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The Fourier series coefficient of a periodic signal, x(t) is defined as

Which of the following statement is correct.
  • a)
    x(t) is real
  • b)
    dx/dt is even 
  • c)
    x(t) is even
  • d)
    All of the above
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The Fourier series coefficient of a periodic signal, x(t) is defined a...
CASE 1: Let us assume that x(t) is real, then x(t) = x*(t). This implies that for x(t) to be real, ak = a*-k. Since this is not true. So, x(t) is not real.
CASE 2: Let us assume that x(t) is even, then x(t) = x(-t) and ak = a–k. Since this is true for this case, hence x(t) is even.
CASE 3: Let us assume

Therefore,

Since bk is not even, So, g(t) is not even.
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Most Upvoted Answer
The Fourier series coefficient of a periodic signal, x(t) is defined a...
CASE 1: Let us assume that x(t) is real, then x(t) = x*(t). This implies that for x(t) to be real, ak = a*-k. Since this is not true. So, x(t) is not real.
CASE 2: Let us assume that x(t) is even, then x(t) = x(-t) and ak = a–k. Since this is true for this case, hence x(t) is even.
CASE 3: Let us assume

Therefore,

Since bk is not even, So, g(t) is not even.
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