Question

The Fourier series representation of any signal x(t) is defined as ___________

(a) $\sum_{k=-\infty}^{\infty}c_k e^{j2πkF_0 t}$

(b) $\sum_{k=0}^{\infty}c_k e^{j2πkF_0 t}$

(c) $\sum_{k=-\infty}^{\infty}c_k e^{-j2πkF_0 t}$

(d) $\sum_{k=-\infty}^{\infty}c_{-k} e^{j2πkF_0 t}$

This question was addressed to me in an interview for internship.

My doubt stems from Frequency Analysis of Continuous Time Signal topic in chapter Frequency Analysis of Signals and Systems of Digital Signal Processing

Answer 1

The correct answer is (a) $\sum_{k=-\infty}^{\infty}c_k e^{j2πkF_0 t}$

Easy explanation: If the given signal is x(t) and F0 is the reciprocal of the time period of the signal and ck is the Fourier coefficient then the Fourier series representation of x(t) is given as $\sum_{k=-\infty}^{\infty}c_k e^{j2πkF_0 t}$.