In MATLAB: Data in Test2-P2.txt contains: 2.73205 2.17618 1.14728 1.18824 2.2980

Question

In MATLAB:

Data in Test2-P2.txt contains:

2.73205 2.17618 1.14728 1.18824 2.29806 2.93185 2.13611 0.868324 0.677273 1.56766 2 1.02575 -0.393194 -0.704345 0.0999601 0.482362 -0.504456 -1.8983 -2.14728 -1.24527 -0.732051 -1.55814 -2.76531 -2.80628 -1.68003 -0.931852 -1.51807 -2.48636 -2.29531 -0.949624 -8.88178e-16 -0.407719 -1.22484 -0.913689 0.518074 1.51764 1.12249 0.280261 0.529244 1.86331 2.73205 2.17618 1.14728 1.18824 2.29806 2.93185 2.13611 0.868324 0.677273 1.56766 2 1.02575 -0.393194 -0.704345 0.0999601 0.482362 -0.504456 -1.8983 -2.14728 -1.24527 -0.732051 -1.55814 -2.76531 -2.80628 -1.68003 -0.931852 -1.51807 -2.48636 -2.29531 -0.949624 3.44169e-15 -0.407719 -1.22484 -0.913689 0.518074 1.51764 1.12249 0.280261 0.529244 1.86331 2.73205 2.17618 1.14728 1.18824 2.29806 2.93185 2.13611 0.868324 0.677273 1.56766 2 1.02575 -0.393194 -0.704345 0.0999601 0.482362 -0.504456 -1.8983 -2.14728 -1.24527 -0.732051 -1.55814 -2.76531 -2.80628 -1.68003 -0.931852 -1.51807 -2.48636 -2.29531 -0.949624 2.9976e-15 -0.407719 -1.22484 -0.913689 0.518074 1.51764 1.12249 0.280261 0.529244 1.86331 2.73205 2.17618 1.14728 1.18824 2.29806 2.93185 2.13611 0.868324 0.677273 1.56766 2 1.02575 -0.393194 -0.704345 0.0999601 0.482362 -0.504456 -1.8983 -2.14728 -1.24527 -0.732051 -1.55814 -2.76531 -2.80628 -1.68003 -0.931852 -1.51807 -2.48636 -2.29531 -0.949624 2.55351e-15 -0.407719 -1.22484 -0.913689 0.518074 1.51764 1.12249 0.280261 0.529244 1.86331 2.73205 2.17618 1.14728 1.18824 2.29806 2.93185 2.13611 0.868324 0.677273 1.56766 2 1.02575 -0.393194 -0.704345 0.0999601 0.482362 -0.504456 -1.8983 -2.14728 -1.24527 -0.732051 -1.55814 -2.76531 -2.80628 -1.68003 -0.931852 -1.51807 -2.48636 -2.29531 -0.949624 2.10942e-15 -0.407719 -1.22484 -0.913689 0.518074 1.51764 1.12249 0.280261 0.529244 1.86331

3. The data in file Test2-P2.txt contains 200 points sampled at 2000Hz from x(t) = 2 . cos(2T-50-t-) + cos(2T-400-r) a. Creat a plot to show the input signal b. Determine the transfer function, HU ), of a 3rd order Butterworth low-pass filter with a cut-off frequency at 200Hz. c. Obtain the transfer function H(s) in Laplace domain. d. Apply Bilinear Transform to obtain the transfer function, H(Z), in discrete-time domain e. Write a C program to filter x(t) using H(Z) f. Create a plot of the filter output

Explanation / Answer

clc;
t=0:1/2000:0.1;
x=2*cos(2*pi*50*t-pi/6)+cos(2*pi*400*t);
subplot(3,1,1)
plot(t,x)
title('i/p signal')
xlabel('t')
ylabel('amplitude')
grid
fc = 200;
fs = 2000;
[b,a] = butter(3,fc/(fs/2));
[h,om]=freqz(b,a)
subplot(3,1,2)
plot(abs(h))
subplot(3,1,3)
plot(om)
H=tf(b,a)
[numd,dend]=bilinear(b,a,fs)
Hd=tf(numd,dend,1/2000)
y=filter(numd,dend,x)

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