Question

Under what conditions the three signals x(t), y(t) and z(t) with period t1 t2 and t3 respectively are periodic?

(a) t1/t2= t2/t3

(b) t1/t2 is rational

(c) All the ratios of the three periods in any order is rational

(d) t1/t2/t3= rational

I had been asked this question during an online interview.

I'd like to ask this question from Periodic Signals topic in division Fourier Series of Signals and Systems

Answer 1

Right answer is (c) All the ratios of the three periods in any order is rational

For explanation I would say: if x(t) , y(t) and z(t) are to be periodic then,

t1/t2 should be rational and simultaneously

t1/t3 should be rational and

t2/t3 should be rational. Hence, all the ratios of the three periods in any order is rational.