Question

Which of the following cannot be the Fourier series of a periodic signal?

(a) x(t) = 2Cost + 4Cos7t

(b) x(t) = 2Cosπt + 4Cos7t

(c) x(t) = Cost + 0.7

(d) x(t) = 2Cost + 4Sin7t

The question was asked at a job interview.

Origin of the question is AM Wave Representation topic in portion Amplitude Modulation of Analog Communications

Answer 1

The correct answer is (c) x(t) = Cost + 0.7

For explanation I would say: x(t) = Cost + 0.7  does not follow Dirchlet’s conditions. Fourier series of a periodic signal will only be applicable if it satisifies Dirchlet’s conditions firstly. Dirichlet integral states that a finite number should have finite number of discontinuities and also have finite number of extrema. x(t) doesn’t satisfy any of the criteria, whereas other options satisfy Dirchlet’s conditions. Thus, x(t) = Cost + 0.7, cannot be the Fourier series of a periodic signal.