83.1 Discrete-Time Fourier Transform For a real sequence xn, X(ejo) and Xre(ejo) are even functions of o, whereas, H(o)and Xim(ejo)are odd functions of a Note: X(ejo)= X(ejo) ejb(o+Tk) I X(ejo)jeje(o) for any integer k uniquely specified for any DTA o The phase function A(@)cannot be§3.1 Discrete-Time Fourier Transform • For a real sequence x[n], | X(ej) | and Xre(ej) are even functions of , whereas, () and Xim(ej) are odd functions of  • Note: X(ej) = | X(ej) |ej(+2k) = | X(ej) |ej() for any integer k • The phase function () cannot be uniquely specified for any DTFT