Question

The Fourier series expansion of a real periodic signal with fundamental frequency f0 is given by gp (t) = \(∑_{n=-∞}^∞ C_n e^{j 2πnf_0 t}\). Given that C3 = 3 + j5. The value of C-3 is ______________

(a) 5 + 3j

(b) -5 + 3j

(c) -3 – j5

(d) 3 – j5

I had been asked this question in a job interview.

This interesting question is from Miscellaneous Examples on Fourier Series in chapter Fourier Series of Signals and Systems

Answer 1

The correct option is (d) 3 – j5

Explanation: Given that C3 = 3 + j5.

We know that for real periodic signal C-k = \(C_k^*\)

So, C-3 = \(C_3^*\) = 3 – j5.