1. Net 222: Communications and networks fundamentals (Practical Part)
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Lab 3: Matlab – Sinusoidal&Exercises

2. Lab Contents Basic exercises Arrays & Matrices Plotting
Sinusoidal signal
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3. Basic exercises Let vector x = [5 2 1 6]: Add 16 to each element
Let y = [ ], multiply x*y
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4. Solution A. B. Adding 16 to vector x in matlab
Multiplying two vectors x and y
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5. Basic exercises
Evaluate the following MATLAB expressions by your hand and use MATLAB for checking your ans.:
2 / 2 * 3
(6 - 2 ) / ^ 2 – 1 A. B.
Hands calculation:
2/2=1
1*3 = 3
In Matlab:

6. How to evaluate an expression ?
(6 - 2 ) / ^ 2 – 1
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7. Basic exercises Let vector t= 2, 4, 6, 8…20: Compute cos^2(t)
%Notice that vector t is a starting form 2 and incremented by 2 till 20
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8. Solution % cos^2(t) is written as cos(t).^2
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9. Basic exercises Let vector t= 2, 4, 6, 8…20: Exp^t(1+ cos(3t))
%Notice that vector t is a starting form 2 and incremented by 2 till 20
exp Exponential.
exp(X) is the exponential of the elements of X, e to the X.

10. How to write an expression in matlab
% exp^t is written as exp(t).
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11. Arrays & Matrices Given an array A = [ 2 4 1 6 7 2 3 5 9]
provide the commands needed to:
assign the first row of A to a vector called x1
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12. Solution %Array in matlab written as each rows separated by ;
%assign the first row till end
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13. Arrays & Matrices Given an array A = [ 2 4 1 6 7 2 3 5 9]
provide the commands needed to:
assign the last 2 rows of A to an array called y
% end-1 is row before the last row
% end is the last row
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14. Arrays & Matrices Given an array A = [ 2 4 1 6 7 2 3 5 9]
provide the commands needed to:
compute the square-root of each element of A
sqrt(X) is the square root of the elements of X.
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15. Group work ! Given an array A = [ 2 4 1 6 7 2 3 5 9]
provide the commands needed to:
compute the square-root of the first row of A
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16. Arrays & Matrices Transpose the following matrices:
B=[ ] A. B.
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17. Plotting Plot sin(x2) on the interval [-5,5] step 0.01
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18. Solution
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19. Plotting The curve equations:
2. Create three curve on the interval [0,2π] step π/100 add legends to the plot
The curve equations:
y1 = sin(x)
y2 = sin(x-0.25)
y3 = sin(x-0.5)

20. Solution
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21. Sinusoidal Time & Frequency domain continuous or discrete signals
Sinusoid Sampling
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22. continuous or discrete signals
Continuous-Time Signals:
A signal is continuous-time signal if the independent variable t is continuous.
Discrete-Time Signals:
A signal is defined at discrete times, a discrete-time signal is often identified as a sequence of numbers, denoted by
A very important class of discrete-time signals is obtained by sampling a continuous-time signal
IN MATLAB: command plot used to sketch the continuous time signals
IN MATLAB: command stem used to sketch the discrete time signals
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23. Plotting Time domain using Matlab
concept
A general sine wave in time domain can be represented by three parameters :
Peak amplitude (A)
Frequency (f)
Phase (φ)
s(t) = A sin(2π f t +Φ)
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24. Plotting Time domain using Matlab
Example:
Plot and stem the time domain signal 7*sin(2*pi*2000*t+pi), t=0:0.05:3
To open the editor click on New -> Script

25. Matlab code Networks and Communication Department f=2000; t=0:0.05:3;
x=7*sin(2*3.14*f*t+3.14);
subplot(2,1,1);
plot(t,x);
xlabel('t');
ylabel('x(t)');
title('time domine continuous');
subplot(2,1,2);
stem(t,x);
xlabel('n');
ylabel('x[n]');
title('time domine discrete');
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26. Run and save
After writing the code click on Run button to save the code and run it .

27. Figure 1
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28. Plotting Frequency domain using Matlab
concept
Using discipline Known as Fourier analysis (any signal is made up of components at various frequencies, in which each component is a sinusoid ).
Eg. s(t) = [(4/π) x (sin(2πft) + (1/3) sin(2π(3f)t)]
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29. Plotting Frequency domain using Matlab
example
Plot each signals alone the show the frequency domain( Fourier) signal
s(t)=[6*sin(2pi*t+pi)+4*sin(2*pi*3t+pi)+ 2*sin(2*pi*5t+3*pi)]
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30. Matlab code
f1=1; f2=3; f3=5; t=0:0.01:5; pi=3.14; %############################# 1 s1=6*sin(2*pi*f1*t+pi); s2=4*sin(2*pi*f2*t+pi); s3=2*sin(2*pi*f3*t+3*pi); subplot(4,1,1); plot(t,s1,'linewidth',2); title('first signal '); grid on ; %############################## 2 subplot(4,1,2); plot(t,s2,'linewidth',2); title('second signal ');
f1=1; f2=3; f3=5;
t=0:0.01:5; pi=3.14;
%############################# 1
s1=6*sin(2*pi*f1*t+pi);
s2=4*sin(2*pi*f2*t+pi);
s3=2*sin(2*pi*f3*t+3*pi);
subplot(4,1,1);
plot(t,s1,'linewidth',2);
title('first signal ');
grid on ;
%############################## 2
subplot(4,1,2);
plot(t,s2,'linewidth',2);
title('second signal ');

31. Con. Matlab code
%############################## 3 subplot(4,1,3); plot(t,s3,'linewidth',2); title('third signal '); grid on ; %############################## Fourier fd=(s1+s2+s3); subplot(4,1,4); plot(t,fd,'linewidth',2); title('Freqency Domaine '); grid on;
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32. Figure 2
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33. Sampling
In signal processing, sampling is the reduction of a continuous signal to a discrete signal.
A sample is a value or set of values at a point in time and/or space.
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34. Con. Sampling
The sampling frequency or sampling rate, fs, is the average number of samples obtained in one second
For functions that vary with time, let s(t) be a continuous function (or "signal") to be sampled, and let sampling be performed by measuring the value of the continuous function every T seconds, which is called the sampling interval dt= 1/fs
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35. Sampling rate
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36. Con. Sampling rate
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37. Sinusoid Sampling
Sample the sinusoid x = sin(2 pi f t), where f = 2 kHz. And t=0:5T
Let x1 be the signal sampled at rate of 10 kHz.
f=2000;
T=1/f;
dt1= 1/10000;
t1=0:dt1:5*T;
x1=sin(2*3.14*f*t1);
stem(t1,x1);

38. Matlab code Networks and Communication Department
Discrete-Time Signals
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39. Figure Networks and Communication Department f=2000; T=1/f;
dt1= 1/10000;
t1=0:dt1:5*T;
x1=sin(2*3.14*f*t1);
plot(t1,x1);
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40. Sinusoid Sampling
Sample the sinusoid x = sin(2 pi f t), where f = 2 kHz. And t=0:5T
Let x2 be the signal sampled at 3 kHz
f=2000;
T=1/f;
dt2= 1/3000;
t2=0:dt2:5*T;
x2=sin(2*3.14*f*t2);
stem(t2,x2);
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41. Sinusoid Sampling
Plot frequency domain sinusoid x = sin(2 pi f t), where sampling frequency Fs = 8000 Hz. At different frequency tones start from 0 till 3, then multiplying the tones with 2
Note : The sampling frequency is sample rate
In the form of an FT it’s easy to filter sound.  For example, when you adjust the equalizer on your sound system, like when changing the bass or treble, what you’re really doing is telling the device to multiply the different frequencies by different amounts before sending the signal to the speakers.

42. Matlab code
f=8000; % sampling frequency t1=0:1/f:3; % time axis %############################ 1 s1=sin(2*3.14*f*t1); s2=sin(2*3.14*f*2*t1); subplot(3,1,1); plot(t1,s1,'linewidth',2); title('first f tone'); grid on ;
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43. Con. Matlab code %########################## 2 subplot(3,1,2);
plot(2*t1,s1,'linewidth',2);
title('second f tone');
grid on ;
fd = (s1+s2);
subplot(3,1,3);
plot(t1,fd,'linewidth',2);
title(' frequncey domain ' ) ;
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44. Figure
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45. The End
Any Questions ?
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