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:

    [​IMG]

    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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