Examples of .r;mdorn signals in tlectroiiict.. When the signal form it,sdf caiilrnot be iiiathematically dcscribed, it raii still be mexsiir~d and a graph can be nbtaiiied, for examplc,
Trang 13c14 17 Drscribing Ilaridoni Signals
Sigiials that ltevr unknown behavioin arc called r w t - d e t e r m 1 r 1 1
.siochastic supals or runrlorrh szqnals Examples of r;mdorn signals in tlectroiiict are
~ ~ ~ t ~ ~ r f r r ~ i i ( ~ ~ ~ signals like antenna, noise, ax er distort ion or tf.lrrmaI resistawe noise, hut uuefril signals c a i ~ also he stoch I 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 ~ ~ ~ t ~ o i i con4,eiit in
TO describe rantiorri signals we cnn first of all try to Start wirh tlir signals thein- stIlvcs When the signal form it,sdf caiilrnot be iiiathematically dcscribed, it raii still
be mexsiir~d and 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 c d c i i l a l c ~ 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 ~ l i ~ e r arid c*alctrlatc 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 do very little
with an output sigiiai calculated from i t
Thc solution to this problc~ii is found not? by considering individual random signals hut instead by ttnalysiiig the procew that, procliacrs the signals In oiir exampie it2 nieaiis that, we should derive general st#alemeuts abottt the noire bc;- havioiir Of coursc, it is inipossiblc to know the miise iignals in individual ampli- firm 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 1 he rmdorn process that prodncrs t k signals as only it giws iiifoi~~~iatiO~i 0x1 all its sample fimctions