Find whether the following signal is periodic or not. x(n) = 5cos(6Πn)

 Find whether the following signal is periodic or not.  x(n) = 5cos(6Πn)

                 Compare the give signal with, x(n) = A cos (2Πfn).

        We get, 2Πfn=6Πn=>f=3, which is rational. Hence this signal is periodic. Its period is given as, F = k/N = 3/1 => N = 1. 

What is the periodicity of the signal x(t) = sin 100πt+ cos150πt?

Compare the given signal with, 

                     X(t) = sin 2πf1t + cos 2πf2 t 

2πf1 t = 100 πt => f1 = 50 T1 = = 

2πf2 t = 150 πt => f2 = 75 T2 = = 

Since = = i.e. rational, the signal is periodic. The fundamental period will be, T=2T1 = 3 T2, i.e. least common multiple of T1 and T2. Here T=2T1=3T2=1/25.