Signals and Systems: A MATLAB® Integrated Approach

http://signalsandsystems.org/wordpress/?page_id=50

1. % Script file for Example 2.8.
   
2. % Copyright (c) 2014 by Oktay Alkin.
   
3. %
   
4. R = 2e6;           % Set R=2 megaOhms and C=1 microFarad.   
   
5. C = 1e-6;
   
6. t = [-1:0.01:8];   % Create a vector of time instants.
   
7. tau = R*C;         % Compute the time constant.
   
8. y = (1-exp(-t/tau)).*(t>=0);   % Compute output signal.
   
9. clf;
   
10. % Graph the output signal. Also mark the time constant with a
    
11. % red dashed line.
    
12. plot(t,y,'b-',[tau,tau],[0,1.2],'r--');
    
13. axis([-1,8,-0.2,1.2]);
    
14. text(tau,-0.05,'\tau');
    
15. title('Output signal y(t) for Example 2.8');
    
16. xlabel('t (sec)');
    
17. ylabel('Amplitude');
    
18. grid;

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1. % Script file for Example 2.9.
   
2. % Copyright (c) 2014 by Oktay Alkin.
   
3. %
   
4. A = 1;        % Set pulse amplitude.
   
5. w = 1;        % Set pulse width.
   
6. t = [-3:0.01:3];   % Create a vector of time instants.
   
7. % Compute the two parts of the signal from Eqns. (2-79) and
   
8. % (2-80).
   
9. y1 = A*(1-exp(-2*w)*exp(-4*t));
   
10. y2 = A*(exp(2*w)-exp(-2*w))*exp(-4*t);
    
11. % Construct the solution vector "y" by combining the two parts
    
12. % "y1" and "y2" with the use of logical operators.
    
13. y = y1.*((t>=-w/2)&(t<w/2))+y2.*(t>=w/2);
    
14. % Graph the output signal. Also show the input pulse with dashed red lines.
    
15. clf;
    
16. plot(t,y,'b-',0.5*w*[-3,-1,-1,1,1,3],A*[0,0,1,1,0,0],'r--');
    
17. axis([-3,3,-0.2,1.2]);
    
18. title('Output signal y(t) for Example 2.9');
    
19. xlabel('t (sec)');
    
20. ylabel('Amplitude');
    
21. grid;

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1. % Script file for Example 2.10.
   
2. % Copyright (c) 2014 by Oktay Alkin.
   
3. %
   
4. A = 1;        % Set pulse amplitude.
   
5. w = 1;        % Set pulse width.
   
6. t = [-3:0.01:3];   % Create a vector of time instants.
   
7. % Compute the responses to u(t+w/2) and u(t-w/2)
   
8. % using Eqns. (2.66) and (2.67).
   
9. y1 = A*(1-exp(-4*(t+0.5*w))).*(t>=-0.5*w);
   
10. y2 = A*(1-exp(-4*(t-0.5*w))).*(t>=0.5*w);
    
11. % Compute the pulse response using superposition. Refer to
    
12. % Eqn. (2.65).
    
13. y = y1-y2;
    
14. % Graph the two step responses y1(t) and y2(t) along with the
    
15. % pulse response y(t) of the system.
    
16. clf;
    
17. subplot(3,1,1)
    
18. plot(t,y1); grid;
    
19. axis([-3,3,-0.2,1.2]);
    
20. title('y_1(t) = A Sys\{ u(t+w/2) \}');
    
21. xlabel('t (sec)');
    
22. ylabel('Amplitude');
    
23. subplot(3,1,2)
    
24. plot(t,y2); grid;
    
25. axis([-3,3,-0.2,1.2]);
    
26. title('y_2(t) = A Sys\{ u(t-w/2) \}');
    
27. xlabel('t (sec)');
    
28. ylabel('Amplitude');
    
29. subplot(3,1,3)
    
30. plot(t,y); grid;
    
31. axis([-3,3,-0.2,1.2]);
    
32. title('y(t) = y_1(t) - y_2(t)');
    
33. xlabel('t (sec)');
    
34. ylabel('Amplitude');

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1. % Script : ex_3_11.m
   
2. %
   
3. n = [0:49];   % Vector of sample indices.
   
4. % First, set alpha=0.1 and compute the constant "c" for it.
   
5. alpha1 = 0.1;           
   
6. c1 = 2*(1-alpha1);  % y[-1] = 2;
   
7. % Compute the natural response.
   
8. yh1 = c1*(1-alpha1).^n;
   
9. % Next try with alpha=0.2.
   
10. alpha2 = 0.2;         
    
11. c2 = 2*(1-alpha2);  % y[-1] = 2;
    
12. % Compute the natural response.
    
13. yh2 = c2*(1-alpha2).^n;
    
14. % Graph the natural responses found.
    
15. clf;
    
16. subplot(2,1,1)
    
17. stem(n,yh1);
    
18. axis([-0.5,49.5,-0.25,2.25]);
    
19. title('Natural response y_{h}(t) of exponential smoother with \alpha=0.1');
    
20. xlabel('Index n');
    
21. ylabel('Amplitude');
    
22. subplot(2,1,2)
    
23. stem(n,yh2);
    
24. axis([-0.5,49.5,-0.25,2.25]);
    
25. title('Natural response y_{h}(t) of exponential smoother with \alpha=0.2');
    
26. xlabel('Index n');
    
27. ylabel('Amplitude');

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