Which of the following is the equation for the Fourier series coefficient?(a) \(\frac{1}{T_p} \int_0^{t_0+T_p} x(t)e^{-j2πkF_0 t} dt\)(b) \(\frac{1}{T_p} \int_{t_0}^∞ x(t)e^{-j2πkF_0 t} dt\)(c) \(\frac{1}{T_p} \int_{t_0}^{t_0+T_p} x(t)e^{-j2πkF_0 t} dt\)(d) \(\frac{1}{T_p} \int_{t_0}^{t_0+T_p} x(t)e^{j2πkF_0 t} dt\)I have been asked this question during an online exam.This is a very interesting question from Frequency Analysis of Continuous Time Signal in portion Frequency Analysis of Signals and Systems of Digital Signal Processing

Which of the following is the equation for the Fourier series coeffici

1.	Which of the following is the equation for the Fourier series coefficient?(a) \(\frac{1}{T_p} \int_0^{t_0+T_p} x(t)e^{-j2πkF_0 t} dt\)(b) \(\frac{1}{T_p} \int_{t_0}^∞ x(t)e^{-j2πkF_0 t} dt\)(c) \(\frac{1}{T_p} \int_{t_0}^{t_0+T_p} x(t)e^{-j2πkF_0 t} dt\)(d) \(\frac{1}{T_p} \int_{t_0}^{t_0+T_p} x(t)e^{j2πkF_0 t} dt\)I have been asked this question during an online exam.This is a very interesting question from Frequency Analysis of Continuous Time Signal in portion Frequency Analysis of Signals and Systems of Digital Signal Processing
Answer» Correct choice is (C) \(\frac{1}{T_p} \int_{t_0}^{t_0+T_p} x(t)e^{-j2πkF_0 t} dt\) For explanation I would say: When we apply integration to the definition of Fourier SERIES REPRESENTATION, we get ckTp=\(\int_{t_0}^{t_0+T_p} x(t)e^{-j2πkF_0 t} dt\) =>ck=\(\frac{1}{T_p} \int_{t_0}^{t_0+T_p} x(t)e^{-j2πkF_0 t} dt\)

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