Question

What is the necessary and sufficient condition for a sum of a periodic continuous time signal to be periodic?

(a) Ratio of period of the first signal to period of other signals should be constant

(b) Ratio of period of the first signal to period of other signals should be finite

(c) Ratio of period of the first signal to period of other signals should be real

(d) Ratio of period of first signal to period of other signal should be rational

The question was asked in an interview for job.

Query is from Periodic Signals topic in chapter Fourier Series of Signals and Systems

Answer 1

The correct choice is (d) Ratio of period of first signal to period of other signal should be rational

To elaborate: The necessary and sufficient condition for a sum of a periodic continuous time signal to be periodic is that the ratio of a period of the first signal to the period of other signals should be rational.

I.e T/Ti = a rational number.