Question

If the signal x(t) is even, what will be the fourier series coefficients?

(a) Real and even

(b) Odd

(c) Real only

(d) Imaginary  and odd

The question was asked in an interview for internship.

I'd like to ask this question from Fourier Series Properties in portion Fourier Series of Signals and Systems

Answer 1

The correct choice is (d) Imaginary  and odd

Explanation: If the signal is real and even,  the fourier series coefficients are conjugate symmetric.

And its fourier series coefficients are imaginary and even.

Xn = X-n*= -Xn.