Question

Check whether x [n] = 7 sin (6πn) is periodic and if it is period calculate its fundamental period?

(a) Periodic with fundamental period 6π

(b) Periodic with fundamental period 3

(c) Periodic with fundamental period 1

(d) Non periodic

I got this question during an interview.

Question is taken from Elementary Signals in section Signals and Systems Basics of Signals and Systems

Answer 1

Right answer is (c) Periodic with fundamental period 1

Explanation: X [n] = 7 sin (6πn) is a periodic discrete time signal with period 1. By substituting w = 6π and m=3 in w=^2πm⁄N  we get N =1.