X-Git-Url: https://git.creatis.insa-lyon.fr/pubgit/?p=CreaPhase.git;a=blobdiff_plain;f=octave_packages%2Fsignal-1.1.3%2Fbutter.m;fp=octave_packages%2Fsignal-1.1.3%2Fbutter.m;h=9d2d00495faacd8c2b4ac8f4ce8a27d36b58d08e;hp=0000000000000000000000000000000000000000;hb=f5f7a74bd8a4900f0b797da6783be80e11a68d86;hpb=1705066eceaaea976f010f669ce8e972f3734b05 diff --git a/octave_packages/signal-1.1.3/butter.m b/octave_packages/signal-1.1.3/butter.m new file mode 100644 index 0000000..9d2d004 --- /dev/null +++ b/octave_packages/signal-1.1.3/butter.m @@ -0,0 +1,176 @@ +## Copyright (C) 1999 Paul Kienzle +## Copyright (C) 2003 Doug Stewart +## Copyright (C) 2011 Alexander Klein +## +## This program is free software; you can redistribute it and/or modify it under +## the terms of the GNU General Public License as published by the Free Software +## Foundation; either version 3 of the License, or (at your option) any later +## version. +## +## This program is distributed in the hope that it will be useful, but WITHOUT +## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or +## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more +## details. +## +## You should have received a copy of the GNU General Public License along with +## this program; if not, see . + +## Generate a butterworth filter. +## Default is a discrete space (Z) filter. +## +## [b,a] = butter(n, Wc) +## low pass filter with cutoff pi*Wc radians +## +## [b,a] = butter(n, Wc, 'high') +## high pass filter with cutoff pi*Wc radians +## +## [b,a] = butter(n, [Wl, Wh]) +## band pass filter with edges pi*Wl and pi*Wh radians +## +## [b,a] = butter(n, [Wl, Wh], 'stop') +## band reject filter with edges pi*Wl and pi*Wh radians +## +## [z,p,g] = butter(...) +## return filter as zero-pole-gain rather than coefficients of the +## numerator and denominator polynomials. +## +## [...] = butter(...,'s') +## return a Laplace space filter, W can be larger than 1. +## +## [a,b,c,d] = butter(...) +## return state-space matrices +## +## References: +## +## Proakis & Manolakis (1992). Digital Signal Processing. New York: +## Macmillan Publishing Company. + +function [a, b, c, d] = butter (n, W, varargin) + + if (nargin>4 || nargin<2) || (nargout>4 || nargout<2) + print_usage; + end + + ## interpret the input parameters + if (!(length(n)==1 && n == round(n) && n > 0)) + error ("butter: filter order n must be a positive integer"); + end + + stop = 0; + digital = 1; + for i=1:length(varargin) + switch varargin{i} + case 's', digital = 0; + case 'z', digital = 1; + case { 'high', 'stop' }, stop = 1; + case { 'low', 'pass' }, stop = 0; + otherwise, error ("butter: expected [high|stop] or [s|z]"); + endswitch + endfor + + + [r, c]=size(W); + if (!(length(W)<=2 && (r==1 || c==1))) + error ("butter: frequency must be given as w0 or [w0, w1]"); + elseif (!(length(W)==1 || length(W) == 2)) + error ("butter: only one filter band allowed"); + elseif (length(W)==2 && !(W(1) < W(2))) + error ("butter: first band edge must be smaller than second"); + endif + + if ( digital && !all(W >= 0 & W <= 1)) + error ("butter: critical frequencies must be in (0 1)"); + elseif ( !digital && !all(W >= 0 )) + error ("butter: critical frequencies must be in (0 inf)"); + endif + + ## Prewarp to the band edges to s plane + if digital + T = 2; # sampling frequency of 2 Hz + W = 2/T*tan(pi*W/T); + endif + + ## Generate splane poles for the prototype butterworth filter + ## source: Kuc + C = 1; # default cutoff frequency + pole = C*exp(1i*pi*(2*[1:n] + n - 1)/(2*n)); + if mod(n,2) == 1, pole((n+1)/2) = -1; end # pure real value at exp(i*pi) + zero = []; + gain = C^n; + + ## splane frequency transform + [zero, pole, gain] = sftrans(zero, pole, gain, W, stop); + + ## Use bilinear transform to convert poles to the z plane + if digital + [zero, pole, gain] = bilinear(zero, pole, gain, T); + endif + + ## convert to the correct output form + if nargout==2, + a = real(gain*poly(zero)); + b = real(poly(pole)); + elseif nargout==3, + a = zero; + b = pole; + c = gain; + else + ## output ss results + [a, b, c, d] = zp2ss (zero, pole, gain); + endif + +endfunction + +%!shared sf, sf2, off_db +%! off_db = 0.5; +%! ##Sampling frequency must be that high to make the low pass filters pass. +%! sf = 6000; sf2 = sf/2; +%! data=[sinetone(5,sf,10,1),sinetone(10,sf,10,1),sinetone(50,sf,10,1),sinetone(200,sf,10,1),sinetone(400,sf,10,1)]; + +%!test +%! ##Test low pass order 1 with 3dB @ 50Hz +%! data=[sinetone(5,sf,10,1),sinetone(10,sf,10,1),sinetone(50,sf,10,1),sinetone(200,sf,10,1),sinetone(400,sf,10,1)]; +%! [b, a] = butter ( 1, 50 / sf2 ); +%! filtered = filter ( b, a, data ); +%! damp_db = 20 * log10 ( max ( filtered ( end - sf : end, : ) ) ); +%! assert ( [ damp_db( 4 ) - damp_db( 5 ), damp_db( 1 : 3 ) ], [ 6 0 0 -3 ], off_db ) + +%!test +%! ##Test low pass order 4 with 3dB @ 50Hz +%! data=[sinetone(5,sf,10,1),sinetone(10,sf,10,1),sinetone(50,sf,10,1),sinetone(200,sf,10,1),sinetone(400,sf,10,1)]; +%! [b, a] = butter ( 4, 50 / sf2 ); +%! filtered = filter ( b, a, data ); +%! damp_db = 20 * log10 ( max ( filtered ( end - sf : end, : ) ) ); +%! assert ( [ damp_db( 4 ) - damp_db( 5 ), damp_db( 1 : 3 ) ], [ 24 0 0 -3 ], off_db ) + +%!test +%! ##Test high pass order 1 with 3dB @ 50Hz +%! data=[sinetone(5,sf,10,1),sinetone(10,sf,10,1),sinetone(50,sf,10,1),sinetone(200,sf,10,1),sinetone(400,sf,10,1)]; +%! [b, a] = butter ( 1, 50 / sf2, "high" ); +%! filtered = filter ( b, a, data ); +%! damp_db = 20 * log10 ( max ( filtered ( end - sf : end, : ) ) ); +%! assert ( [ damp_db( 2 ) - damp_db( 1 ), damp_db( 3 : end ) ], [ 6 -3 0 0 ], off_db ) + +%!test +%! ##Test high pass order 4 with 3dB @ 50Hz +%! data=[sinetone(5,sf,10,1),sinetone(10,sf,10,1),sinetone(50,sf,10,1),sinetone(200,sf,10,1),sinetone(400,sf,10,1)]; +%! [b, a] = butter ( 4, 50 / sf2, "high" ); +%! filtered = filter ( b, a, data ); +%! damp_db = 20 * log10 ( max ( filtered ( end - sf : end, : ) ) ); +%! assert ( [ damp_db( 2 ) - damp_db( 1 ), damp_db( 3 : end ) ], [ 24 -3 0 0 ], off_db ) + +%!demo +%! sf = 800; sf2 = sf/2; +%! data=[[1;zeros(sf-1,1)],sinetone(25,sf,1,1),sinetone(50,sf,1,1),sinetone(100,sf,1,1)]; +%! [b,a]=butter ( 1, 50 / sf2 ); +%! filtered = filter(b,a,data); +%! +%! clf +%! subplot ( columns ( filtered ), 1, 1) +%! plot(filtered(:,1),";Impulse response;") +%! subplot ( columns ( filtered ), 1, 2 ) +%! plot(filtered(:,2),";25Hz response;") +%! subplot ( columns ( filtered ), 1, 3 ) +%! plot(filtered(:,3),";50Hz response;") +%! subplot ( columns ( filtered ), 1, 4 ) +%! plot(filtered(:,4),";100Hz response;")