Question

How is the exponential Fourier series represented?

(a) X(t) = ∑Xne^jnwt + wt

(b) X(t) = 1/T∑Xne^jnwt

(c) X(t) = ∑Xne^jnwt

(d) X(t) = T*∑Xne^jnwt

The question was posed to me during an internship interview.

The question is from Fourier Series topic in portion Fourier Series of Signals and Systems

Answer 1

Right choice is (c) X(t) = ∑Xne^jnwt

For explanation I would say: The exponential Fourier series is represented as – X(t)=∑Xne^jnwt. Here, the X(t) is the signal and Xn=1/T∫x(t)e^-jnwt.