41 - 17 Describing Naiidorii Sigiials - A ranclom process is callcd statoonnry if its statistical properties miot change with tinit This appwrs to be the case for 11ie two random processes in Figure 17.4, wliilc in Figure 17.2, it is clew that tlic linear expected value changes with tirnc For a precis(>definition we start with a second-ordrr cxpccted \-due as in (17,!3) If it is lorrrird froni a signal whose statistical properties not chaxigc with tirne, then t h e expected value does i i o l charigt if both time points tj nut1 t are shifted by the billne amount At: The expccted value does not depend ox1 the individual time points irtstcacl on thcir difference We c a i itse fliih pxoperty to titifine tl amid 12, but _ 23: Stationary tdom pi*oeesc as stationary z.f I f s second-order ~rpecttduulws only depend of ohswved tinre poznts z = tl - 12 - In (17.7) we cvtisidcred dctcrininistic signals as a spccial case of random signals, for which the linear cbxpec.tetl value is eqial to the current functrrm value This means that dctwninistic signals can only be stationary if they are rotistant, in nrinistic signal that changes with tirnc is thcrr)fore not statiorrery for tiirite random signals, as i?, signal tlial i s z ( m before or after H ical properties and cannot be stationary certain point in time changes its s From this cicfinition for ~ C C C d valurs we can derive t l r c properties of fiist omder expected v d l ( r ( t , ) ,r(t2))== g(r(t,))are a special case of se