%Long list of butterworth (lowpass) filter designs
%
%For example: data was sampled at 100Hz. Building a butterworth filter
%with cutoff of 20 Hz would have Wn = 0.4 for 20 Hz
%(Wn = 1 corresponds to 50Hz, half the sample rate)
%
%Apply filter using fil = filter(b,a,raw);
%
% for i=1:1:10
% for j=0.1:0.1:0.9
% [b,a] = butter(i,j);
%
% cmd = ['%[b, a] = butter(' num2str(i) ', ' num2str(j) ')'];
% disp(cmd);
% disp(['b = [' num2str(b) '];']);
% disp(['a = [' num2str(a) '];']);
% disp(' ');
% end
% end
%[b, a] = butter(1, 0.1)
b = [0.13673 0.13673];
a = [1 -0.72654];
%[b, a] = butter(1, 0.2)
b = [0.24524 0.24524];
a = [1 -0.50953];
%[b, a] = butter(1, 0.3)
b = [0.33754 0.33754];
a = [1 -0.32492];
%[b, a] = butter(1, 0.4)
b = [0.42081 0.42081];
a = [1 -0.15838];
%[b, a] = butter(1, 0.5)
b = [0.5 0.5];
a = [1 -5.5511e-017];
%[b, a] = butter(1, 0.6)
b = [0.57919 0.57919];
a = [1 0.15838];
%[b, a] = butter(1, 0.7)
b = [0.66246 0.66246];
a = [1 0.32492];
%[b, a] = butter(1, 0.8)
b = [0.75476 0.75476];
a = [1 0.50953];
%[b, a] = butter(1, 0.9)
b = [0.86327 0.86327];
a = [1 0.72654];
%[b, a] = butter(2, 0.1)
b = [0.020083 0.040167 0.020083];
a = [1 -1.561 0.64135];
%[b, a] = butter(2, 0.2)
b = [0.067455 0.13491 0.067455];
a = [1 -1.143 0.4128];
%[b, a] = butter(2, 0.3)
b = [0.13111 0.26221 0.13111];
a = [1 -0.74779 0.27221];
%[b, a] = butter(2, 0.4)
b = [0.20657 0.41314 0.20657];
a = [1 -0.36953 0.19582];
%[b, a] = butter(2, 0.5)
b = [0.29289 0.58579 0.29289];
a = [1 -2.6368e-016 0.17157];
%[b, a] = butter(2, 0.6)
b = [0.39134 0.78267 0.39134];
a = [1 0.36953 0.19582];
%[b, a] = butter(2, 0.7)
b = [0.505 1.01 0.505];
a = [1 0.74779 0.27221];
%[b, a] = butter(2, 0.8)
b = [0.63895 1.2779 0.63895];
a = [1 1.143 0.4128];
%[b, a] = butter(2, 0.9)
b = [0.80059 1.6012 0.80059];
a = [1 1.561 0.64135];
%[b, a] = butter(3, 0.1)
b = [0.0028982 0.0086946 0.0086946 0.0028982];
a = [1 -2.3741 1.9294 -0.53208];
%[b, a] = butter(3, 0.2)
b = [0.018099 0.054297 0.054297 0.018099];
a = [1 -1.76 1.1829 -0.27806];
%[b, a] = butter(3, 0.3)
b = [0.049533 0.1486 0.1486 0.049533];
a = [1 -1.1619 0.69594 -0.13776];
%[b, a] = butter(3, 0.4)
b = [0.098531 0.29559 0.29559 0.098531];
a = [1 -0.57724 0.42179 -0.056297];
%[b, a] = butter(3, 0.5)
b = [0.16667 0.5 0.5 0.16667];
a = [1 -3.3307e-016 0.33333 -1.8504e-017];
%[b, a] = butter(3, 0.6)
b = [0.25692 0.77075 0.77075 0.25692];
a = [1 0.57724 0.42179 0.056297];
%[b, a] = butter(3, 0.7)
b = [0.37445 1.1234 1.1234 0.37445];
a = [1 1.1619 0.69594 0.13776];
%[b, a] = butter(3, 0.8)
b = [0.52762 1.5829 1.5829 0.52762];
a = [1 1.76 1.1829 0.27806];
%[b, a] = butter(3, 0.9)
b = [0.72944 2.1883 2.1883 0.72944];
a = [1 2.3741 1.9294 0.53208];
%[b, a] = butter(4, 0.1)
b = [0.0004166 0.0016664 0.0024996 0.0016664 0.0004166];
a = [1 -3.1806 3.8612 -2.1122 0.43827];
%[b, a] = butter(4, 0.2)
b = [0.0048243 0.019297 0.028946 0.019297 0.0048243];
a = [1 -2.3695 2.314 -1.0547 0.18738];
%[b, a] = butter(4, 0.3)
b = [0.018563 0.074252 0.11138 0.074252 0.018563];
a = [1 -1.5704 1.2756 -0.4844 0.076197];
%[b, a] = butter(4, 0.4)
b = [0.046583 0.18633 0.2795 0.18633 0.046583];
a = [1 -0.7821 0.67998 -0.18268 0.030119];
%[b, a] = butter(4, 0.5)
b = [0.093981 0.37592 0.56389 0.37592 0.093981];
a = [1 -2.2551e-016 0.48603 -4.6876e-018 0.017665];
%[b, a] = butter(4, 0.6)
b = [0.16718 0.66872 1.0031 0.66872 0.16718];
a = [1 0.7821 0.67998 0.18268 0.030119];
%[b, a] = butter(4, 0.7)
b = [0.27541 1.1017 1.6525 1.1017 0.27541];
a = [1 1.5704 1.2756 0.4844 0.076197];
%[b, a] = butter(4, 0.8)
b = [0.43285 1.7314 2.5971 1.7314 0.43285];
a = [1 2.3695 2.314 1.0547 0.18738];
%[b, a] = butter(4, 0.9)
b = [0.66202 2.6481 3.9721 2.6481 0.66202];
a = [1 3.1806 3.8612 2.1122 0.43827];
%[b, a] = butter(5, 0.1)
b = [5.9796e-005 0.00029898 0.00059796 0.00059796 0.00029898 5.9796e-005];
a = [1 -3.9845 6.4349 -5.2536 2.1651 -0.35993];
%[b, a] = butter(5, 0.2)
b = [0.0012826 0.0064129 0.012826 0.012826 0.0064129 0.0012826];
a = [1 -2.9754 3.806 -2.5453 0.88113 -0.12543];
%[b, a] = butter(5, 0.3)
b = [0.0069332 0.034666 0.069332 0.069332 0.034666 0.0069332];
a = [1 -1.9759 2.0135 -1.1026 0.32762 -0.040709];
%[b, a] = butter(5, 0.4)
b = [0.02194 0.1097 0.2194 0.2194 0.1097 0.02194];
a = [1 -0.98533 0.97385 -0.38636 0.11116 -0.011264];
%[b, a] = butter(5, 0.5)
b = [0.052786 0.26393 0.52786 0.52786 0.26393 0.052786];
a = [1 -4.6491e-016 0.63344 -2.0438e-016 0.055728 -3.0935e-018];
%[b, a] = butter(5, 0.6)
b = [0.10837 0.54187 1.0837 1.0837 0.54187 0.10837];
a = [1 0.98533 0.97385 0.38636 0.11116 0.011264];
%[b, a] = butter(5, 0.7)
b = [0.20189 1.0094 2.0189 2.0189 1.0094 0.20189];
a = [1 1.9759 2.0135 1.1026 0.32762 0.040709];
%[b, a] = butter(5, 0.8)
b = [0.35416 1.7708 3.5416 3.5416 1.7708 0.35416];
a = [1 2.9754 3.806 2.5453 0.88113 0.12543];
%[b, a] = butter(5, 0.9)
b = [0.59994 2.9997 5.9994 5.9994 2.9997 0.59994];
a = [1 3.9845 6.4349 5.2536 2.1651 0.35993];
%[b, a] = butter(6, 0.1)
b = [8.5766e-006 5.1459e-005 0.00012865 0.00017153 0.00012865 5.1459e-005 8.5766e-006];
a = [1 -4.78714 9.64952 -10.4691 6.44111 -2.12904 0.295172];
%[b, a] = butter(6, 0.2)
b = [0.00034054 0.0020432 0.0051081 0.0068108 0.0051081 0.0020432 0.00034054];
a = [1 -3.5794 5.6587 -4.9654 2.5295 -0.70527 0.083756];
%[b, a] = butter(6, 0.3)
b = [0.0025851 0.01551 0.038776 0.051701 0.038776 0.01551 0.0025851];
a = [1 -2.3797 2.9104 -2.0551 0.87792 -0.20987 0.021832];
%[b, a] = butter(6, 0.4)
b = [0.010313 0.061877 0.15469 0.20626 0.15469 0.061877 0.010313];
a = [1 -1.1876 1.3052 -0.67433 0.26347 -0.051753 0.0050225];
%[b, a] = butter(6, 0.5)
b = [0.029588 0.17753 0.44382 0.59176 0.44382 0.17753 0.029588];
a = [1 -1.164e-015 0.7777 -5.2358e-016 0.1142 -7.0192e-017 0.0017509];
%[b, a] = butter(6, 0.6)
b = [0.070115 0.42069 1.0517 1.4023 1.0517 0.42069 0.070115];
a = [1 1.1876 1.3052 0.67433 0.26347 0.051753 0.0050225];
%[b, a] = butter(6, 0.7)
b = [0.14773 0.88639 2.216 2.9546 2.216 0.88639 0.14773];
a = [1 2.3797 2.9104 2.0551 0.87792 0.20987 0.021832];
%[b, a] = butter(6, 0.8)
b = [0.28941 1.7364 4.3411 5.7881 4.3411 1.7364 0.28941];
a = [1 3.5794 5.6587 4.9654 2.5295 0.70527 0.083756];
%[b, a] = butter(6, 0.9)
b = [0.543298 3.25979 8.14947 10.866 8.14947 3.25979 0.543298];
a = [1 4.78714 9.64952 10.4691 6.44111 2.12904 0.295172];
%[b, a] = butter(7, 0.1)
b = [1.2296e-006 8.6075e-006 2.5823e-005 4.3038e-005 4.3038e-005 2.5823e-005 8.6075e-006 1.2296e-006];
a = [1 -5.58898 13.5047 -18.2709 14.9365 -7.3738 2.0344 -0.241873];
%[b, a] = butter(7, 0.2)
b = [9.0349e-005 0.00063244 0.0018973 0.0031622 0.0031622 0.0018973 0.00063244 9.0349e-005];
a = [1 -4.1823 7.8717 -8.5309 5.7099 -2.3492 0.54826 -0.055845];
%[b, a] = butter(7, 0.3)
b = [0.00096289 0.0067403 0.020221 0.033701 0.033701 0.020221 0.0067403 0.00096289];
a = [1 -2.7825 3.9668 -3.4052 1.8759 -0.65095 0.13085 -0.011663];
%[b, a] = butter(7, 0.4)
b = [0.0048421 0.033895 0.10168 0.16947 0.16947 0.10168 0.033895 0.0048421];
a = [1 -1.3893 1.675 -1.0539 0.50855 -0.14483 0.026252 -0.0020297];
%[b, a] = butter(7, 0.5)
b = [0.016565 0.11596 0.34787 0.57979 0.57979 0.34787 0.11596 0.016565];
a = [1 -4.8572e-017 0.91997 4.9692e-017 0.1927 1.1289e-017 0.0076835 -4.2652e-019];
%[b, a] = butter(7, 0.6)
b = [0.045311 0.31718 0.95154 1.5859 1.5859 0.95154 0.31718 0.045311];
a = [1 1.3893 1.675 1.0539 0.50855 0.14483 0.026252 0.0020297];
%[b, a] = butter(7, 0.7)
b = [0.108 0.75599 2.268 3.7799 3.7799 2.268 0.75599 0.108];
a = [1 2.7825 3.9668 3.4052 1.8759 0.65095 0.13085 0.011663];
%[b, a] = butter(7, 0.8)
b = [0.23631 1.6542 4.9626 8.271 8.271 4.9626 1.6542 0.23631];
a = [1 4.1823 7.8717 8.5309 5.7099 2.3492 0.54826 0.055845];
%[b, a] = butter(7, 0.9)
b = [0.491806 3.44264 10.3279 17.2132 17.2132 10.3279 3.44264 0.491806];
a = [1 5.58898 13.5047 18.2709 14.9365 7.3738 2.0344 0.241873];
%[b, a] = butter(8, 0.1)
b = [1.7626e-007 1.41e-006 4.9352e-006 9.8703e-006 1.2338e-005 9.8703e-006 4.9352e-006 1.41e-006 1.7626e-007];
a = [1 -6.39036 18.0003 -29.1711 29.7314 -19.5056 8.041 -1.90367 0.1981];
%[b, a] = butter(8, 0.2)
b = [2.396e-005 0.00019168 0.00067087 0.0013417 0.0016772 0.0013417 0.00067087 0.00019168 2.396e-005];
a = [1 -4.78451 10.445 -13.4577 11.1293 -6.02526 2.07927 -0.417217 0.0372001];
%[b, a] = butter(8, 0.3)
b = [0.00035844 0.0028675 0.010036 0.020073 0.025091 0.020073 0.010036 0.0028675 0.00035844];
a = [1 -3.1846 5.1829 -5.2162 3.4955 -1.573 0.46074 -0.07978 0.0062257];
%[b, a] = butter(8, 0.4)
b = [0.0022718 0.018175 0.063612 0.12722 0.15903 0.12722 0.063612 0.018175 0.0022718];
a = [1 -1.5906 2.0838 -1.5326 0.86944 -0.31918 0.08209 -0.012247 0.00086137];
%[b, a] = butter(8, 0.5)
b = [0.0092673 0.074138 0.25948 0.51897 0.64871 0.51897 0.25948 0.074138 0.0092673];
a = [1 -2.145e-015 1.0609 -1.8348e-015 0.29089 -4.8597e-016 0.02043 -5.0603e-017 0.00017177];
%[b, a] = butter(8, 0.6)
b = [0.029261 0.23409 0.81931 1.6386 2.0483 1.6386 0.81931 0.23409 0.029261];
a = [1 1.5906 2.0838 1.5326 0.86944 0.31918 0.08209 0.012247 0.00086137];
%[b, a] = butter(8, 0.7)
b = [0.078902 0.63122 2.2093 4.4185 5.5231 4.4185 2.2093 0.63122 0.078902];
a = [1 3.1846 5.1829 5.2162 3.4955 1.573 0.46074 0.07978 0.0062257];
%[b, a] = butter(8, 0.8)
b = [0.192873 1.54299 5.40045 10.8009 13.5011 10.8009 5.40045 1.54299 0.192873];
a = [1 4.78451 10.445 13.4577 11.1293 6.02526 2.07927 0.417217 0.0372001];
%[b, a] = butter(8, 0.9)
b = [0.445084 3.56067 12.4624 24.9247 31.1559 24.9247 12.4624 3.56067 0.445084];
a = [1 6.39036 18.0003 29.1711 29.7314 19.5056 8.041 1.90367 0.1981];
%[b, a] = butter(9, 0.1)
b = [2.526e-008 2.2734e-007 9.0936e-007 2.1218e-006 3.1828e-006 3.1828e-006 2.1218e-006 9.0936e-007 2.2734e-007 2.526e-008];
a = [1 -7.19144 23.1362 -43.6819 53.3153 -43.6086 23.8956 -8.45602 1.7531 -0.162195];
%[b, a] = butter(9, 0.2)
b = [6.3519e-006 5.7167e-005 0.00022867 0.00053356 0.00080034 0.00080034 0.00053356 0.00022867 5.7167e-005 6.3519e-006];
a = [1 -5.38622 13.3786 -19.9617 19.624 -13.137 5.97321 -1.77518 0.312381 -0.024765];
%[b, a] = butter(9, 0.3)
b = [0.00013337 0.0012004 0.0048015 0.011203 0.016805 0.016805 0.011203 0.0048015 0.0012004 0.00013337];
a = [1 -3.5863 6.5587 -7.552 5.9363 -3.2606 1.2421 -0.31458 0.047856 -0.0033201];
%[b, a] = butter(9, 0.4)
b = [0.0010654 0.0095886 0.038354 0.089493 0.13424 0.13424 0.089493 0.038354 0.0095886 0.0010654];
a = [1 -1.7916 2.5319 -2.1182 1.3708 -0.60904 0.19933 -0.043105 0.0058043 -0.00035558];
%[b, a] = butter(9, 0.5)
b = [0.0051819 0.046637 0.18655 0.43528 0.65292 0.65292 0.43528 0.18655 0.046637 0.0051819];
a = [1 -6.5356e-016 1.201 -4.804e-016 0.4085 -1.1608e-016 0.042661 -8.4317e-018 0.00096666 -5.3661e-020];
%[b, a] = butter(9, 0.6)
b = [0.018887 0.16998 0.67993 1.5865 2.3798 2.3798 1.5865 0.67993 0.16998 0.018887];
a = [1 1.7916 2.5319 2.1182 1.3708 0.60904 0.19933 0.043105 0.0058043 0.00035558];
%[b, a] = butter(9, 0.7)
b = [0.057621 0.51859 2.0743 4.8401 7.2602 7.2602 4.8401 2.0743 0.51859 0.057621];
a = [1 3.5863 6.5587 7.552 5.9363 3.2606 1.2421 0.31458 0.047856 0.0033201];
%[b, a] = butter(9, 0.8)
b = [0.157369 1.41632 5.66529 13.219 19.8285 19.8285 13.219 5.66529 1.41632 0.157369];
a = [1 5.38622 13.3786 19.9617 19.624 13.137 5.97321 1.77518 0.312381 0.024765];
%[b, a] = butter(9, 0.9)
b = [0.402735 3.62461 14.4985 33.8297 50.7446 50.7446 33.8297 14.4985 3.62461 0.402735];
a = [1 7.19144 23.1362 43.6819 53.3153 43.6086 23.8956 8.45602 1.7531 0.162195];
%[b, a] = butter(10, 0.1)
b = [3.6197e-009 3.6197e-008 1.6289e-007 4.3436e-007 7.6014e-007 9.1216e-007 7.6014e-007 4.3436e-007 1.6289e-007 3.6197e-008 3.6197e-009];
a = [1 -7.9923 28.9122 -62.3154 88.5877 -86.7671 59.281 -27.8903 8.64568 -1.59424 0.132768];
%[b, a] = butter(10, 0.2)
b = [1.6836e-006 1.6836e-005 7.5761e-005 0.00020203 0.00035355 0.00042426 0.00035355 0.00020203 7.5761e-005 1.6836e-005 1.6836e-006];
a = [1 -5.98759 16.6722 -28.2588 32.1598 -25.6017 14.4057 -5.64707 1.47373 -0.230919 0.0164796];
%[b, a] = butter(10, 0.3)
b = [4.9614e-005 0.00049614 0.0022326 0.0059536 0.010419 0.012503 0.010419 0.0059536 0.0022326 0.00049614 4.9614e-005];
a = [1 -3.98765 8.09441 -10.4763 9.42334 -6.08421 2.83526 -0.936403 0.208912 -0.0283359 0.00176963];
%[b, a] = butter(10, 0.4)
b = [0.00049945 0.0049945 0.022475 0.059934 0.10489 0.12586 0.10489 0.059934 0.022475 0.0049945 0.00049945];
a = [1 -1.9924 3.0195 -2.8185 2.0387 -1.0545 0.41445 -0.11572 0.022499 -0.0026689 0.00014876];
%[b, a] = butter(10, 0.5)
b = [0.0028964 0.028964 0.13034 0.34757 0.60825 0.7299 0.60825 0.34757 0.13034 0.028964 0.0028964];
a = [1 -8.7289e-016 1.3404 -1.0058e-015 0.54535 -3.0468e-016 0.077041 -8.9291e-017 0.0031655 -3.6529e-018 1.6779e-005];
%[b, a] = butter(10, 0.6)
b = [0.012187 0.12187 0.5484 1.4624 2.5592 3.071 2.5592 1.4624 0.5484 0.12187 0.012187];
a = [1 1.9924 3.0195 2.8185 2.0387 1.0545 0.41445 0.11572 0.022499 0.0026689 0.00014876];
%[b, a] = butter(10, 0.7)
b = [0.042067 0.42067 1.89301 5.04804 8.83406 10.6009 8.83406 5.04804 1.89301 0.42067 0.042067];
a = [1 3.98765 8.09441 10.4763 9.42334 6.08421 2.83526 0.936403 0.208912 0.0283359 0.00176963];
%[b, a] = butter(10, 0.8)
b = [0.128373 1.28373 5.77679 15.4048 26.9583 32.35 26.9583 15.4048 5.77679 1.28373 0.128373];
a = [1 5.98759 16.6722 28.2588 32.1598 25.6017 14.4057 5.64707 1.47373 0.230919 0.0164796];
%[b, a] = butter(10, 0.9)
b = [0.364374 3.64374 16.3968 43.7248 76.5184 91.8221 76.5184 43.7248 16.3968 3.64374 0.364374];
a = [1 7.9923 28.9122 62.3154 88.5877 86.7671 59.281 27.8903 8.64568 1.59424 0.132768];
