Question

(MATLAB question)

"ecg_signal.mat" converted to a .csv file yields the following data;

1. In the lab we analyzed filtering 60 Hz power-line noise from ECG signal using a digital (signal processing) filter. Now let's try to an analog (circuit) filter approach to remove the 60 Hz line-noise. Following is an active twin-T notch filter with transfer function: 2R 2R Here m is the ratio of the two feedback mR 2C resistance which determines the gain and quality for the filter. The drop frequency of this twin-1T notch filter is fdrop-1/4tRC. For designing a 60 Hž drop filter, let's use R 10 k Ω and C-133 nF (a) For m3( 0 . 8 , 0 . 9 } plot the magnitude and phase response of H ( ω) with a range of f-w/2TT [0, 200 Hz] (b) Consider the ECG signal used during the class (ecq signal.mat) as the input (x (t)-ecg) of a 60 Hz twin-T notch filter with m-0.9. Using the functions fft( ) and if ft( ) , determine the X ω ) , z ( ω ) , and z (t ) [2( t ) is the output signal from the twin-T notch filter! . Plot x( t ) , X f )·Ži f ) , and z ) in a 4x1 subplot for the range of -250 s f 3 250 and 0st< 2.5 [Please pay attention to the proper use offftshift () and ifftshift() while solving this problem.]

This is only part of the whole .mat file. Please show how to analyze the whole signal from this snapshot.

Answer 1

The transfer function of the twin-T notch filter is, (1+m)(2joRC) +1) H)(2jaRC) +4(1-m)joRC+1 (a) The following is the MATLAB code to plot the magnitude and phase and phase of H (o):

m=[0.8,0.9];
C=133*10^(-9);
R=10000;
f=0:0.1:200;
w=2*pi*f;
H1=((1+m(1))*((2*i*w*R*C).^2+1))./((2*i*w*R*C).^2+4*(1-m(1))*i*w*R*C+1);
H2=((1+m(2))*((2*i*w*R*C).^2+1))./((2*i*w*R*C).^2+4*(1-m(2))*i*w*R*C+1);
figure
subplot(2,1,1)
plot(f,abs(H1))
title('Magnitude and phase for m=0.8')
xlabel('f')
ylabel('Magnitude')
subplot(2,1,2)
plot(f,angle(H1))
xlabel('f')
ylabel('Phase (rad)')

figure
subplot(2,1,1)
plot(f,abs(H2))
title('Magnitude and phase for m=0.9')
xlabel('f')
ylabel('Magnitude')
subplot(2,1,2)
plot(f,angle(H2))
xlabel('f')
ylabel('Phase (rad)')

The plots are shown below. X Figure 1 File Edit View Insert Tools Desktop Window Help Magnitude and phase for m-0.8 2 1.5 1 0.5 0 0 100 140 60 120 160 180 200 f 2 0 -2 0 60 120 180 80 100 140 160 200 f 80 40 40 20 20 Phase (rad) Magnitude

Figure 2 File Edit View Tools Desktop Window Help Insert Magnitude and phase for m-0.9 2 1.5 1 0.5 0 60 80 100 120 140 160 180 200 f 2 1 -1 -2 0 60 100 120 140 160 180 200 f 80 40 40 20 20 Phase (rad) Magnitude

(b)

The following is the MATLAB code:

ecg_signal=load('ecg_signal.mat', '-ascii');

x=ecg_signal(:,2);

m=[0.8,0.9];

C=133*10^(-9);

R=10000;

f=0:0.1:200;

w=2*pi*f;

H2=((1+m(2))*((2*i*w*R*C).^2+1))./((2*i*w*R*C).^2+4*(1-m(2))*i*w*R*C+1);

X=fft(x);

Z=X*H2;

z=ifft(Z);

subplot(4,1,1)

N1=length(x);

t= linspace(0, 2.5, N1);

plot(t,x)

xlabel('t')

ylabel('x(t)')

subplot(4,1,2)

N2=length(x);

f= linspace(-250, 250, N2);

plot(f,fftshift(abs(X)))

xlabel('f')

ylabel('X(f)')

subplot(4,1,3)

plot(f,fftshift(abs(Z)))

xlabel('f')

ylabel('Z(f)')

subplot(4,1,4)

plot(t, (abs(z)))

xlabel('t')

ylabel('z(t)')

The plots are shown below Figure 1 File Edit View Tools Desktop Window Help Insert 1 0 1 0 0.5 2.5 1.5 10 5 250 150 100 100 150 200 250 -200 -50 0 f 20 10 -250 -150 -100 -50 50 100 150 200 250 -200 0 2 0.5 1.5 2 2.5 Note: Consider the ecg_signal.mat without headings (t,ecg) Also the final plot changes, if the whole .mat file is loaded into MATLAB. 50 ()7