Unformatted text preview: 33 Crosscorrelaticin and Crosscovariance  Let X(t ) and Y6) be random processes deﬁned on the same space with means pﬂt)
,uyt( ). The crosscorrglatzon gives a measure 0f how similar two diﬁerent processes/ /sig11a_ls are for diﬁerent points in time t 3 my D R)? U"; 3 t2) ELXK£JE£X3 [3523 Rhwtﬂ Ewwvme When two Sign de are independent of one another they are said to be orthogonal and Rpm/(t s)  0 for 11111: 5 e T. RWLJVHM Imam]? O“: 9.1m? hr} 7)! o The crosseomriance is given by}? CXYU, 3) : E {(XW  Mﬂtll (Y(5) '“ HHS)“
: szbf, S) — HXUWYiS) X(t) and Y(t) are said to be uncorrelated when C‘Xy(t 5) — (l for all t 5 E T As such t 5 (,5 I‘ll X "J independenj 010?
Rxﬂ )— MX( lie/(5) aRVl fulﬁl“ EEV‘jWI—Wﬂﬂﬂtﬂ Fer example, X (t) IS a. random process and Y(t) 18 independent mouse 4
Liv/t 35 f #41330 0 Example: consider tWo random processes X (t) and Y( (t) deﬁned below.
X03) = sin(t + G) Y(t) ': cos(t + B) whereBN Um’fmm(—7r 7?) 32> ‘F: _§T I‘(9 3‘.”le (a) What IS the mean function for X(t)? ...
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 Fall '07
 Carlton

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