Wiley signals and systems e book TLFe BO 423

17. Describing Rmdorri Signals

408

random process A

random process B

Figuse 17.2: Randoiri processes A and I3 with a diffwirig distribution between thc indlviduitl smiple furletions

Taking the positive square root of the variancr giwt.; the standard deviutzorr
a z ( t ) . Variitricte and standard deviation are measures for the spread of the amplitudr around the linear averitge for a randnnl signal. The rttlldo~xrprocess A in
Figure 17.2 deariy has a lower variarice tlrrari random pro(
The linear average arid the variance are by far the most frequently used firstordcr pxprctcd values. When combined with second-order exp
sufficknt to chara rise many common random signals. For general raridorn signals it is possible to define inore first-order expected wliicv by choosing a different
f ( x ) in (17 3).

E

x

~ 17.2
~ ~

A general characterisation with firsbordcr expected values is obtained by
pntting
j ( z ) = E ( @ - ).
into (17.3) and determining tbr expected valuc dependent

011

tht. threshold 0. We

l