Question

Let x1(t) and x2(t) be periodic signals with fundamental periods T1 and T2 respectively. Which of the following must be a rational number for x(t)=x1(t)+x2(t) to be periodic?

(a) T1+T2

(b) T1-T2

(c) T1/T2

(d) T1*T2

This question was posed to me during an interview.

This interesting question is from Classification of Signals in section DSP – Basic Signaling of Digital Signal Processing

Answer 1

Right option is (c) T1/T2

The explanation: Let T be the period of the signal x(t)

=>x(t+T)=x1(t+mT1)+x2(t+nT2)

Thus, we must have

mT1=nT2=T

=>(T1/T2)=(k/m)= a rational number.