Let X[k] denote the N-point DFT of the N-point sequence x[n].

(a) Show that if

x[n] = − x[N – 1 – n],

then X[0] = 0. Consider separately the cases of N even and N odd.

(b) Show that if N is even and if

x[n] = x[N – 1 – n],

 then X[N/2] = 0.