The N-point DFT of the N-point sequence x[n] = e j (/N) n2 , for N even,

The N-point DFT of the N-point sequence x[n] = e^{–j (π/N) n2}, for N even, is X[k] = √Ne^{– jπ/4} e^{j(π/N) k2}.

Determine the 2N-point DFT of the 2N-point sequence y[n] = e^{– j(π/N) n2}, assuming that N is even.