12 T h e Soectrurn of Discrete Signals 310 The Parseval rel:la,tionshipc a n be obtained property with g [ k ]= f"[k:]: H,S A special casc of t,he mul~,$lit:nd~ior~ (12.50) As with contiimons-timr sigiials, the Parseval relatioiiship st iltes that the energy of ii time sipital dcfiiied hrrr by \umniation of I,f[k] I', c m also be formd by iiii (>grating with respect to lF(e'")12 in tlw frecluencp-dornain erties of the sier \Ve definc even aiicl odd sequences so that, the symmetry axis goc~,exactly tliroiigli the clement 2[01: Even sequences Ckld set~ucllccs sY[k]= a'Y[-k] xu [k]= -II' I , [ -k ] (12.51) (12.52) Accordingly, for odd sequences zu[Ol= Every sequence ~ [ kcan ] be split iiito an even tind an ocld part: (12.53) (12.54) Adding both equations confirms that: Z g [ k ]4-r u [ k ]= z [ k ] (12.55)