Question

I need help with number 2 . Please answer in MATLAB thank you!

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: (1+m)((2joRC? +1 Z(a) 2R 2R Here m is the ratio of the two feedback 2C R resistance which determines the gain and quality for the filter. The drop frequency of this twin-T filter is fdrop-1/4TRC. For designing a 60 Hz drop filter, let's use R-10 k Ω and C-133 nF. (a) For m-10 . 8 , 0 . 9 } plot the magnitude and phase response of H ( ω ) with a range of f-w/2T [0, 200 Hz) (b) Consider the ECG signal used during the class (ecg 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 ifft().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), Z(f), and z (t) in a 4x1 subplot for the range of -250s f s 250 and 0Sts2.5. [Please pay attention to the proper use of fftshift() and ifftshift () while solving this problem.] 2. Calculate the energy of time domain signal x (t) and z (t) for the range of 0Sts2.5 Also calculate the energy of these signals in frequency domain using Parseval's theorem. PlotEnergy(X) and Energy (Z)as a function of frequency f in a 2x1 subplot (Energy vs frequency plot is know as energy spectrum of a signal)

Answer 1

The following is the MATLAB code to calculate the energy of signals x(t) and z(t) in both time and frequency domains and plot Energy(X) and Energy(Z) as a function of frequency:

ecg_signal=load('ecg_signal.mat', '-ascii');
x=ecg_signal(:,2);
t=ecg_signal(:,1);
m=[0.8,0.9];
C=133*10^(-9);
R=10000;
N=length(x);
f= linspace(-250, 250, N);
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);
Ex=sum(abs(x.^2));
fprintf('Energy of signal x(t) in time domain is: \n')
disp(Ex)
Ez=sum(abs(z.^2));
fprintf('Energy of signal z(t) in time domain is: \n')
disp(Ez)
Exf=sum(abs(X.^2))/N;
fprintf('Energy of signal x(t) in frequency domain is: \n')
disp(Ex)
Ezf=sum(abs(X.^2))/N;
fprintf('Energy of signal z(t) in frequency domain is: \n')
disp(Ez)
Energyx(1)=0;
for i=2:N
    Energyx(i)=Energyx(i-1)+(X(i))^2;
end
subplot(2,1,1)
plot(f,abs(Energyx/N))
xlabel('f')
ylabel('Energy(X)')
Energyz(1)=0;
for i=2:N
    Energyz(i)=Energyz(i-1)+(Z(i))^2;
end
subplot(2,1,2)
plot(f,abs(Energyz/N))
xlabel('f')
ylabel('Energy(Z)')

The following is the MATLAB output:

Energy of signal x(t) in time domain is:
    4.8968

Energy of signal z(t) in time domain is:
   17.6890

Energy of signal x(t) in frequency domain is:
    4.8968

Energy of signal z(t) in frequency domain is:
   17.6890

The plot is shown below:

250 100 -200 -150 -100 -50 0 50 150 200 250 f 10 5 250 -200 100 200 250 -150 -100 -50 0 50 150 f Energy(Z) Energy(X)

Note: The values and the waveforms changes based on the uploaded ecg_signal.