Ranclom PoceS- Spectnad
Chanacienistics
Spet
and Hs
Dens ity
hayenlu
nho
pectnal pmopenties ofa deBenmnistiC Sianal )
spe
t h e F yaien
X
(t)
is also Xouh
as
gven 6
tnansfun mX(u)
he
ane
d
sPerHnum of (t).
Jwt
X(w) e
dw
atenpBing
in
to
(2)
to a
appy E¢(0)
ondom pnses,
inmediatly eNonten poablens
The
painc ipal
pnobleM is
4he fact thak
X{w)
may nit ems
of the noess Thus,
Funtuns
e
we
tene
nardom pno eesS
on mas of the sample
a
of
lon
cescnupt
a syectnad
beraue
COnclude th»t
is not Feasdle
spertnum
desBy
voltoge
a
ukihzing
ot eMSt.
Such a
specthum moy
Othen
pngbems
On the
aeip
Such a
f
othenhond,
}i0n
wtn
amjse
Of
the
we
powen
in
tunn
a
insteaol
of
FnequOn(y
oun
nondem
o
,
as
powen
y
densi
pnicess
volFage,
odoes exist
Scalled
af tenfun
hs
Funttlon
ane Msdcngl
tqansfons
iF Lapla/e
it
to the
AS a
neWt
tpeof
spectnum
Randum
Sprinum
df {he
thef
praeg
Spectum
hebwen density
nandom p0DC©S
Let x(t be a
Xt)
So
oW
=
Tt<TT
Ct)
elseuhent
long
as T
Is
has bonded
AT )
fnite,
The Founior
<w
X 1S
tnonsFom
XW)
satisfy
will
vaiatrun
h04t
pneSuMe thaf
we
(t)E
,) d
T
m CE)
contalned
The ehengY
Since n t )
Founien tnonsfopble,
ECT)Rdt
The
awenage
its
powel
ylw)]*dud
PT)
TT) s
PET)
the intonval (T, TLs
ehengy
Xy{®) y Panseal's theoneM
is
be nclatd to
m
tt)dt
n
Kt)
oven
the menval
xudw
27
hc point, C
tbeive. thod
lxJu)|?
ths
pen
T
rnum be cause
sity pectnu
hegnat
idn
pawen no sults Ahnou
HouWCen, it doS hat the funct on hat
ne ag
two
seek, fof
ons
d oes not ncpneset
) 1t
powen
in
an entine
Sample funckiun
1s
powel ih once sample fnrtun
the
dnly
*n
the paDCSS
I does nut nepnesent
prores
fon the nardlon
densrty
Spectnal
Hene, the pouwen
kmut 7>bo ard tok1rg
tk
setting
by
ton be dbta hed
value of Fq (1
ox enpected
2T
T
L
This uation
PCo CesSXE)
xx
avenage pouCN
the
oicaBes
be
ean
obtangd
by tak1n*
n
a nadom
avenage
of ts
Second mOmert
x
7
tat toy,
sHafiomay
w h d e - s c r n s c
thaf i
Fun aa pnoress,
pnoe
x?
ELxa=
af
is a
least
Hence
cunStart
spectlua
We
dehsity
t H H p O u E N _
Pxx
Pxy
we
I
by
obtained
S
defne
the
a
tnequency
powen
andoL
m pn0ess
i,
density
domalh
integnd (on.
fog tho
speIt u
EIKA)|7
2T
powen
narphoM
of the
poreS
eawenage
Px
)dw
Pacble
IF the nancloy
pnocess
s
nepnesentecl
as
xltJ= A,coswot te)
hene
uynd
(
A, Orc
wh ane
neal
dstnubudted
6n
VOiahle wn Fonply
avenoge
7hen, Find ot the
GivEn
xt)
=
1
Constavns and
the mtIval
pw
te)
A roswat
otte)
cus
ET A+A
2
AtA
2e) de
C o s wt +
(osh ut+20) de
han
t2) da
os t
os
ub t). cesae) Sn2wt) 5siM ®)e
usóstin -
Sinlt) Ftune)
2
0t Sin 2
Sinut-)
2
Hng
t
[ xH)
A
Ih
-Sirut)
eq"li)
A-A
).
Sin6ust
E[x#]}
7
LIm
ET
dt