Discrete-Time Fourier Transform Definition The discrete-time fourier transform(dtFt) X(eJo)of a sequence xn is given by (e1)=∑xnle1on In general, X(eJo) is a complex function of the real variable o and can be written as X(e10)=Xe(e/0)+jm(e0) Copyright C 2001, S K. MitraCopyright © 2001, S. K. Mitra 2 Discrete-Time Fourier Transform • Definition - The discrete-time Fourier transform (DTFT) of a sequence x[n] is given by • In general, is a complex function of the real variable w and can be written as ( ) jw X e ( ) jw X e   =− − = n j j n X e x n e w w ( ) [ ] ( ) ( ) ( ) w w w = + j im j re j X e X e j X e