11.1 - BME 240 - Spring2024

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Signal analysis in the frequency domain Week 11.1 - BME 240 – Spring2024
BB: TAEMG3.txt data Sample frequency was 500 Hz 1. Plot the frequency spectrum of raw EMG signals 2. Remove the frequency at 60 Hz (58-62Hz) using band stop filter (Butter, 4 th order); 3. Remove the frequency at 180 Hz (178-182 Hz) using band step (Butter 4 th order). 4. Plot the frequency spectrum after band stop filter. 5. Plot the EMG after removing the noise.
[newfile, newpath] = uigetfile('*.*', 'Select result File'); cd(newpath); filenameH2='TAemg3.txt'; dataH_2=load(filenameH2); figure(1); figure;plot(dataH_2); N1=length(dataH_1); fe1=fft(dataH_1); f1=(1:N1)*fs/N1; figure;plot(f1(1:(N1/2)-1),abs(fe1(2:(N1/2))));
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0 50 100 150 200 250 0 50 100 150 200 250 0 50 100 150 200 250 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 X 180 Y 1.91192 What kind of filter should we use?
filtfilt Zero-phase forward and reverse digital IIR filtering. Y = filtfilt (B, A, X) filters the data in vector X with the filter described by vectors A and B to create the filtered data Y. filter One- dimensional digital filter. Y = filter (B,A,X) filters the data in vector X with the filter described by vectors A and B to create the filtered data Y.
butter Butterworth digital and analog filter design. [B, A] = butter (N, Wn) designs an Nth order lowpass digital Butterworth filter and returns the filter coefficients in length N+1 vectors B (numerator) and A (denominator). The cutoff frequency Wn must be 0.0 < Wn < 1.0, with 1.0 corresponding to half the sample rate fs/2. [B,A] = butter(N,Wn,' high ') designs a highpass filter. [B,A] = butter(N,Wn,' low ’) designs a lowpass filter. [B,A] = butter(N,Wn,' stop ') is a bandstop filter if Wn = [W1 W2].
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WN=[55/(fs/2) 65/(fs/2)]; [b,a]=butter(4,WN, 'stop' ); xemgn=filtfilt(b,a,xemg); figure;plot(xemgn); 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 Band stop filter
xemg=xemgn; N=length(xemg); xfe=fft(xemg); fs=500; T=N/fs; f=(1:N)*fs/N; figure;plot(f(1:(N/2)-1),abs(xfe(2:(N/2)))) 0 50 100 150 200 250 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
wn=[55/(fs/2) 65/(fs/2)]; [b,a]=butter(4,wn, 'stop' ); xemgn1=filtfilt(b,a,dataH_1(:)); figure;plot(xemgn1); fe2=fft(xemgn1); figure;plot(f1(1:(N1/2)-1),abs(fe2(2:(N1/2)))); wn=[178/(fs/2) 182/(fs/2)]; [b,a]=butter(4,wn, 'stop' ); xemgn2=filtfilt(b,a,xemgn1); fe3=fft(xemgn2); figure;plot(f1(1:(N1/2)-1),abs(fe3(2:(N1/2)))); figure;plot(xemgn2);
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wn=[10/(fs/2)]; [b,a]=butter(4,wn, 'high' ); xemgn3=filtfilt(b,a,xemgn2); figure;plot(xemgn3); fe5=fft(xemgn3); figure;plot(f1(1:(N1/2)-1),abs(fe5(2:(N1/2)))); Remove low frequency noise What kind of filter should we use?
EMG after high-pass filtering with cutoff frequency at 10Hz
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wn=[20/(fs/2)]; [b,a]=butter(4,wn, 'high' ); xemgn3=filtfilt(b,a,xemgn2); figure;plot(xemgn3); fe5=fft(xemgn3); figure;plot(f1(1:(N1/2)-1),abs(fe5(2:(N1/2))));
Example EMG signals with electrical stimulation induced artifacts
[newfile, newpath] = uigetfile( '*.*' , 'Select result File' ); cd(newpath); filenameH5= 'T11_80Hz' ; dataH_5=load(filenameH5); figure; subplot(3,1,1);plot(dataH5(5,:)); subplot(3,1,2);plot(dataH5(6,:)); subplot(3,1,3);plot(dataH5(7,:));
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xemg=dataH(4,:); N=length(xemg); xfe=fft(xemg); fs=500; T=N/fs; f=(1:N-1)*fs/N; figure;plot(f(1:(N/2)-1),abs(xfe(2:(N/2))));
WN=[75/(fs/2) 85/(fs/2)]; [b,a]=butter(4,WN, 'stop' ); dataH1(4,:)=filtfilt(b,a,dataH(4,:)); WN=[235/(fs/2) 245/(fs/2)]; [b,a]=butter(4,WN, 'stop' ); dataH2(4,:)=filtfilt(b,a,dataH1(4,:)); WN=[95/(fs/2) 105/(fs/2)]; [b,a]=butter(4,WN, 'stop' ); dataH3(4,:)=filtfilt(b,a,dataH2(4,:)); WN=[55/(fs/2) 65/(fs/2)]; [b,a]=butter(4,WN, 'stop' ); dataH4(4,:)=filtfilt(b,a,dataH3(4,:));
[b1,a1]=butter(4,20/(fs/2), 'high' ); % low pass at 20 Hz dataH5(4,:)=filtfilt(b1,a1,dataH4(4,:)); After removed the noises
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[newfile, newpath] = uigetfile( '*.*' , 'Select result File' ); cd(newpath); filenameH5= 'position.txt' ; dataH_5=load(filenameH5); figure;plot(dataH_5);
wn=10/250; [b1,a1]=butter(4,wn, 'low' ); xpe=filtfilt(b1,a1,dataH_1); xpen=fft(xpe); figure;plot(f(1:(N/2)-1),abs(xpen(2:(N/2)))) figure;plot(xpe); Low pass filter
xpe=filtfilt(b1,a1,dataH_5); xpen=fft(xpe); figure;plot(fp(1:(Np/2)-1),abs(xpen(2:(Np/2)))) figure;plot(xpe); 0 50 100 150 200 250 0 5000 10000 15000 0 1 2 3 4 5 6 7 8 9 10 0 1000 2000 3000 4000 5000 6000 7000 8000
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filenameH6= 'vertforce.txt' ; dataH_6=load(filenameH6); figure;plot(dataH_6);
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force=dataH_6; N=length(force); xfe=fft(force); fs=500; T=N/fs; f=(1:N-1)*fs/N; figure;plot(f(1:(N/2)-1),abs(xfe(2:(N/2))));
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[b1,a1]=butter(4,25/(fs/2), 'low' ); % low pass at 25 Hz forcen=filtfilt(b1,a1,force); figure;plot(forcen);
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dxpe=diff(xpe,1)/(1/fs); figure;plot(dxpe); diff Difference and approximate derivative. diff (X), for a vector X, is [ X(2)-X(1) X(3)-X(2) ... X(n)-X(n-1)].
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figure;plot(forcen); df=diff(forcen,1); figure;plot(df);
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emg1=interp(signal(peakind(1):peakind(2),1),100); ln=length(signal(peakind(1):peakind(2))) length(emg1) figure;plot(emg1); emg2=downsample(emg1,ln); length(emg2)
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Synchronized position signals
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[b1,a1]=butter(4,10/(fs/2), 'low' ); % low pass at 10 Hz p1=filtfilt(b1,a1,position);
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step=800; shift=300; st=1; for i=1:60 [maxv,indv]=max(p1(st:st+step)); peak(i)=maxv; peakind(i)=indv+st; st=peakind(i)+shift; end figure;plot(p1); hold on ;plot(peakind,peak, 'r*' ); Find the peaks
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xemgn1=dataH5(6,:); for j=1:10 emg1=interp(xemgn1(peakind(j):peakind(j+1)),300); lg=peakind(j+1)-peakind(j); emg1_d(j,:)=downsample(emg1,lg); end figure; subplot(1,1,1);plot(mean((emg1_d)));xlim([1 300]) Interp and downsample EMG signals
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Averaged EMG signals (baseline)
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si=15; for j=1:10 emg1=interp(xemgn1(peakind(j+si):peakind(j+1+si)),300); lg=peakind(j+1+si)-peakind(j+si); emg1_dsi(j,:)=downsample(emg1,lg); end figure; subplot(1,1,1);plot(mean((emg1_dsi)));xlim([1 300])
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figure;plot(abs(mean(emg1_d))); hold on ;plot(-abs(mean(emg1_dsi)), 'r' ); Compare the differences emgcomp1=[sum(abs(mean(emg1_d))) sum(abs(mean(emg1_dsi)))] emgcomp1 = 0.2769 0.3003 emgcomp=[rms(abs(mean(emg1_d))) rms(abs(mean(emg1_dsi)))] area RMS emgcomp = 0.0016 0.0019
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ankle_xyz_baseline.txt Load file xRa, yRa, zRA, thet2R Fs=500 Hz. Run fft for the first 3 column data Run low pass filter with cut off at 10 hz Plot the frequency spectrum of the position signals to confirm. Based on column 4 data to segment the data (max peaks, 31 steps) Interp 100 points for each cycle Downsample to 100 points for each cycle Average x, y, z across 30 cycles (multiply -1 to the average y). Plot3 ensemble-averaged profiles of these position data.
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-200 -100 0 100 200 300 400 500 500 520 540 560 580 600 620 640 660 680 700
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[newfile, newpath] = uigetfile( '*.*' , 'Select result File' ); cd(newpath); filenameH1= 'ankle_xyz_baseline.txt' ; dataH_1=load(filenameH1); fs=500; N=length(dataH_1(:,1)); figure; subplot(4,1,1);plot(dataH_1(:,1)); subplot(4,1,2);plot(dataH_1(:,2)); subplot(4,1,3);plot(dataH_1(:,3)); subplot(4,1,4);plot(dataH_1(:,4));
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0 0.5 1 1.5 2 2.5 3 10 4 0 200 400 0 0.5 1 1.5 2 2.5 3 10 4 -700 -600 -500 0 0.5 1 1.5 2 2.5 3 10 4 300 350 400 0 0.5 1 1.5 2 2.5 3 10 4 50 100
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fs=500; t=(1:N)/fs; f=(1:N)*fs/N; X1=fft(dataH_1(:,1)); X2=fft(dataH_1(:,2)); X3=fft(dataH_1(:,3)); figure;subplot(3,1,1);plot(f(1:N/2-1),abs(X1( 2 :N/2))); subplot(3,1,2);plot(f(1:N/2-1),abs(X2( 2 :N/2))); subplot(3,1,3);plot(f(1:N/2-1),abs(X3( 2 :N/2))); fft to get frequency spectrum
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0 50 100 150 200 250 0 1 2 3 10 6 0 50 100 150 200 250 0 5 10 10 5 0 50 100 150 200 250 0 1 2 10 5 m=20*((N/2)/250) figure;subplot(3,1,1);plot(f(1:m-1),abs(X1(2:m))); subplot(3,1,2);plot(f(1:m-1),abs(X2(2:m))); subplot(3,1,3);plot(f(1:m-1),abs(X3(2:m))); 0 2 4 6 8 10 12 14 16 18 20 0 1 2 3 10 6 0 2 4 6 8 10 12 14 16 18 20 0 5 10 10 5 0 2 4 6 8 10 12 14 16 18 20 0 1 2 10 5
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[b,a]=butter(4,10/(fs/2), 'low' ); dataH_1n(:,1)=filtfilt(b,a,dataH_1(:,1)); dataH_1n(:,2)=filtfilt(b,a,dataH_1(:,2)); dataH_1n(:,3)=filtfilt(b,a,dataH_1(:,3)); X1n=fft(dataH_1n(:,1)); X2n=fft(dataH_1n(:,2)); X3n=fft(dataH_1n(:,3)); figure;subplot(3,1,1);plot(f(1:m-1),abs(X1n(2:m))); subplot(3,1,2);plot(f(1:m-1),abs(X2n(2:m))); subplot(3,1,3);plot(f(1:m-1),abs(X3n(2:m)));
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0 2 4 6 8 10 12 14 16 18 20 0 1 2 3 10 6 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 10 5 0 2 4 6 8 10 12 14 16 18 20 0 0.5 1 1.5 2 10 5 base frequency is 0.76 Hz Cadence =0.76*60 =46 steps/minute
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signal=dataH_1(:,4); step=800; shift=300; st=1; for i=1:43 [maxv,indv]=max(signal(st:st+step)); peak(i)=maxv; peakind(i)=indv+st; st=peakind(i)+shift; end figure;plot(signal(:,:)); hold on ;plot(peakind,peak, 'r*' );
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0 0.5 1 1.5 2 2.5 3 10 4 40 50 60 70 80 90 100 110
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for j=1:30 x1d=interp(dataH_1n(peakind(j):peakind(j+1),1),100); y1d=interp(dataH_1n(peakind(j):peakind(j+1),2),100); z1d=interp(dataH_1n(peakind(j):peakind(j+1),3),100); lg=peakind(j+1)-peakind(j); x1dn(j,:)=downsample(x1d,lg); y1dn(j,:)=downsample(y1d,lg); z1dn(j,:)=downsample(z1d,lg); end x1dnave=mean(x1dn(:,:)); y1dnave=mean(y1dn(:,:)); z1dnave=mean(z1dn(:,:)); figure;plot(x1dnave,-y1dnave) figure;plot3(x1dnave,-y1dnave,z1dnave)
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x1dnstd=std(x1dn(:,:)); y1dnstd=std(-y1dn(:,:)); figure;plot(x1dnave,-y1dnave) hold on ;plot(x1dnave+x1dnstd,-y1dnave-y1dnstd, '-.' ) hold on ;plot(x1dnave-x1dnstd,-y1dnave+y1dnstd, '-.' ) -200 -100 0 100 200 300 400 500 520 540 560 580 600 620 640 660 680 700
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Load file emgbase3.txt First column is TA emg, second column is MG emg, and third column is position signal. Sample frequency was 500 Hz. 1) Run fft to plot the frequency spectrum of TA and MG. 2) Run high pass 4 th order butter filtering to remove low frequency noises (cutoff 10 Hz) 3) Run band stop butter filter to remove noise 60 Hz. 4) Run fft to plot the frequency spectrum of filtered TA and MG. 5) For the third column data run low pass 4 th order butter filtering to remove high frequency noises (cutoff frequency 10 Hz). 6) Find the max peaks of filtered position signals (30 cycles, third column data ). 7) Segment the TA and MG based on the position data to different cycles. Run interp to insert 300 points of the TA and MG for each cycle. 8) Run downsample to reduce the length of the TA and MG of each cycle to 300 points. 9) Average the TA and MG signals across 30 cycles. 10) Plot the averaged TA and MG signals ICP
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