Question

Sum of a periodic and aperiodic signal always be an aperiodic signal.

(a) True

(b) False

I had been asked this question in unit test.

My question comes from Channel in section Elements of Communication System of Analog Communications

Answer 1

The correct option is (b) False

For explanation I would say: Periodic signal is a signal which repeats itself after a regular interval. While Aperiodic Signal does not repeat itself at regular interval of time.

For example: Let f(x) = sin(x), be a periodic function with period 2π and g(x) = −sin(x) + sin(√2x), be an aperiodic function. Now the sum of both i.e. f(x) + g(x) = sin(√2x), which is a periodic function.

Therefore, the sum of a periodic and aperiodic signal can be periodic.