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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*T2This 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»

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.



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