Question

5. (10 Pts) Discrete time signals Determine if the following signals are periodic. If yes, give the fundamental periods. x[n] = sin (10.) ne 리721 12

Answer 1

X(n) = sin (pi n/12) We know that for a signal x(n) = sin (w_0 n) to be periodic w_0/2 pi = M/N = Rational number - (1) where: N = fundamental time period m = smallest positive integer Now, using the criteria defined by equation (1) for the given signal, we get pi/12/2 pi = M/N M/N = 1/24 (Rational number) which implies that signal x(n) is periodic Now using the above relation for m = 1 N = 24 Note: N - 24 is the fundamental period of signal x(n) = sin (pi n/12) y(n) = e^- j n/3 We know that for a signal y(n) = e^- j w n to be periodic w_0/2 pi = M/N = rational number Now, using above criteria for the given signal y(x), we get - 1/3/2 pi = M/N