Discrete-Time Fourier Transform(DTFT Xre(ejo) and xim(e /o)are, respectively, the real and imaginary parts of X(e/o), and are real functions of o X(eJo)can alternately be expressed as X(ejo)=r(ejo )eje(o) where 6(0)=arg{X(e/0)} 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