cwmod02
TRANSCRIPT
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Summary: Continuous-wave (Analog) Modulation
Modulated Signal Mathematical Expression Bandwidth
(!)
"ype o# $e
-modulation
%igure o#
Merit(%&M)
Areas o#
Application
Double Side-BandSuppressed Carrier
(DSB-SC)
)cos()()( t t mt cSC DSB ω=ϕ −2 B Coherent 1 Radio Systems
AmplitudeModulation (AM)
)cos()()cos()( t t mt At cc AM ω+ω=ϕ 2 B Coherent or Non-coherent
m
m
P A
P
+2
Radio Systems
uadrature
AmplitudeModulation (AM)
)sin()()cos()()( 21 t t mt t mt ccQAM ω+ω=ϕ 2 B Coherent 1 Chrominance
!" si#nals
Sin#le Side-Band(SSB) )sin()($)cos()()( t t mt t mt ccSSB ωω=ϕ B Coherent 1 !elephoneSystems
Sin#le Side-Band plus Carrier
(SSB%C)
sin)($)cos()()cos()( t mt t mt At ccC SSB ω+ω=ϕ + B Non-Coherent
m
m
P A
P
+2
!elephoneSystems
"esti#ial Side-Band
("SB))sin()()cos()()( t t mt t mt c scVSB ω±ω=ϕ (1&2') B Coherent 1 !" Systems
"esti#ial Side-Band plus Carrier
("SB%C)
si)()cos()()cos()( t mt t mt At sccC VSB ±ω+ω=ϕ+
(1&2') B Non-coherent
m
m
P A
P
+2
!" Systems
reuency
Modulation (M) ))(cos()(
∫ ∞−ττ+ω=ϕ
t
f c FM
d mk t At 2(∆ f % B) Coherent (*++)
or Non-coherent 22
2
,
-
B
P k m f
π
Radio and !"
Audio
*hase Modulation(*M)
))(cos()( t mk t At pc PM +ω=ϕ 2(∆ f % B) Coherent (*++)or Non-coherent
m p P k 2 Radio and !"Audio
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'otations
• m(t ). m1(t ). and m2(t ) are baseband si#nals /ith band/idths 2π B rad0s or B &
• ωc32π f c is the carrier 4reuency in rad0s ( f c >> B)&
• )($ t m is the ilbert trans4orm o4 m(t ). de4ined as5 ∫ ∞
∞−
ττ−
τ
π=
π= d
t
mt m
t t m
)(1)(6
1)($
• ms(t ) is obtained by passin# m(t ) throu#h a 4ilter /ith 4reuency response5 )7()(8)( ciciQ H H j H ω+ω−ω−ω=ω . /here H i(ω) is the
9esti#ial 4ilter&
• :n the e;pressions o4 ϕSSB(t ) and ϕSSB%C (t ). the minus (-) si#n is 4or upper side-band (<SB) case and the plus (%) si#n is the lo/er side-band
(+SB) case&
• :n the e;pressions o4 ϕVSB(t ) and ϕVSB%C (t ) the plus (%) si#n is 4or upper 9esti#ial side-band (<SB) case and the minus (-) si#n is the lo/er9esti#ial side-band (+SB) case&
• SSB and "SB modulations are sometimes re4erred to as SSB-SC and "SB-SC&
• :n practice M and *M are not used in their pure theoretical 4orms& :nstead. a mi;ture o4 both schemes is used and the resultin# modulated
si#nal ta=es the 4orm ))()(cos()( ∫ ∞−
ττ−τ+ω=ϕt
c EM d t hmt At . /here h(t ) is the impulse response o4 a 4ilter called >pre-emphasis 4ilter>&
(Notice that i4 h(t )3k pδ(t ). /e #et *M si#nal and i4 h(t )3k f u(t ). /e #et M si#nal& u(t ) is the unit step 4unction&)
• ?M is de4ined as5 ?M 3 SNR o0SNR i. /here SNR i and SNR o are. respecti9ely. the si#nal-to-noise ratios at the input and output o4 the
recei9er& ?M #i9es the #ain (or loss) o4 the recei9er in terms o4 SNR&
• P m is the a9era#e po/er o4 the messa#e si#nal m(t ) and is de4ined as5 ∫ ∞
∞−
ωω
π
= d S P mm
)(
2
1. /here S m(ω) is the *SD o4 m(t )&
• ?M e;pressions 4or M and *M are 9alid 4or both narro/-band and /ide-band cases& o/e9er. ?M 4or AM may also be applied to NBM
and NB*M since the latter are similar to AM modulation&
• !he comparison bet/een M and *M per4ormances can be made by ta=in# the ratio ?M *M0?MM 3 (2π Bm p)20(m p@)
2& :4 this ratio is #reater
than 1. *M is superior than M. other/ise M is superior&
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