Find the fundamental period T of the following signal

 Here the three frequency components are, 

2Π f1 n = nΠ/2 => f1 = 1/4 therefore N1 = 4 

         2Π f2 n = nΠ/8 => f2 = 1/16 therefore N2 = 16 

         2Π f3 n = nΠ/4 = > f3 = 1/8 therefore N3 = 4

    Here f1, f2 and f3 are rational, hence individual signals are periodic. The overall signal will also be periodic since N1/N2 = 4/16 =1/4 and N2 / N3 =16/8 = 2. The period of the signal will be least common multiple of N1, N2 and N3 which is 16. Thus fundamental period, N = 16.