Under the assumpi 1011 tliat these processes are also stationdry for the sectiorr shown, we can charac- ion function:, q z 2 P ailcl pvv t, shown in Figure 17 7.. The anto-correlaliorr
Trang 117.4 Correlathi Fimctions 41 9
i ~ ~value: ~ ~pZ2(~1) ~ = ~ i- ~p'' ~> pzz{z) ~ ~ r ~ i
Itmer bound: pJz( z) 2 -0; $ 11:
(17.3.1)
(17 35)
(17.36) hold for all ~ t ~ t i o i i a r y ranciom signals t ( l ) , but, (17.37) only holds when
distantly separ2zted values do rot correlate In Examplc 17.7, (1 7.37) does not
hold, for example,
Example 17.8
Iii Examplc 17.4 we corisidered two ranclom processes A m d I( -vc.liose saxxi-
p l ~ fiinctions c*lemly have statistical interdepeitdencies Under the assumpi 1011
tliat these processes are also stationdry for the sectiorr shown, we can charac-
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 riow-
srctionv throngh c p r z ( f i , t ~ ) and p z , v ( t l , t l ) in Figure 17.5, along the I I or 1 2 aAis
The anto-correlaliorr function pJ ( T) in particiilar i.; very sirnilar to the auto-
correlation 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 dgnif-
icantlt faster changes in the t ~ ~ i ~ ~ e ~ a v i ( ~ i ~ r of: rnncEoiii process f3 in Figurc 17.4
are also expressctf by i~ fastei deray of the a u t ~ ~ c ~ ~ ~ r l c a t i o r i function p q u J z) from
its maxiiniim valrie in Figiiic 17.7 The r ~ ~ ~ ~ ~ i ~ ~ ~ ~ i r i value P , ~ ( O ) itself is eyuill to
e t h a n with their auto-coir