41 I 17.3 Stationarv H mdom Processes Example 17.4 Figure 17.4 shows tvliicli pmperties ol a rarirlorri signal clre represenl ed by second-order expected values %‘lwrandom processes A arid B hm-r identical firstorder expected vatraes in particular their distribution function Fl,jt) (0)= Pf,!ti(@) (Example 17.2) Tlie sample frxiictions ttf random prnrcsh A chmgp mach morr slowly with timc, however, tlrtzri thosc of process B We can therefore expect a much greater t.aliir of auto-correlation firriction pZ5(tl,Cz) for A’s neighbouring e ~ a ~ iqoy~y (~f l ,t z > for 13 This i s values tl and 12 than for the ~ ~ ~ t o - c ~ ) r rfmction confirmed hy the measured ACFs shown in Figure 17.5 rand^^ process A rand~mprocess E3 - t * t Figure 17.4: Illustration of two raiidain processes A4and XJ with iderititat Emt-order expctt,cd values ancl differing becolid-orcler expected values Expected valucs of first- aiid second-order are by Iar the niosl important in practical applic‘ations Many descriptions of stocbastic funrtioiis rely d e l y on these two However, advauced models of complicated random processes resort! a140 to higher-order expccted values This ernergiiig branch of signal analysis i s therefore called lazqhar-order.stnttstacs In Section 172.1 we considered various possible methods for calculatiiig expected One of i h s e w a b expressing the ensembte inem with the timemerage The conditions tinder which this is possible will be explaitird in this section WI~LE~