# Choosing A & alpha complex constants for a sequence

Discussion in 'Homework Help' started by tquiva, Sep 2, 2011.

1. ### tquiva Thread Starter Member

Oct 19, 2010
176
1
Problem:

I've been working on this problem, but I'm not entirely sure if I did it correctly since all the graphs for each instance seems the same as another. Here's my Matlab code. Any suggestions or advice for part (e)? I really don't know how to find the complex constants A and alpha for x
[*]=x[-*]

Code ( (Unknown Language)):
1. % PROBLEM 4
2.
3. star=-5:0.1:5
4.
5. % (a) When all components of the time sequence take only real values, the
6. % sequence is a real time sequence.
7.
8.
9. % To get real number from complex constants, set exponential equal to 1.
10. % Therefore, theta=0 for complex constant A*exp(i*theta)
11. A=a*exp(i*0);
12. alpha=b*exp(i*0);
13.
14. s=A*alpha^2*heaviside(star),
15.
16. plot3(star,real(s),imag(s),star,real(s),imag(s),'o')
17.
18. % (b) If some of the components take complex values, it is a complex time
19. % sequence.
20.
21. a=1; b=2;
22. A=a*exp(i*2);
23. alpha=b*exp(i*3);
24. s=A*alpha^2*heaviside(star),
25. plot3(star,real(s),imag(s),star,real(s),imag(s),'o')
26.
27. plot(star,s),xlabel('*'),ylabel('s
28. [*]'),title('Imaginary s
29. [*]')
30.
31. % (c) A sequence is bounded if there is a finite positive number say B such
32. % that the magnitudes of all the sequence components are bounded above B.
33.
34. B=1;
35. a=2; b=3;
36. A=a*exp(i*2);
37. alpha=b*exp(i*3);
38. s=A*alpha^2*heaviside(star),
39. plot(star,s),xlabel('*'),ylabel('s
40. [*]'),title('Imaginary s
41. [*]')
42.
43. % (d) If a sequence has finite energy, then the parameters must have
44. % parameters strictly less than unity.
45.
46. a=1; b=1/2;
47. A=a*exp(i*2)
48. alpha=b*exp(i*3)
49. s=A*alpha^2*heaviside(star),
50. plot(star,s),xlabel('*'),ylabel('s
51. [*]'),title('Imaginary s
52. [*]')
53.
54. % (e) An even sequence is a sequence where x
55. [*]=x[-*]

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