83.1 Discrete-Time Fourier Transform Definition The discrete-time fourier transform TFT)X(eJo ) of a sequence xn is given by X(e O )=∑xnle on 1=-00 n general, X(ejo )is a complex function of the real variable o and can be written as X(ejo)=xre(eJo)+j Xim(ejo)§3.1 Discrete-Time Fourier Transform • Definition - The discrete-time Fourier transform (DTFT) X(ej) of a sequence x[n] is given by   =− − = n j j n X e x n e   ( ) [ ] X(ej) = Xre(ej) + j Xim(ej) In general, X(ej) is a complex function of the real variable  and can be written as