Write a Matlab code to generate the signal y(t)=10*(cos(2*pi*f1*t)+ cos(2*pi*f2*t)+ cos(2*pi*f3*t)), where f1=500 Hz, f2=750 Hz and f3=1000 Hz. Plot the signal in time domain.
MATLAB Code to plot the signal in time domain
clc;
clear all;
close all;
f1 = 500;
f2 = 750;
f3 = 1000;
t = 0:0.0000001:0.05;
y = 10*(cos(2*pi*f1*t) + cos(2*pi*f2*t) + cos(2*pi*f3*t));
plot(t,y);
grid on;
xlabel('Time, t(s)');
ylabel('y(t)');
title('Plot of the signal y(t)');
After running the code, we get the following plot
To sketch the Fourier Transform of the Signal
MATLAB Code
clc;
clear all;
close all;
f1 = 500;
f2 = 750;
f3 = 1000;
fs = 3*f3;
Ts = 1/fs;
n = 0:1000;
y = 10*(cos(2*pi*f1*n*Ts) + cos(2*pi*f2*n*Ts) +
cos(2*pi*f3*n*Ts));
w = 0:pi/100000:pi;
Y = y*exp(-j*n'*w);
figure
plot(w/(2*pi)*fs,abs(Y));
grid on;
xlabel('Frequecny, f (Hz)');
ylabel('|Y(\Omega)|');
title('Magnitude Spectrum of the input Signal');
After running the code we get the output as
To extract the frequency f1
We have to use a low pass filter with a cut off frequency greater than 500Hz. So I am using 600 Hz. I am using a Butterworth filter with an order of 31
MATLAB Code
clc;
clear all;
close all;
f1 = 500;
f2 = 750;
f3 = 1000;
fs = 3*f3;
Ts = 1/fs;
n = 0:1000;
y = 10*(cos(2*pi*f1*n*Ts) + cos(2*pi*f2*n*Ts) +
cos(2*pi*f3*n*Ts));
w = 0:pi/100000:pi;
[b,a] = butter(31,2*600/fs); % Butterworth Low Pass filter of
order 31 and cut off frequency of 600 Hz
yout = filter(b,a,y);
w = 0:pi/100000:pi;
Yout = yout*exp(-j*n'*w);
figure
plot(w/(2*pi)*fs,abs(Yout));
grid on;
xlabel('Frequecny, f (Hz)');
ylabel('|Y_{0ut}(\Omega)|');
title('Magnitude Spectrum of the output Signal');
The result obtained
From the frequency response plot we can see that the signal with frequency 500 Hz is extracted
To extract the frequency f2
We have to use a band pass filter with a cut off frequency greater than 500Hz and less than 1000Hz.. So I am using 600 Hz and 900 Hz as the cut off frequencies. I am using a Butterworth filter with an order of 31
MATLAB Code
clc;
clear all;
close all;
f1 = 500;
f2 = 750;
f3 = 1000;
fs = 3*f3;
Ts = 1/fs;
n = 0:1000;
y = 10*(cos(2*pi*f1*n*Ts) + cos(2*pi*f2*n*Ts) +
cos(2*pi*f3*n*Ts));
w = 0:pi/100000:pi;
[b,a] = butter(31,[2*600/fs 2*900/fs], 'bandpass'); %
Butterworth Band Pass filter, Order 31 & cut off frequency 600
& 900Hz
yout = filter(b,a,y);
w = 0:pi/100000:pi;
Yout = yout*exp(-j*n'*w);
figure
plot(w/(2*pi)*fs,abs(Yout));
grid on;
xlabel('Frequecny, f (Hz)');
ylabel('|Y_{0ut}(\Omega)|');
title('Magnitude Spectrum of the output Signal');
The result obtained
From the frequency response plot we can see that the signal with frequency 750 Hz is extracted
To extract the frequency f3
We have to use a high pass filter with a cut off frequency greater than 750Hz and less than 1000Hz. So I am using 900 Hz. I am using a Butterworth filter with an order of 31
MATLAB Code
clc;
clear all;
close all;
f1 = 500;
f2 = 750;
f3 = 1000;
fs = 3*f3;
Ts = 1/fs;
n = 0:1000;
y = 10*(cos(2*pi*f1*n*Ts) + cos(2*pi*f2*n*Ts) +
cos(2*pi*f3*n*Ts));
w = 0:pi/100000:pi;
[b,a] = butter(31, 2*900/fs, 'high'); % Butterworth High Pass
filter of order 31 and cut off frequency of 900 Hz
yout = filter(b,a,y);
w = 0:pi/100000:pi;
Yout = yout*exp(-j*n'*w);
figure
plot(w/(2*pi)*fs,abs(Yout));
grid on;
xlabel('Frequecny, f (Hz)');
ylabel('|Y_{0ut}(\Omega)|');
title('Magnitude Spectrum of the output Signal');
The result obtained
From the frequency response plot we can see that the signal with frequency 1000 Hz is extracted
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