41 17.4 Correlathi Fimctions i ~ ~value: ~ Itmer bound: ~pZ2(~1) ~ =~ pJz(z) i~ p' -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 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 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 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