430 17, Describing Random Signals From the representation of white noise in r,hc time-domain 17.79 and in the frequency-domain 17.78, we see that, a white iioise s i g a d niust have inf
Trang 1430 17, Describing Random Signals
From the representation of white noise in r,hc time-domain (17.79) and in the frequency-domain (17.78), we see that, a white iioise s i g a d niust have infinite p0WeT:
(1 7.80)
63 White noisc is tlierefore a11 idealisation that ca,nixo,ot actually be realised I)e- spite this it has extrenidy simple forins of power dciisity spcctrum arid auto- rorrdation function that, are very iisctiil, and the ideaJstlisatiomi can be justified if the white noise signal is high- or low-pass filtered, and the highest frequency com- ponents suppressed Thib lends t o a rcfincd nzodci for raridam processes: band- limited whitre noise with zt r e ~ t ~ n ~ ~ ~ a r power density spectrum
and finite power
u m n x
pnn (0) =: No - 4
73-
It, characterises noise processes whose p0~7er is evcrrly
limit* w ~ ~ * ~ ~ Figure 17.11 stiows the power density
correIation function
(17.81)
(17.83) distributed below a band sItectrxm and the auto-
Figure 17.11: Band-limited white noiw in the frrqwncy-clomain and time-domain
The concepts discussed so fw for corittinuous rarzdom signals can c~tstsily be extmdod
to random seqnences, A s most of the r ~ ? ~ s o n i ~ ~ and ~ ~ ~ ~ i v a ~ , i 0 n is very similar,