Wiley signals and systems e book TLFe BO 445

17, Describing Random Signals

430

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 sigad niust have infinite
p0WeT:
(17.80)
--63

White noisc is tlierefore a11 idealisation that ca,nixo,ot actually be realised. I)espite this. it has extrenidy simple forins of power dciisity spcctrum arid autororrdation 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 components suppressed. Thib lends t o a rcfincd nzodci for raridam processes: bandlimited whitre noise with zt r e ~ t ~ npower
~ ~ ~density
a r spectrum
(17.81)

and finite power
pnn (0) =:

umnx

No 734

(17.83)

It, characterises noise processes whose p0~7eris evcrrly distributed below a band
limit* w ~ ~ Figure
* ~ ~ 17.11
.
stiows the power density sItectrxm and the autocorreIation function.

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~tstsilybe extmdod
to random seqnences, A s most of the r ~ ? ~ s oand
n i ~~ ~ ~ ~ i v ais~very
, i 0 nsimilar,