桑林半学期课件第4章模拟调制

1广义平稳随机过程M(t)~RM,PM(f"f>W PM(f)=搬移，其频带在中心频率fc(fc»W)ct=Accos(2pfct+fc2

3mtst)Acoswctf0ttcostAtft幅度调制：Att相位调制：ft随mt成比例变dft

随mt4smt)Acmtcoswctf0mt)∼Ac,wc,f0∼假定mt)«Mw w

w+w

e

+Mw-w

ejf0f0=

AMw+w+Mw-w2 5·htmt) s·ht

htwwcttcoswt w)=1Mw+w+Mw-wHw 2

mt,mt,ht不同

SDSB(t)=m(t) cos(wct+θc

m(t

Accos(wct

t=m(t=m(t)c(t)7mtsmttwctst=m(t)c(t)=Acm(t)cos(2pfct+fctAcm(t8mt)cosWct)=Asinwct =T=W

ATt-9m(t M(ft C(f

Acd(f-f)+d(f+f) ttctS(f)=M(f)*C(f

2 c=M(f)*Acd(f-f)+d(ff2f=

M(f-f)+M(f+f2 带宽扩展

fif˛fc,fc+Wf˛fc-W,fc例.已知m(t)=acos2pfmt和ct，fm st=m(t)c(t)=Acacos2pfmtcos2pfc

fc==Acacos2p(f- )t+cos2p( + )t

Acad(f-f+

)+d(f+f-

)

Acad(f- - )+d(f+ +

m

(t)=Acacos2p( - (t)=Acacos2p( + 2 2m(t)fiM(t),s(t)fi PM(f)~广义平t=s(tM)cos =s(t== c

∼Tp2

2 -

R(t)p

R(t,t 2

A2 AcR(0)=c (0)=cm2tAc

(0)m2t：基带信号的 平均功率Ps

=

A A

+

(f+f 4例4.2.2M(t)均值为零ff

P(f)=1-F,

£

< A2

0,f-f-

>,f-F<f<f+4

A2Ps(f)=

1-f+fc

,-f-F<f<-f+4

0,r(t)=s(t)=Acm(t)cos(2pfct+fcr(t

pft+f

tcos

-f+m(t)cos4pft+f+f 2

yt=1Amtcosf-f

-f= yt=1Amt st)=Acmtcoswct+Apcoswc

A2

p<

m2(t

直 调制信

SAM(t)=[m0+m'(t)]cos(wt+θ m'm'f

SAMt∼t+'t

htt=tcost要求mt)£ 1+mt>a=mt)£mt

mt

mt)=() m()

\st)Ac1amnt2pfc ~调幅系数a£已调信号的包络与调制信号成比例变化 mma<

a>若a> ttt.t=20cosp，求mnt和调制指数a.st)=1+0.1cos3000pt+0.5cos6000ptsp105tmta=mt

=0.1+0.5=()mt)=mt() m

0.1cos3000pt+0.5cos6000ptmt‹fiM(f)mnt‹fiMn(ftt=Accos2pfct+ tcos++ (f-f+ (f+f2

22st=5cos1800pt20cos2000pt5cos1)st=2010.5cos2p100t)cos2p1000tt fm=ct)=20cos fc=Ac= a= tS(f=Acd(f-f+d(f+f+Acad(f-f+ 2 +d(f-fc-fm+d(f+fc-fm+d(f+fc+fmP=

Aa

·4= P=

·2= 2 2 m(t)fiM(t),s(t)fi PM(f)~广义平t=1+)cosS(t

1+m(t)cos2pfc}Accos2pf

∼Tpfcfs(t1)1 22

2 -

2 R(t)p

R(t,t 2

c1+ A AR(0)=c1+ (0)=

1+a2R 2 2

R(0)=c1+a2 (0)=c+ca2

2

> >

ca22Mn2M

a2 M M1+a2

a2M=nM=1+a2 c1+a2

A2 P(f= Rt)=

1+

2 4= c4

(f-fc+

++ ssAMt·tmot2pmat)=s tcos2pt2pcos2p=

1+mt1+cospft o to2

t

1mt2t=1+)cosmt)£ Ac1mt0~yt=g1+g2mtg1~直流部分g2~增益因 4.2.3单边带调幅(SSB

HLSB(fHLSB(f1-f

sgn(fsgn(f-fcf (f)=1sgn(f+ )-sgn(f- 2

SLSB(f)=SDSB(f)HLSB(f= M(f+ )+M(f- 1sgn(f+ )-sgn(f- c

2

∵sgn(f+fc)M(f+fc)+M(f-fc=sgn(f+fc)M(f+fc)+M(f-fc-sgn(f-fc)M(f+fc)+M(f-fc=M(f+fc)-sgn(f-fc)M(f-fc\ (f)=AcM(f+ )+M(f-

tcos

+

M(f+ sgn(f+ )-M(f- sgn(f- Acˆtsin 4.2.3单边带调幅(SSBt=tcoscˆtsin又 HUSB(f=1-HLSB(ft=tcoscˆtsin4.2.3SSB信号的产生——smmm(t)·4.2.3例SSB信号的产生——+sm+-2ˆ-2–ˆ-USB4.2.3单边带调幅(SSBmtcos2pfmt，ct=2Accos2pltsin2psLSBt=Accos2pfmtcos2pfct+Acsin2pfmtsin2ptsUSBt=Accos2pfmtcos2pfct-Acsin2pfmtsin2pfctfctsDSBt=sLSBt+sUSBttt=2Accos2pfmtcos2p4.2.3单边带调幅(SSB PM(f)~广义平sSSBt=AcMtcos2pfct–Acˆtsin2p =AcRe

t

tej2pfctRt=A2 s2pft n2pf c

f<(f-f+ (f+f f>

2 (f-f+

(f+f

f<

= =A2

=1

ct

>t

4.2.3单边带调幅(SSBrt

·2p

yott=t=tcosyot=sts2pfct+f=1Amtcosf∓1Aˆtsinf 单边带调幅(SSBt=tcosˆtsintˆtsintcost

c=12mt)m2t)12mt)m2t)ˆ2tA++

q =arctgˆt)提取包络：at=x1时，1+x»x1时，1+x»1+

2mt

，()

+mt= 1+

»A+mt残留边带调幅(VSBsVSB=

AcM(f-

+

2 H(f=4.2.4残留边带调幅(VSB残留边带滤波特性H(f= f-

+

t=tcosf+f

+M

Hf-

+

+Mf+2

Hf+f4

4

fifi c04 f- + f+cc,fHH(ffc+H(ffc=常数,f£4.2.4残留边带调幅(VSBHH(ffc+H(ffc=常数,f£离散大载波VSBAM作业：P1214.4

smt+smt+nt

ttcoswctsinwc tcost =s2

ttt

=n2t)=N

SN=m SN=mt2i i() o oS 2o()N2o o()G=Ni4.4AWGNttcoswctsinwctcostPnPn(f-fffN0 Pn(fcfs =s2s

Pn= =

=N sDSBt=Acm(t)cos(2pfct+fcttcostsin= 02N =NSPR= c2i =N0B=ittcos(2ptcostsin2p=1Am(t)cos(f-f)+1ntcosf+ntsinf

2 f=fc

1Am(t)+nt2 2yt)=1Am(t)+nt 2 P= P= oP= o= NS4 Pn=Pn=N0B= S N N= =G= SN

=2N sSSBt=Acm(t)cos2pfctˆ(t)sin2pfcttˆtt+tˆt-t = =R=N S =N0B=i=PR =NS=PR =NS2

=1Amt+ntPo= c4 =1 = NB=1N GG=比较DSB-SC与SSB-SC = 若解调器输入端DSB与SSB信号的平均功率PR相同，且输入噪声双边功率谱密度N0/2相同，则有=N0N N=N0N N t=tt=ttctts2ptsinA2 R2ni00\ = c1+a2 R2ni00

=

B=2N相干解调

yt=1A1+amt+nt c y't)=1Aamt+1nt M SM

Aca=

a2 N

1

1+a2 N

Mn S

a2

=h N

1+a2 N N a2调制效率

MnMM其中 Mn

m2t(mt (

= (mt (

Ma= =M

3Ma=Mn

c1+ n+ c(2+2st)t=ctc1+ n+ c(2+2st)Vrt大信噪比情况

nst)Ac1+amnt

Vrt»Ac1+amntnctyot=Acamnt+nct结论：大信噪比下，包络检波的性能与相干解调相同小信噪比情况c1+c1+m t(2+ t+22nct)+2Acnc+amnt

t nct或nst 12n(2A t 21+amtn()n»

VV

x1时，1+x»x1时，1+x»1+

tnnn

2t)

n=Vtn

t

tnVnt) n4.4抗噪声性能(例t，RM=10000t,2

mt)6,信道衰减80dBN

要求SN

50dB.试求各调制方式下的PT及Bc解

W= 10logPT= S

PT=10

N N

N

= =

=50dB=T\P=2·105WTBC=2W= 4.4抗噪声性能(例

S

= =

=N

N

T\P=2·105WTBC= =AM，调幅系数

SN =N

N

=h =2M( M( mt MMh

=RM)= 0.82·= 0.22

0.22·PT=

1+0.84.4抗噪声性能(例\PT=Bc=2W=st=Ac1+0.8mnt2pfctA2AP=

=

2 Mn

=M M

Ac=\st=1189.71+0.8mtcos2pf 作业：P1244.11st=Accos2pfct+ftqt=2pfct+ftt

t=

+1

调相系统ft=kpmt

ft随mtDf= dft=kp dmt 调制指数：bpDfmaxkpmaxmt

mt线性变化Df=1df=kmt2pdt t

fft=f

t

=

=

mt

W~m(t)W W例mt=acos2pfmt, ct=Accos2p

ft=kpmtst=Accos2pfct+kpacos2pfmtbp=kpafFM:ft=f

mtttt

kffm

st

pft

kf

sin2pfAccos2 fm b=

mt)k=fm

\st=Accos2pfct+bfsin2pfmt kpmt ft=

mttttkp t+f=2p kfmt st=Accos2pfct+ft：ftst=Accos2pfctcosft-Acsin2pfctsinft»Accos2pfct-Acftsin2pt若ft=2pkA

mt

AckfM(f-fc

M(f+fcS(f)= cd(f+ +d(f-

f-f f+f KFKFdt·2+sNBFMt=t==ReAej2pfctejbsin2pfmt m ∼周期函数T=1 m1Cn=0

fmejbsin2p e-j2pnfmt=

2p

nbn

=

Jbej2pnfmnns

j2pnfmt j2pfct(=ReAcJnb bcosfctnS(f)

nnn

b

+d(f+fc+nf

kb¥1)2

n+

Jnb= kJnb

kk+

b=J-b；b=-b¥nn

J2bb1时

b

b2

;

b当n>b+1时 b 10.5

J J40-0.0

10ntbcostnS(f)=AcJb)d(f-f- +d(f+f+ 2 2nmt为单频信号，但已调信号却有无限多频率分量n=0：载频分量J0b,fc处;n0：边频分量Jnb,对称分布在载频两侧，间隔为fmn的增大使得Jnb逐渐下降，n>b+1的边频分量可忽略.有效带宽：Bc=2b+1)fm 宽带调频b>5)Bc=2b+ Hzb1时,Bc»2fm,只存在fc fc–fm分量 ~窄带调频J0=-0.260, J13=0.339, J23=0.486, =0.309,3=0.132.SFMSFM(f)J-2J2232-2J42cfc0JJf 1 2tbcost2S(f)=Ac2

b +d(f+f+ ¥nn¥n

P=

t

c =

J

sA2A =

J2b

2n=-

c 边频功率：PfPs=Pc'+Pf

= cJ2n2n

b·2=A2J

b变化时，角调信号总功率不变，但Pc'、Pf' 例mt)cos20ptct)10cos2pfct.调频,kf50.求st=Acos2pft+ m =10cos2pft+2p·50· cos b =k

mt)fm

=50·1=t=bcosts

+AN2AN 2n=-

JAn25=99%·JAn2NJn025+2·JJn0

5=N=Bc=2Nfm=2·6·10=

.f0fVCO==Acftsin2pft)

nfc-nft)==c

w1

DwDwβ·n1Dwn1DwsFwwcwc=n1w1-wDw=n1DwβF=n1F1

(t)=Acos[w1t+f(tsF(t)=Acos[(n1w1-w2)t+n1f(t4.3.3 t m st)=-Aw+ mtsinwt+ m

4.3.3调频到调幅的变换2：使用调谐电路的上升频率特性鉴频器带宽/解调器输出噪声带宽：已调信号带宽cc4.3.3调频负反馈解调 f =fc-ft cos2pft+2p tdt

(t)= cos2p t+2p

t

- te(t)= cos2p t+2pt

t

t IF

-

- m(t)= m(t

m(t)=k

m(t 1+ke(t

1 cos22f IF2f

k t+t+2p -¥mt)dtt+vkf 4.3.3tt=t ft=2pkt

mttsot=

t

fot=

vtet=1AAsinft-ft

»1AAft-ft

o fet4.3.3

=j-t fet-fot

vt

=j(f-kvV(f2pk2pkvtv=jf-jfje(f)G(fV

=

)G

)= Gk

)jf若

G(f) <=<

vt)= dft)=kf mt 作业 4.5.1角度调制的抗噪声性能S

限幅Si 限幅Si

SiNNi

ni(t)=Vn(t)cos[wct+qnA2Si= AA2

i= Ni=

FM

Ni 2noBFMSi(t)+ni(t)=Accos[wct-2pKFMf

+Vn(t)cos(wct+qn

Accos(wctj(ta1Vn(tcos(wct+qn(ta2B(tcos(wct+y(t)aaaa2ffAc>>

11

Vn(t)sin(qn(t)-Ac+

(t)

-»f1+

Ac

sin(qn(t)-»f1

Vn(t)Ac

sin(qn(t)-V(t)=kd

df(t)=kddj(t)+d{Vn(t)sin[qn(t)-

2p

So(t)

kd

f

=K =K

设：K

nd(t)=Vn(t)sin[qn(t)-

no(t)

dnd

-

k

A2k A2Pno(f)=

|H(f) ( )2=no

f

|f|£

W Pn(f)df

-

22S 3A2K2f =

= |f(t) 22}A2

=3

max W

|f(t)

So 3AcK

S b2 P

|f(t) n 增益

=So No

=3

FMSi Ni

|f(t)

W=

B

=2(1+b2

|f(t)

(1+b)»3b yt)=wt+qt+ -t t+-t»wt+qt+ -t Vt) A

i= = =10 no2(bFM+1)Wo ( =20(b+1)onW门 调频常规调幅调制指数 =输入信号功率Si| Si| (AM有效功率只有13)输入噪声功率Ni| =noB =2no(1+b )fNi| =noB =2nof解调增益 (1+ 2调制带宽B =2(1