From Defiriil ion 24 it is ecluill 10 the time average m.. We will get to knoa the other expected values better in the lollowing sections, iu particaular t irv auto-correlatioii and cros
Trang 117.4 Correlation Funrtioiis 4 1 7
For the linear expected value, in accorilarrce with (17.lf, (17.14) arid (17.18) vie ohtaiii
T
(17.22)
As ergodir f u n c t i o n s arc sttitiwtiry, the finrar average p i s (iikc all other first
order expected valires) indeperitleiil of time From Defiriil ion 24 it is ecluill 10 the time average m AS LEE time average c m in t31iis case ktc iorincd from a i y sample
fimrtittn, the st~mplc f i ~ ~ r l , ~ ( ~ ~ iii ( 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-correlatioii and crosh-corrclation fiirrctions As me only use
second-order rxpectetl vaiizes LPL the f o r m of (1 7.20), we;lk crgodicitv i d 1 br A sufficiciit pic>-rccluisite
First WP cwnsider c o l d a t ion functions of purely r e d signals The restllts will latcr bc cxtencled to toinplex signals