Question

1. Determine whether or not each of the following signals is periodic. In case a signal is periodic, specify its period. sin(411t n+2) • cos? (in) . Can we use the formula, f = min ( - 14|1 - 4 + l{\), to find the period of sin(fnt n) or cos(2ft n)?

Answer 1

there are many ways to find whether the signal is periodic or not

I have mentioned some methods in pic

(1) Sin (4172+2) constant 9in 1 TnXC992 +694ITNxsin 2 a constant N Nis 21 .2 N₂ = 2 = 2 4IT 41 4IT T (2.1 CosGTn) x(n) [let) For a signal to be periodic a(n) = x(n+N) where Nis Period Let no n(o) = N(N) =) () C092(6): 1 *(1) Cos*(*) - + 1 Crational) Hence periodic - 1 => N, EN, EN ? (Period) * (2) - Coy(47) + n (5) Cos" () - 1 (0) = 4(3) Hence periodic & period is N=30 Formula of period is N = 27 (3) NO, Le Can't use the formula fa min (1/2 - 1 4 2 1 - 2 + 1 + 1) to sin (2fTn) or Cos (2f1n) we can proof it by putting fz1 then famin ( H +) - min(4-**-***) = min (0, 1) = 0, But in sin (25) period: 211 =10 where his discrete angular frequency 2TT