Wiley signals and systems e book TLFe BO 444

17.5. Power Density Specl,ra

429

Example 17.11
Ab 8x1 example we will consider the power drnsity spectrtxin in Figrrre 17.10
for tlie speech ~ i g ~ ifrom
a l Example 27.9. As expected, it is real and positive. anti
as the speech signal is, of courbe, itself rpi&valucd, the power density spectrum
is also an even function. In Figure 17.10 therefore, only the positive frequencies
are shown. The toncent,ration of power density in t,he 100 Hz region is clearly
rec(~~~iiseab1~.
This resnlt agreeh .viiith the rough ~ s t ~ i ~ ~ i of
a t ittir
o~~
i n ~ ~ c n t a 1
speech frequenry in Example 17 9-

Figrtrc 17.111: Paww density spcctriirn of the speech signal from Figure 17.10

29.5.

bite Noise

Many iiiterfcrence sources, like amplifier noise or radio iiiterferente, cc2n be described by rmdoni processes with a power density spectrum that is almost curistant
over a Iltrge mige of frrquencies. Such random processes are ofteii approximated
by an idealised process, whose pomw density spectrum i s not freyutwy dependent:

Since all frequtmcies occur evenly. the idealised process is called wh7te nose. T h e
name is dcrivcd finin the term 'white light', which represpnts B uniform mixture
of. every coluiir in tine spectrum.

T h e ~ ~ i ~ ~ c o r r €unction
e l a t i ~of~pi-hike
~ noise can only be r ~ ~ r e s e n by
~ eitc dis~
tribution, the t3clta impulse:
(Pr.&* ( r )-L: F-"(NbI

=r

No S( z) .

(17.79)

This means that, samples of white noise taken at diEerent limes do not correlatr.