matlab，巴特沃思 [英] matlab, butterworth
问题描述
我需要应用巴特沃斯过滤器.为了证明我的截止频率，我想绘制残差与截止频率的关系，如右图所示:
使用左图所示的表达式计算残差.
我想应用二阶低通巴特沃斯滤波器.我的采样频率是 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 我得到了这个: 但这对我来说似乎不正确.我做错了什么? 您需要设置您想要的截止频率.例如，如果您知道希望 -3dB 点位于 15 Hz，则可以像这样过滤数据.. 只要改变 使用您在代码中使用的 编辑 为了根据您提供的信息获得您正在寻找的情节，我将使用以下脚本... 如果我在脚本中使用您的数据，我会得到如下所示的输出.. ...这与您在脚本链接中提出的输出相差不远... I need to apply a Butterworth filter. In order to prove my cutoff frequency, I wish to plot the residuals vs cutoff frequency, as shown in the image on the right: Residuals are computed using the expression shown in the image on the left. I want to apply a second-order low-pass Butterworth filter. My sample frequency is 40 Hz. Using "The cutoff frequency Wn must be 0.0 < Wn < 1.0, with 1.0
corresponding to half the sample rate". This is my code, where And I got this: But this does not seem to be right to me. What am I doing wrong? You need to set where you want your cutoff frequency. For example, if you know you want the -3dB point to be at 15 Hz, you can filter your data like so . . Just change the value of Using EDIT To get the plot you are looking for given the information you have provided, I would use the following script ... If I use your data in my script, I get an output that looks like this. .
..which isn't too far of the output you posed in a link from your script ... 这篇关于matlab，巴特沃思的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！x 是未过滤的数据:fs = 40;%//正如你所说的 40 Hzfc = 15；%//你的截止频率(Hz)[b,a] = 黄油(2, fc/(fs/2));y = 过滤器(b，a，x)；％//输出fc的值就可以改变截止频率...filtfilt 将有效地将滤波器的阶数加倍，因为您对信号进行了两次过滤(一次正向和一次反向).如果您想使用二阶零相位离线过滤，请在使用 filtfilt 之前将阶数更改为 1.fs = 40;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; 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399.065647300000; 400.495105800000; 402.316133400000; 402.820439400000; 404.135953800000; 404.902676700000; 407.071295400000; 408.901028400000; 409.339043500000; 410.856690000000; 411.741902100000; 411.572607400000; 410.578750600000;410.866900900000; 411.043940500000; 412.270310500000; 413.150341400000; 413.186237200000; 410.641084600000; 407.405695900000; 405.509177300000; 402.693585500000; 399.684704300000; 394.426107300000; 391.519533600000; 388.224900900000; 383.278789800000; 378.307242300000; 372.739602700000; 368.478280700000; 362.863358800000; 361.304001000000; 362.435018000000; 364.634794200000; 367.973272500000; 370.867271600000; 375.950784200000; 377.760681400000;379.167124200000; 379.646290600000; 379.508894500000; 379.045460000000; 378.591352500000; 384.507430200000; 384.886844300000; 383.932432300000; 386.799684400000; 391.060092500000; 393.418588700000; 394.132615800000; 394.432453800000; 398.324667600000; 397.096586200000; 398.005721400000; 400.474732000000; 400.328915300000; 401.058421000000; 403.238428000000; 402.724730000000; 403.253563800000; 404.687953000000; 405.079930400000; 405.219330800000; 407.047728400000; 407.595529300000; 408.057711800000; 408.539252700000; 409.836387000000; 410.123266400000; 410.313569400000; 412.099500000000; 412.793454600000; 413.372957300000; 415.066474200000; 413.971619400000; 414.254327400000; 415.198047500000; 416.134740700000; 417.933600600000; 417.211507700000; 417.097779400000; 417.708317200000; 414.171904400000; 412.326958700000; 410.969281800000; 403.879401900000; 399.416247400000; 393.297210900000; 389.540637800000; 384.152425200000; 376.404144800000; 372.813625800000; 366.430311000000; 361.093876700000; 358.405677900000; 358.336124000000; 358.933857600000; 363.550827300000; 368.513013500000; 373.555796400000; 377.399377100000; 382.541254000000; 385.282657700000; 389.342241000000; 390.319845400000; 390.834423800000;390.247456200000;392.237231500000;393.850930200000;398.146367200000;400.318802200000;392.237231500000;393.850930200000;400.318802200000;450.60040;450.604004N = 数字(x)；dw = 0.01;wc = dw:dw:1-dw;R=zeros(size(wc));对于 nn =1:numel(wc)[b,a]=butter(1,wc(nn));%//由于 filtfilt 可能导致订单减少y = filtfilt(b,a,x);R(nn)=sqrt( sum((x-y).^2)/N );结尾fAxis = wc*(fs/2);绘图(fAxis，R)；xlabel('fc [Hz]');ylabel('残差')help butter reads:
x is the unfiltered data:x = 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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) % <------ !!!!
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
fc to change the cutoff frequency . . .filtfilt as you have used in your code will effectively double the order of your filter because you are filtering the signal twice (once forwards and once reversed). If you want zero-phase offline filtering with 2nd order, change the order to 1 before using filtfilt.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')
