Wiley signals and systems e book TLFe BO 434

41 9

17.4. Correlathi Fimctions

i

~

~value:
~

Itmer bound:

~pZ2(~1)
~ =~
pJz(z)

i~ p'

2 -0; $. 11:

>

~ pzz{z)
~
~ (17.3.1)
r
~
(17 35)

(17.36) hold for all ~ t ~ t i o i i a ranciom

ry
signals t ( l ) , but, (17.37) only holds when
distantly separ2zted values do rot correlate. In Examplc 17.7, (17.37) does not
hold, for example,

Example 17.8
Iii Examplc 17.4 we corisidered two ranclom processes A m d I( -vc.liose saxxip l ~fiinctions c*lemly have statistical interdepeitdencies. Under the assumpi 1011
tliat these processes are also stationdry for the sectiorr shown, we can charace t h a n with their auto-coir
ion function:, q z 2( P) ailcl pvv(t),shown in
Figure 17 7. They ale illustrated in Figure 17.7, mid ale t-ountl hiiiiplv as riowsrctionv throngh c p r z ( f i , t ~and
)
p z , v ( t l , t lin
) Figure 17.5, along the I I or 1 2 aAis.
The anto-correlaliorr function pJ ( T) in particiilar i.; very sirnilar to the autocorrelation function fIomii Fignrc 17.6. In this casc, lio\vever, the Imear average i s
zero, which i s also visible from the sample furwtionc; in Figurc 17.4. 'Yhe dgnificantlt. faster changes in the t ~ ~ i ~ ~ e ~ of:
a vrnncEoiii
i ( ~ i process
~r
f3 in Figurc 17.4
are also expressctf by i~ fastei deray of the a u t ~ ~ c ~ ~ ~ r l cfunction
a t i o r i p q uz)
J from
its maxiiniim valrie in Figiiic 17.7. The r ~ ~ ~ ~value
~ i P ,~~ ( O~ ) ~itself
~ iis reyuill
i
to

i