Modulation:FM5PM
Angle
n(t) A,COS(2Tfc+
u(t)
0(+)
Kp/k
filt) f, + +(H)
+
=
(PM)
P(=(imacerate
*
ofmax
max[/mcHl]
(PM)
max[/m(x11]
(FM)
W
=
=
II fr
Angle-Mod:
Approx:COSO(H
↳
=15
if
(H
very similar
=>
Angle
Mod.
actual
by
CHO(H
1
to
conventional AM mod.
sinusoidal
bandwidth is
finite
a
a
Sin
effective
but can
site
define
bandwidth
sel's
EAcJn(B)cos(2A(f ntm)t)
+
UCH
=
Frequencies:f, thtm
- -
n
#
=
harmonics
of
Jn)P
En!
J-n1)=
EEnee
A5n()
=
Le
bharmonics:
right, cleft
one
13
to E
at
↳E
5) J, ) 2Ti
=
+
e
after
(ie
the
tifu
deviation
Max
-
constants
frequency
phase deviation
Max
freq.
in
PM
deviation in FM
modulation
bandwidth
max[(mit)
=
x
=
* Narrowband
-
I
=
=
->
a
Pmax
max/m(t)]
30 k max[/m(+1)
Bp kp
phase/freq.
instantaneous
Bp/++
=
=
->
Ofmax
akp,B1 a
Bp
-
Amaxe
(FM)
K,
=
fi
(Fi
(PML
P(=(am
~Omax=Kp
modulated signal
+
+
=
indices
of mit
CH. C
r(t) x(t) +n(t)
f
i
n
i
Meet
57(x) p(x)
stationthe
sense
=
Atten. Channel:90dB
fa(x)
PDF:
PR & P+
=
①BASE BAND
F(b) Fx(a)
↳ also
-
written
*
(f)df
=f
fix) 0
Sn1) FT(RwI))
PDF
=
ot
fax-
, (t) (
G(m,02
*
AWGN
=
=
⑫B
****
-1(n(t)) fSnlf) et
=
(additive White
G.
CONST.
③-
placx)
1fxd*
>
x (x) -
=
(f) y
p(x(x) 1
p(12 x)
=
-
h(+)
=
y(t)
->
k
em
-
=
Pr AcPm
Pr Nok
=
=
G(0,1)
(m 0,0 1)
=
=
p(x) 1onesix=
H(0)
mx
=
ESXCH] g+
TM)=
=
p(2x35) Q(5)
=
-
QC
#
p(xx 1) 1
-
=
-
unitymeant
m
Q(l)
=
[1 a2Pmn)
=
+
Prcuses(a2Pmn)
Pr NoW
=
E(x1x< ] (E)
S*f,
=
P(i)Ixi-m
=
=
f(x-mifax
-
E [x]
=
-
de
m2
Average:
ESxCH] Sx1 f(x)dx=
=
TME Average:
*
=
Ix1Hdt
fxf(x)
-
ax
[rit?
xxs ):
**
variance
statistical
A
xcmctl
=
=
=>
matmct)
Pmn=
P
Expectation
E[IX-ml]
m(t)
Mn(H) =
0.e
*
ECE)
m
=
to en
m
=
logscale
9
IPress are
aiBiennainitiate
intern
my
Gaussian PDF
NORMALIZED
*
logscale
are
=>
=
3
amwe
-Sir(meie
df
=
()
I
Noise)
bc BW 00
PN 08
-
FM
2k
->
=>
*
=
RNIt) e DY
power spec density:
IP => + 3
IP
Pr Pm
Rild
=
gives
=
NO MOD
-
(SmIf)
Rm(t) 16sinc (10xt)
i
RElt,;(z)
POWER of NOTSE
2
=
=
Gaussian
=
=
Of f(x) 1&
log (I (
90 10
I
p(acx =
b)
xPm
=
-
wt anot
time