Question

Which of the following is a Dirichlet condition with respect to the signal x(t)?

(a) x(t) has a finite number of discontinuities in any period

(b) x(t) has finite number of maxima and minima during any period

(c) x(t) is absolutely integrable in any period

(d) all of the mentioned

The question was posed to me in a job interview.

This intriguing question comes from Frequency Analysis of Continuous Time Signal in portion Frequency Analysis of Signals and Systems of Digital Signal Processing

Answer 1

Right option is (d) all of the mentioned

Easiest explanation: For any signal x(t) to be represented as Fourier series, it should satisfy the Dirichlet conditions which are x(t) has a finite number of discontinuities in any period, x(t) has finite number of maxima and minima during any period and x(t) is absolutely integrable in any period.