Show that the spectrum in part b is simply the fourier

Question

Consider the signal x(n) = α*(n), |α|

(a) Determine the spectrum X(ω).

(b) The signal x(n) is applied to a decimator that reduces the rate by a factor of 2. Determine the output spectrum.

(c) Show that the spectrum in part (b) is simply the Fourier transform of x(2n).