Wiley signals and systems e book TLFe BO 432

4 17

17.4. Correlation Funrtioiis

For the linear expected value, in accorilarrce with (17.lf, (17.14) arid (17.18)
vie ohtaiii

T

(17.22)
i s (iikc all other first
order expected valires) indeperitleiil of time. From Defiriil ion 24 it is ecluill 10 the
As ergodir functions arc sttitiwtiry, the finrar average p

time average

m.

AS LEE

time average c m in t31iiscase ktc iorincd from a i y sample

fimrtittn, the st~mplcf i ~ ~ r iii
l ,( ~
f 7.22)
( ~ ~is rio 1c)iige~riidrkivf hy an iurkx (cnirrptiw
(17.18)}.
We will get to knoa the other expected values better in the lollowing sections,
iu particaular t irv auto-correlatioiiand crosh-corrclation fiirrctions. As me only use
second-order rxpectetl vaiizes LPL the f o r m of (17.20), we;lk crgodicitv i d 1 br. A

sufficiciit pic>-rccluisite.
First WP cwnsider c o l d a t ion functions of purely red signals. The restllts will
latcr bc cxtencled to toinplex signals.