Wiley signals and systems e book TLFe BO 325

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= 0. 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)