Question

When a continuous signal is a mixture of two continuous periodic signals, what is its periodicity?

(a) LCM of the  periods of the two signals, provide their ratio is unity

(b) LCM of the periods of the two signals, provide their ratio is rational

(c) HCF of the  periods of the two signals, provide their ratio is rational

(d) LCM of the  periods of the two signals provide their ratio is real

I had been asked this question in an international level competition.

This intriguing question originated from Periodic Signals in section Fourier Series of Signals and Systems

Answer 1

Right option is (b) LCM of the periods of the two signals, provide their ratio is rational

For explanation: When a continuous signal is a mixture of two continuous periodic signals if their time periods are T1 and T2, and their ratio is rational number, then, the periodicity of the continuous time signal will be the LCM of T1 and T2.