| 3907 | 62 ## Plot the pass band, stop band and phase response of @var{h} rather |
| 63 ## than returning them. | |
| 3367 | 64 ## @end deftypefn |
| 904 | 65 |
| 3367 | 66 ## Author: jwe ??? |
| 2314 | 67 |
| 5377 | 68 function [h_r, f_r] = freqz (b, a, n, region, Fs) |
| 566 | 69 |
| 3893 | 70 if (nargin < 1 || nargin > 5) |
| 6046 | 71 print_usage (); |
| 3893 | 72 elseif (nargin == 1) |
| 2303 | 73 ## Response of an FIR filter. |
| 3893 | 74 a = n = region = Fs = []; |
| 566 | 75 elseif (nargin == 2) |
| 2303 | 76 ## Response of an IIR filter |
| 3893 | 77 n = region = Fs = []; |
| 566 | 78 elseif (nargin == 3) |
| 3893 | 79 region = Fs = []; |
| 566 | 80 elseif (nargin == 4) |
| 3893 | 81 Fs = []; |
| 5443 | 82 if (! ischar (region) && ! isempty (region)) |
|
11587
c792872f8942
all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents:
11523
diff
changeset
|
83 Fs = region; |
| 3893 | 84 region = []; |
| 85 endif | |
| 86 endif | |
| 87 | |
| 5377 | 88 if (isempty (b)) |
| 89 b = 1; | |
| 90 endif | |
|
11587
c792872f8942
all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents:
11523
diff
changeset
|
91 if (isempty (a)) |
|
c792872f8942
all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents:
11523
diff
changeset
|
92 a = 1; |
| 3893 | 93 endif |
| 94 if (isempty (n)) | |
|
11587
c792872f8942
all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents:
11523
diff
changeset
|
95 n = 512; |
| 3893 | 96 endif |
| 97 if (isempty (region)) | |
| 98 if (isreal (b) && isreal (a)) | |
| 99 region = "half"; | |
| 100 else | |
| 101 region = "whole"; | |
| 102 endif | |
| 103 endif | |
|
11587
c792872f8942
all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents:
11523
diff
changeset
|
104 if (isempty (Fs)) |
|
c792872f8942
all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents:
11523
diff
changeset
|
105 if (nargout == 0) |
|
c792872f8942
all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents:
11523
diff
changeset
|
106 Fs = 2; |
|
c792872f8942
all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents:
11523
diff
changeset
|
107 else |
|
c792872f8942
all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents:
11523
diff
changeset
|
108 Fs = 2*pi; |
| 3893 | 109 endif |
| 566 | 110 endif |
| 111 | |
| 5583 | 112 a = a(:); |
| 113 b = b(:); | |
| 566 | 114 |
| 8506 | 115 if (! isscalar (n)) |
| 116 ## Explicit frequency vector given | |
| 5377 | 117 w = f = n; |
| 8506 | 118 if (nargin == 4) |
| 119 ## Sampling rate Fs was specified | |
| 5377 | 120 w = 2*pi*f/Fs; |
| 566 | 121 endif |
| 5986 | 122 k = max (length (b), length (a)); |
| 123 hb = polyval (postpad (b, k), exp (j*w)); | |
| 124 ha = polyval (postpad (a, k), exp (j*w)); | |
|
8667
a89198168175
freqz.m: freqz.m: fix for long input
Ben Abbott <bpabbott@mac.com>
parents:
8517
diff
changeset
|
125 else |
| 5583 | 126 ## polyval(fliplr(P),exp(jw)) is O(p n) and fft(x) is O(n log(n)), |
| 6653 | 127 ## where p is the order of the polynomial P. For small p it |
| 5377 | 128 ## would be faster to use polyval but in practice the overhead for |
| 129 ## polyval is much higher and the little bit of time saved isn't | |
| 130 ## worth the extra code. | |
|
8667
a89198168175
freqz.m: freqz.m: fix for long input
Ben Abbott <bpabbott@mac.com>
parents:
8517
diff
changeset
|
131 k = max (length (b), length (a)); |
|
a89198168175
freqz.m: freqz.m: fix for long input
Ben Abbott <bpabbott@mac.com>
parents:
8517
diff
changeset
|
132 if (k > n/2 && nargout == 0) |
|
a89198168175
freqz.m: freqz.m: fix for long input
Ben Abbott <bpabbott@mac.com>
parents:
8517
diff
changeset
|
133 ## Ensure a causal phase response. |
|
a89198168175
freqz.m: freqz.m: fix for long input
Ben Abbott <bpabbott@mac.com>
parents:
8517
diff
changeset
|
134 n = n * 2 .^ ceil (log2 (2*k/n)); |
|
a89198168175
freqz.m: freqz.m: fix for long input
Ben Abbott <bpabbott@mac.com>
parents:
8517
diff
changeset
|
135 endif |
|
a89198168175
freqz.m: freqz.m: fix for long input
Ben Abbott <bpabbott@mac.com>
parents:
8517
diff
changeset
|
136 |
|
a89198168175
freqz.m: freqz.m: fix for long input
Ben Abbott <bpabbott@mac.com>
parents:
8517
diff
changeset
|
137 if (strcmp (region, "whole")) |
|
a89198168175
freqz.m: freqz.m: fix for long input
Ben Abbott <bpabbott@mac.com>
parents:
8517
diff
changeset
|
138 N = n; |
|
a89198168175
freqz.m: freqz.m: fix for long input
Ben Abbott <bpabbott@mac.com>
parents:
8517
diff
changeset
|
139 else |
|
a89198168175
freqz.m: freqz.m: fix for long input
Ben Abbott <bpabbott@mac.com>
parents:
8517
diff
changeset
|
140 N = 2*n; |
|
a89198168175
freqz.m: freqz.m: fix for long input
Ben Abbott <bpabbott@mac.com>
parents:
8517
diff
changeset
|
141 endif |
|
a89198168175
freqz.m: freqz.m: fix for long input
Ben Abbott <bpabbott@mac.com>
parents:
8517
diff
changeset
|
142 |
|
a89198168175
freqz.m: freqz.m: fix for long input
Ben Abbott <bpabbott@mac.com>
parents:
8517
diff
changeset
|
143 f = Fs * (0:n-1).' / N; |
|
a89198168175
freqz.m: freqz.m: fix for long input
Ben Abbott <bpabbott@mac.com>
parents:
8517
diff
changeset
|
144 |
|
a89198168175
freqz.m: freqz.m: fix for long input
Ben Abbott <bpabbott@mac.com>
parents:
8517
diff
changeset
|
145 pad_sz = N*ceil (k/N); |
|
a89198168175
freqz.m: freqz.m: fix for long input
Ben Abbott <bpabbott@mac.com>
parents:
8517
diff
changeset
|
146 b = postpad (b, pad_sz); |
|
a89198168175
freqz.m: freqz.m: fix for long input
Ben Abbott <bpabbott@mac.com>
parents:
8517
diff
changeset
|
147 a = postpad (a, pad_sz); |
|
a89198168175
freqz.m: freqz.m: fix for long input
Ben Abbott <bpabbott@mac.com>
parents:
8517
diff
changeset
|
148 |
|
a89198168175
freqz.m: freqz.m: fix for long input
Ben Abbott <bpabbott@mac.com>
parents:
8517
diff
changeset
|
149 hb = zeros (n, 1); |
|
a89198168175
freqz.m: freqz.m: fix for long input
Ben Abbott <bpabbott@mac.com>
parents:
8517
diff
changeset
|
150 ha = zeros (n, 1); |
|
a89198168175
freqz.m: freqz.m: fix for long input
Ben Abbott <bpabbott@mac.com>
parents:
8517
diff
changeset
|
151 |
|
a89198168175
freqz.m: freqz.m: fix for long input
Ben Abbott <bpabbott@mac.com>
parents:
8517
diff
changeset
|
152 for i = 1:N:pad_sz |
|
a89198168175
freqz.m: freqz.m: fix for long input
Ben Abbott <bpabbott@mac.com>
parents:
8517
diff
changeset
|
153 hb = hb + fft (postpad (b(i:i+N-1), N))(1:n); |
|
a89198168175
freqz.m: freqz.m: fix for long input
Ben Abbott <bpabbott@mac.com>
parents:
8517
diff
changeset
|
154 ha = ha + fft (postpad (a(i:i+N-1), N))(1:n); |
|
a89198168175
freqz.m: freqz.m: fix for long input
Ben Abbott <bpabbott@mac.com>
parents:
8517
diff
changeset
|
155 endfor |
|
a89198168175
freqz.m: freqz.m: fix for long input
Ben Abbott <bpabbott@mac.com>
parents:
8517
diff
changeset
|
156 |
| 566 | 157 endif |
| 158 | |
| 3893 | 159 h = hb ./ ha; |
| 160 | |
| 8506 | 161 if (nargout != 0) |
| 162 ## Return values and don't plot. | |
| 3907 | 163 h_r = h; |
| 5377 | 164 f_r = f; |
| 8506 | 165 else |
| 166 ## Plot and don't return values. | |
| 5377 | 167 freqz_plot (f, h); |
| 7151 | 168 endif |
| 3907 | 169 |
| 566 | 170 endfunction |
| 5377 | 171 |
| 172 %!test # correct values and fft-polyval consistency | |
| 173 %! # butterworth filter, order 2, cutoff pi/2 radians | |
| 174 %! b = [0.292893218813452 0.585786437626905 0.292893218813452]; | |
| 175 %! a = [1 0 0.171572875253810]; | |
| 176 %! [h,w] = freqz(b,a,32); | |
| 177 %! assert(h(1),1,10*eps); | |
| 178 %! assert(abs(h(17)).^2,0.5,10*eps); | |
| 179 %! assert(h,freqz(b,a,w),10*eps); # fft should be consistent with polyval | |
| 180 | |
| 181 %!test # whole-half consistency | |
| 182 %! b = [1 1 1]/3; # 3-sample average | |
| 183 %! [h,w] = freqz(b,1,32,'whole'); | |
| 184 %! assert(h(2:16),conj(h(32:-1:18)),20*eps); | |
| 185 %! [h2,w2] = freqz(b,1,16,'half'); | |
| 186 %! assert(h(1:16),h2,20*eps); | |
| 187 %! assert(w(1:16),w2,20*eps); | |
| 188 | |
| 189 %!test # Sampling frequency properly interpreted | |
| 5986 | 190 %! b = [1 1 1]/3; a = [1 0.2]; |
| 191 %! [h,f] = freqz(b,a,16,320); | |
| 5583 | 192 %! assert(f,[0:15]'*10,10*eps); |
| 5986 | 193 %! [h2,f2] = freqz(b,a,[0:15]*10,320); |
| 5377 | 194 %! assert(f2,[0:15]*10,10*eps); |
| 5986 | 195 %! assert(h,h2.',20*eps); |
| 196 %! [h3,f3] = freqz(b,a,32,'whole',320); | |
| 5583 | 197 %! assert(f3,[0:31]'*10,10*eps); |