(a) Derive the condition for which the discrete time complex exponetial signal x[n] is periodic.
$ x[n] = e^{jw_{o}n} $ $ x[n] = x[n+N] = e^{jw_{o}(n+N)} = e^{jw_{o}n}e^{jw_{o}N} $ to be periodic $ e^{jw_{o}N} = 1 = e^{j2\pi k}} $ $ \therefore w_{o}N = 2\pi k $ $ \rightarrow w_{o}/2\pi = K/N \rightarrow $Rational number $ \therefore w_{o} / 2\pi $ shold be a rational number
