Question

What is Fourier series?

(a) The representation of periodic signals in a mathematical manner is called a Fourier series

(b) The representation of non periodic signals in a mathematical manner is called a Fourier series

(c) The representation of non periodic signals in terms of complex exponentials or sinusoids  is called a Fourier series

(d) The representation of periodic signals in terms of complex exponentials or sinusoids  is called a Fourier series

I got this question in a job interview.

My question is taken from Fourier Series in section Fourier Series of Signals and Systems

Answer 1

Correct choice is (d) The representation of periodic signals in terms of complex exponentials or sinusoids  is called a Fourier series

For explanation I would say: The Fourier series is the representation of non periodic signals in terms of complex exponentials, or equivalently in terms of sine and cosine waveform leads to Fourier series. In other words, Fourier series is a mathematical tool that allows representation of any periodic wave as a sum of harmonically related sinusoids.