17 Drscribing Ilaridoni Signals 3c14 Sigiials that ltevr unknown behavioin arc called rwt-deter m r 1 siochastic supals or runrlorrh szqnals Examples of r;mdorn signals in tlectroiiict are ~ ~ ~ t ~ ~ rsignals f r r ~ like i i (antenna, ~ ~ ~ noise, ax er distort ion or tf.lrrmaI resistawe noise, hut uuefril signals c a i ~also he stoch 1x1 c.oinrnunications it is pointless already krrowii to the rcwiver Jn fact, for a receiver, the less that can bc predicted, the greatrr t h i ~~ ~ f ~ r i con4,eiit ~ ~ ~ t ~ino i i I TOdescribe rantiorri signals we cnn first of all try to Start wirh tlir signals theinstIlvcs When the signal form it,sdf caiilrnot be iiiathematically dcscribed, it raii still be mexsiir~dand a graph can be nbtaiiied, for examplc, in Figurcs 17.1 mid 17.2 It is mt known whether Fourier, 1,aplare or convolut ioii irifegrals of t h t random signalh exist, or whether the iiicthods nsrd to cdciilalc~the sp funrtiovi art> weii tlefined Even whc t existetice of an integral is certain, the r + sulting ;pcctruni or outpiit signal is again it randoni v:iriablc whose behaviour we caiinot rriakr m y genmal statements about IVe can for exampie, iiiterprrt the signal in Figiirc 17.1 as the noise of an ~ ~ n r ~ larid i ~ ec*alctrlatc r the response of a post-connect ed sy In Thcs kntm&dge of this output sigrial, however c'anitot he transtcrrrd to other sitnations, as another amplifirr of the same kind would produce another noise signal, rz ( t ) The first amplifier would aiso never repeat the noise 4gnaI x ~ ( t )so , we cnn very little with an output sigiiai calculated from i t Thc solution to this problc~iiis found not? by considering individual random signals hut instead by ttnalysiiig the procew that, procliacrs the signals In oiir exampie it2nieaiis that, we should derive general st#alemeutsabottt the noire bc;havioiir Of coursc, it is inipossiblc to know the miise iignals in individual amplifirm in advance liistcad, the typical noise ponver can be given, for example This h w two Ggnifisaiit admritages: the given noise power is a determinis;tic property which can br cdnilat.ed irt a norrnal way, it, is tiic same for all amplifiers of a particrtlar iiiotlel We need to introdiicc some nrw terms to extexid our discussion to general random signals A process that prodrtces random sign& will be (died a randoin pmctss The emttixety of all random signals that it, can prodixccb is caIIed an rnsernble of vandoni signds Iiidividiial rantioixr signals (e.g., x l ( t ) ,x z ( t ) , x7(t)in Figure 17.1) a r called ~ sample fur ons or retzlrsatzons of a random p~ocess.We will concentrate OKI he rmdorn process that prodncrs t k signals as only it giws iiifoi~~~iatiO~i 0x1 all its sample fimctions