Discrete-Time Fourier Transform(DTFT) Xre(eJo) and Xim(ejo) are, respectively, the real and imaginary parts of X(eJo), and are real functions of o X(e/o)can alternately be expressed as X(eo)=X(e jo )e jo( o) where 6(0)=ag{X(e/) Copyright C 2001, S K MitraCopyright © 2001, S. K. Mitra 3 Discrete-Time Fourier Transform (DTFT) • and are, respectively, the real and imaginary parts of , and are real functions of w • can alternately be expressed as where ( ) jw X e ( ) jw re X e ( ) jw Xim e ( ) jw X e ( ) ( ) ( ) w w  w = j j j X e X e e ( ) arg{ ( )} w  w = j X e