What is the periodicity of the signal x(t) = sin 100πt + cos 150πt?

 Compare the given signal with x(t) = sin 2πf1t + cos 2πf2t

sin2πf1t = 100πt 🡺 f1=50 🡺 T1=1/f1=1/50 

sin2πf2t = 150πt🡺f2=75 🡺 T2=1/f2=1/75 

Since T1/T2 = (1/50)/(1/75)= 3/2 i.e. rational, the signal is periodic.

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