matlab，butterworth

Question

我需要应用巴特沃斯滤波器。为了证明我的截止频率，我希望绘制残差与截止频率，如右图所示：

使用左侧图像中显示的表达式计算残差。

我想应用二阶低通巴特沃斯滤波器。我的采样频率为40 Hz。

使用help butter读取：

  

“截止频率Wn必须为0.0

这是我的代码，其中x是未经过滤的数据：

x = [386.321780100000;383.587759000000;381.800054600000;380.023872700000;376.516637700000;372.766842600000;367.938632100000;362.564671700000;356.119399400000;349.780736400000;345.535196800000;342.487775500000;343.327007400000;347.044262000000;352.155104000000;357.638520100000;363.112515900000;367.005736600000;369.969518400000;370.788505900000;370.727950800000;369.648907400000;371.655303500000;373.985894500000;374.662538300000;375.416536900000;377.716554500000;381.078738000000;384.060026700000;386.001162100000;386.230440100000;387.427096800000;388.211446400000;387.377444300000;387.621577500000;388.724233300000;389.431947300000;390.055687800000;389.897747100000;390.568256500000;390.976876100000;391.697054400000;392.307437700000;392.379471700000;393.675472100000;394.860379300000;395.811096400000;396.381388400000;398.085646700000;398.901758100000;400.678034200000;401.383476200000;402.159903200000;403.830729400000;404.584496200000;403.345648000000;402.534291300000;402.043024900000;400.591963700000;400.661529800000;401.214493200000;398.942282600000;396.136849800000;395.044892200000;391.983771800000;386.594017600000;383.401605600000;380.970551400000;376.310714500000;370.553521300000;366.878466900000;359.667106200000;352.458992900000;348.570689900000;343.701101100000;342.403147200000;345.523482600000;348.358285100000;351.430608400000;355.299118900000;358.338253800000;361.871167300000;365.253629000000;366.719133600000;371.786174300000;371.057137200000;371.100155400000;373.306458800000;376.272386700000;378.730711200000;382.095951400000;382.902277600000;383.461876500000;385.863290900000;386.271992900000;387.578084600000;388.651095700000;389.696072800000;390.282441000000;391.093495300000;391.289613800000;392.301607600000;392.159602900000;393.842911300000;393.546366500000;393.143725400000;394.750351600000;396.162576400000;397.561458700000;400.072731200000;401.171161400000;402.670562400000;403.090483400000;403.375118800000;403.742372900000;402.928992600000;403.625379400000;402.703021800000;404.445457900000;402.694859900000;404.492961300000;403.197389000000;400.246386500000;399.305927400000;395.243039500000;390.789534800000;386.215227800000;382.125630300000;378.740613300000;374.144220800000;369.667304900000;363.266125400000;358.880981700000;353.666361700000;352.930119300000;352.415712500000;354.932272100000;357.965910000000;363.210217400000;365.696508000000;368.583631400000;369.891869100000;370.457067900000;370.084533700000;371.254514800000;369.990608500000;372.512902900000;372.107388100000;372.389762900000;375.236476100000;377.180620200000;380.163700300000;383.752406800000;384.716569800000;386.690217000000;386.478825700000;387.136547300000;387.061047000000;387.614793500000;387.825040300000;388.859724400000;389.817438600000;390.783390500000;390.843715700000;391.629490100000;391.243866000000;391.117297600000;390.968419100000;392.245959800000;393.020590700000;394.630712100000;397.104264900000;397.023543100000;398.694405500000;399.038632200000;399.893340600000;401.723041400000;401.471017100000;402.798789400000;401.796557800000;401.510791300000;401.239454200000;402.555012900000;403.052252000000;402.218771700000;400.672248600000;398.567749700000;395.930037700000;393.687816300000;389.643818200000;385.300569800000;381.968732100000;379.096336600000;373.408813900000;368.723420200000;362.338487600000;357.422170600000;353.912378500000;351.497230900000;352.752737900000;355.645486800000;360.977540300000;365.115011900000;369.417573800000;374.421265000000;375.741261200000;379.482460500000;379.373812300000;381.356734700000;384.563742700000;385.998075700000;387.353239700000;387.846571200000;390.153373800000;394.202352800000;395.963324800000;398.282343000000;400.269374600000;400.557049800000;401.282810600000;402.133647600000;402.901177300000;404.506791700000;404.483256500000;405.463024500000;407.374795800000;407.037477400000;407.818079800000;408.022211200000;409.331968900000;410.195044600000;410.400538600000;411.138077700000;412.780554100000;413.371996900000;414.366633900000;416.607984600000;416.909471500000;417.903319900000;418.807274800000;418.131025900000;418.614937400000;419.355146400000;419.839171900000;420.622516800000;420.840936000000;421.415952700000;422.329106100000;419.791224700000;418.657891400000;416.303727400000;413.424186000000;409.239999100000;404.994917000000;401.405607300000;396.443609500000;391.830650800000;386.712834300000;379.305649600000;371.974335100000;367.876575200000;364.538574800000;364.350451800000;364.972675300000;368.720855400000;372.201352100000;374.288222600000;377.680482600000;378.799850200000;380.521041100000;380.363991200000;382.176218700000;384.164502100000;384.020557500000;387.386685800000;389.172806500000;391.352743100000;394.966380800000;397.758792800000;399.853885000000;399.654978000000;400.448029000000;402.805451900000;403.892553200000;403.862181700000;404.869756300000;406.689487700000;407.688509300000;407.899500500000;408.580087900000;410.215761300000;411.184311500000;412.070551500000;412.954576000000;4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wc = 0.001:0.001:1 % <----- !!!
R = zeros(1, length(wc)-1);
for nn = 1:length(wc)-1
    [B,A] = butter(2,wc(nn));
    xprime = filtfilt(B,A,x);
    R(1,nn) = sqrt(1/length(x)*(sum(abs(x-xprime).^2)))
end         
plot(wc(1:end-1)*20,R) % <------ !!!!

我得到了这个：

但这对我来说似乎不对。我做错了什么？

Answer 1

您需要设置截止频率的位置。例如，如果您知道-3dB点为15 Hz，则可以像这样过滤数据。 。

fs = 40; %// 40 Hz as you said
fc = 15; %// your cutoff in Hz
[b,a] = butter(2, fc/(fs/2));

y = filter(b,a,x); %// output

只需更改fc的值即可更改截止频率。 。

使用代码中使用的filtfilt将有效地使过滤器的顺序加倍，因为您要过滤信号两次（一次前进，一次反转）。如果您想要使用第二个订单进行零阶段离线过滤，请在使用filtfilt之前将订单更改为1。

修改

要获得您提供的信息，我会使用以下脚本...

fs = 40;

x = 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N = numel(x);

dw = 0.01;
wc = dw:dw:1-dw;

R=zeros(size(wc));
for nn =1:numel(wc)
    [b,a]=butter(1,wc(nn)); %//Potentially an order less because of filtfilt
    y = filtfilt(b,a,x);
    R(nn)=sqrt( sum((x-y).^2)/N );
end


fAxis = wc*(fs/2);

plot(fAxis,R);
xlabel('fc [Hz]'); ylabel('residuals')

如果我在脚本中使用您的数据，我会得到一个如下所示的输出。 。

..这不是你在脚本链接中提出的输出太远......