Which of the following relation is correct between Fourier transform X(F) and Fourier series coefficient ck?(a) ck=X(F0/k)(b) ck= 1/TP (X(F0/k))(c) ck= 1/TP(X(kF0))(d) none of the mentionedThe question was posed to me by my college professor while I was bunking the class.This interesting question is from Frequency Analysis of Continuous Time Signal in division Frequency Analysis of Signals and Systems of Digital Signal Processing

Which of the following relation is correct between Fourier transform X

1.	Which of the following relation is correct between Fourier transform X(F) and Fourier series coefficient ck?(a) ck=X(F0/k)(b) ck= 1/TP (X(F0/k))(c) ck= 1/TP(X(kF0))(d) none of the mentionedThe question was posed to me by my college professor while I was bunking the class.This interesting question is from Frequency Analysis of Continuous Time Signal in division Frequency Analysis of Signals and Systems of Digital Signal Processing
Answer» Correct choice is (c) ck= 1/TP(X(kF0)) The best I can explain: Let us consider a signal x(t) whose FOURIER TRANSFORM X(F) is GIVEN as X(F)=\(\int_{-∞}^∞ x(t)e^{-j2πF_0 t}dt\) and the Fourier series coefficient is given as ck=\(\frac{1}{T_p} \int_{-∞}^∞ x(t)e^{-j2πkF_0 t}dt\) By comparing the above two EQUATIONS, we get ck=\(\frac{1}{T_p} X(kF_0)\)

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