Unformatted text preview: E [ X t X s ] = E [ X t X s ] = R X ( s,t ) , and so we can write λ m φ m ( t ) = ZT 2T 2 φ m ( s ) R X ( t,s ) ds. Let us now resume our study of the correlation between X n and X m , which are coefﬁcients of X ( · ) according to the eigenfunction Φ , E [ X m X n ] = E h h x,φ m i h x,φ n i i = E " ZT 2T 2 x ( s ) φ m ( s ) ds ZT 2T 2 x ( t ) φ n ( t ) dt # = ZT 2T 2 ZT 2T 2 φ m ( s ) E [ X s X t ] φ n ( t ) ds dt = ZT 2T 2 ZT 2T 2 φ m ( s ) R X ( s,t ) φ n ( t ) ds dt = ZT 2T 2 λ m φ m ( t ) φ n ( t ) dt = λ m δ ( mn ) . 1...
View
Full
Document
This note was uploaded on 01/25/2011 for the course ECE 514 taught by Professor Krim during the Fall '08 term at N.C. State.
 Fall '08
 Krim

Click to edit the document details