Lecture3AmplitudeModulationIILecture3†常规双边带调幅(StandardAmplitudeModulation)†抑制载波双边带调幅(Double-Side幅度调制IIBand,DSB)AmplitudeModulation†单边带调幅(Single-SideBand,SSB)†残留边带调幅(Vestigial-SideBand,VSB)F（ω+ωC）/2SDSB(ω)F（ω-ωC）/2ω-ωc+ωmωcSSB频域-ωc-ωm-ωC0ωc-ωmωc+ωmSSB频域SUSB(ω)‡正负符号函数ωωcSSB—USB/LSB-ωc-ωm-ωC0ωc+ωmSgn(ω)=1|ω|>01HUSB(ω)-1|ω|<0B=f=BSSBm‡以下边带为例ωωcη=100%-ωC01SLSB(ω)S(ω)=[]F(ω+ω)+F(ω−ω)DSB2ccω1-ωC-ωc+ωm0ωc-ωmωcH(ω)=[]Sgn(ω+ωc)−Sgn(ω−ωc)HLSB(ω)21ω-ωC0ωcSSB频域SSB频域SSHSSB()ω=DSB()ωω()1=++−⎡⎤FF()()ωωωω12⎣⎦ccSFSgn()ωωωωω=+[()(+)SSB4cc1⋅+−−⎡⎤Sgn()()ωωωωSgn−−FSgn()()]ωωωω−2⎣⎦cccc11=+[(FSgnωωωω)(+)+−++[(FFωωωωcc)()]4cc4+−FSgn()()ωωccωω+−+FSgn()()ωωccωω−−−FSgn()()]ωωccωω−1SSB频域SSB频域SDSB(ω)F(ω+ωc)F(ω-ωc)F(ω+ωc)Sgn(ω+ωc)F(ω-ωc)Sgn(ω+ωc)-F(ω+ωc)Sgn(ω-ωc)-F(ω-ωc)Sgn(ω-ωc)ω-ωC0ωcωωSgn(ω+ωc)-ωC0ωc-ωC0ωc（a）（b）F(ω-ωc)Sgn(ω-ωc)ωSSSB(ω)-ωC0ωc-1-ωCω0ωcωSgn(ω-ωc)-ωC0ωc1（a）+（b）F(ω+ωc)Sgn(ω-ωc)ω-ωC0ωcSSB的时域表示SSB的时域表示希尔伯特(Hilbert)变换1F−111∞f(τ)[]F(ω+ωc)+F(ω−ωc)⎯⎯→f(t)⋅cosωctfˆ(t)=∫dτ=H[f(t)]42π−∞t−τ1[]F(ω+ω)Sgn(ω+ω)−F(ω−ω)Sgn(ω−ω)Fˆ(ω)=F{H[f(t)]}=-jF(ω)Sgn(ω)4cccc希尔伯特滤波器H(ω)=-jSgn(ω)1h=−{}F(ω+ωc)[][]−jSgn(ω+ωc)−F(ω−ωc)−jSgn(ω−ωc)|Hh(ω)|φ(ω)4j1π/21−11=−[]Fˆ(ω+ω)−Fˆ(ω−ω)⎯F⎯→=fˆ(t)sinωt4jcc2c0ω0ω-π/2SSB的时域表示SSB调制—滤波法−1FSSSB(ω)=SDSB(ω)H(ω)∴SLSB()ω⎯⎯→11ˆf(t)SDSB(t)SLSB()t=+f()costtωcf()sinttωc22乘法器边带滤波器SSSB(t)同理C(t)=cosωt11ˆcS()t=−f()costtωf()sinttωUSB22cc2SSB调制—相移法SSB相干解调S(t)S(t)S(t)ˆSSB乘法器P边带滤波器dSSSB(t)=f(t)cosωct±f(t)sinωctf(t)乘法器f(t)cosωct本地载波cosωctˆStftSSB()=()cosωωctft∓()sinct-π/2-π/2ΣSSSB(t)⎡⎤ˆStp()==SSSB()tCtd()ft()cosωωωct∓ft()sinctcosctsinωct⎣⎦ˆftˆ111LPF1()f(t)sinωct=+ft()ft()cos2ωωt∓ftˆ()sin2t⎯⎯⎯→ft()乘法器22cc22Lecture3AmplitudeModulationII滤波法产生VSB信号†常规双边带调幅(StandardAmplitude‡关键:Hv(ω)的截止特性在|ω|=ωc点Modulation)上相对于1/2幅度点呈奇对称†抑制载波双边带调幅(Double-Sidef(t)SDSB(t)SVSB(t)残留边带Band,DSB)乘法器滤波器†单边带调幅(Single-SideBand,SSB)†残留边带调幅(Vestigial-SideBand,VSB