Consider a stable discrete-time signal x[n] whose discrete-time Fourier transform X(e j ) satisfies the equation X

Consider a stable discrete-time signal x[n] whose discrete-time Fourier transform X(e^jω) satisfies the equation 

X (e^jω) = X (e^j(ω–π))

and has even symmetry, i.e., x[n] = x[– n].

(a) Show that X(e^jω) is periodic with a period π. 

(b) Find the value of x[3]. 

(c) Let y[n] be the decimated version of x[n], i.e., y[n] = x[2n]. Can you reconstruct x[n] from y[n] for all n. if yes, how? If no, justify your answer.