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Let x(t) be a continuous time periodic signal with fundamental period T = 1 seconds. Let {ak} be the complex Fourier series coefficients of x(t), where k is integer valued. Consider the following statements about x(3t):
I. The complex Fourier series coefficients of x(3t) are {ak} where k is integer valued
II. The complex Fourier series coefficients of x(3t) are {3ak} where k is integer valued
III. The fundamental angular frequency of x(3t) is 6π rad/s
For the three statements above, which one of the following is correct?
  • a)
    only II and III are true (B)
  • b)
    only I and III are true
  • c)
    only III is true
  • d)
    only I is true
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Let x(t) be a continuous time periodic signal with fundamental period ...
Fourier series coefficient ak is unaffected by scaling operating. Thus (I) is true and (II) is false.
T = 1sec for x(t) and if it compressed by ‘3’ then the resultant period T = 1/3

Thus (III) is correct.
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Let x(t) be a continuous time periodic signal with fundamental period T = 1 seconds. Let {ak} be the complex Fourier series coefficients of x(t), where k is integer valued. Consider the following statements about x(3t):I. The complex Fourier series coefficients of x(3t) are {ak} where k is integer valuedII. The complex Fourier series coefficients of x(3t) are {3ak} where k is integer valuedIII. The fundamental angular frequency of x(3t) is 6π rad/sFor the three statements above, which one of the following is correct?a)only II and III are true (B)b)only I and III are truec)only III is trued)only I is trueCorrect answer is option 'B'. Can you explain this answer?
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