北京邮电大学：《通信系统原理》课程教学课件（PPT讲稿）第四章 模拟调制系统

第四章 模拟调制系统·1.引言一调制的定义一调制的分类一线性调制原理一非线性调制----角度调制一调制系统的比较（抗噪声性能分析和比较）－ FDM原理一总结一重点：调制系统的抗噪声性能

• 1. 引言 – 调制的定义 – 调制的分类 – 线性调制原理 – 非线性调制-角度调制 – 调制系统的比较（抗噪声性能分析和比较） – FDM原理 – 总结 – 重点：调制系统的抗噪声性能 第四章 模拟调制系统

1.调制的定义: Definition:A baseband waveform has a spectral magnitudethat is nonzero for frequencies in the vicinity of the originand negligible elsewhere.Definition:A bandpass waveform has a spectral magnitudethat is nonzero for frequencies in some band concentratedabout a frequency f- ±f,where f>>0.The spectralmagnitude is negligible elsewhere. f. is called the carrierfrequency.f may be arbitrarily assigned.Definition:Modulation is the process of imparting thesource information onto a bandpass signal with a carrierfrequency fc by the introduction of amplitude and/or phaseperturbation.This bandpass signal is called the modulatedsignal s(t),and the baseband source signal is called themodulating signal m(t)

• Definition:A baseband waveform has a spectral magnitude that is nonzero for frequencies in the vicinity of the origin and negligible elsewhere. • Definition:A bandpass waveform has a spectral magnitude that is nonzero for frequencies in some band concentrated about a frequency f= ±fc ,where fc>>0.The spectral magnitude is negligible elsewhere. fc is called the carrier frequency.fc may be arbitrarily assigned. • Definition:Modulation is the process of imparting the source information onto a bandpass signal with a carrier frequency fc by the introduction of amplitude and/or phase perturbation.This bandpass signal is called the modulated signal s(t),and the baseband source signal is called the modulating signal m(t). 1.调制的定义

Diagram of a typical modulation system.modulationm(t)s(t)ModulatorBaseband signalBandpass signalCarriercosoctLocalModulatingoscillatorsignalModulated signal

• modulation Diagram of a typical modulation system m(t) Baseband signal Modulating signal Modulator s(t) Bandpass signal Modulated signal Local oscillator cosωc t Carrier

: Bandpass communication systems(t)m(t)ModulatorchannelBandpassBaseband signalsignal noisecosoctCarrierLocalModulated signalModulatingoscillatorsignalm'(t)DemodulatorCorruptedCorruptedbaseband signalbandpass signal

• Bandpass communication system m(t) Baseband signal Modulating signal Modulator s(t) Bandpass signal Local oscillator cosωc Carrier t Modulated signal channel Demodulator m’(t) Corrupted baseband signal Corrupted bandpass signal noise

2.线性调制系统·调制系统的分类：幅度调制（线性调制），非线性调制（角度调制）和数字调制(PCM)线性调制：AM,DSB-SC,SSB,VSB

• 调制系统的分类：幅度调制（线性调制），非线性调 制（角度调制）和数字调制（PCM） • 线性调制：AM,DSB-SC,SSB,VSB 2.线性调制系统

Complex envelope representationAll banpass waveforms can be represented by theircomplex envelope forms.Theorem:Any physical banpass waveform can berepresented by:v(t)=Re(g(t)ejoct)Ret.j:real part of .1.g(t) is called the complex envelope ofv(t),and f is the associated carrier frequency.Two otherequivalent representations are:v(t)=R(t)cos[0ct+0(t)]andv(t)=x(t)cos oct-y(t)sin Octwhere g(t)=x(t)+jy(t)=R(t) eje(t)

• All banpass waveforms can be represented by their complex envelope forms. • Theorem:Any physical banpass waveform can be represented by: v(t)=Re{g(t)ejωc t} Re{.}:real part of {.}.g(t) is called the complex envelope of v(t),and fc is the associated carrier frequency.Two other equivalent representations are: v(t)=R(t)cos[ωc t+θ(t)] and v(t)=x(t)cos ωc t-y(t)sin ωc t where g(t)=x(t)+jy(t)=R(t) ejθ(t) Complex envelope representation

Representation of modulated signals:The modulated signals→ a special type of bandpasswaveformSo we haves(t)=Re(g(t)ejoctthe complex envelope is function of the modulating signalm(t):g(t)=g[m(t)]g[.]: mapping functionAll type of modulations can be represented by a specialmapping function g[.]

• Representation of modulated signals • The modulated signals a special type of bandpass waveform • So we have s(t)=Re{g(t)ejωc t} the complex envelope is function of the modulating signal m(t): g(t)=g[m(t)] g[.]: mapping function All type of modulations can be represented by a special mapping function g[.]

. Complex envelope functions for various types ofmodulationType of modulationmapping functions g(m)AMlinear(?)A.[1+m(t)]linearDSB-SCAcm(t)SSBlinearAc[m(t)±jm'(t)]AcejDpm(t)PMnon-linearI m(t)dtjDfFMnon-linearA.e

• Complex envelope functions for various types of modulation • Type of modulation mapping functions g(m) AM Ac[1+m(t)] linear(?) DSB-SC Acm(t) linear SSB Ac[m(t)±jm’(t)] linear PM Ace jDpm(t) non-linear FM  non-linear − t jDf m t dt c A e ( )

Spectrum of bandpass signals·Bandpass signal's spectrum complex envelope'sspectrumTheorem:If a bandpass waveform is represented byv(t)=Re(g(t)ejoct)then the spectrum of the bandpass waveform isV(f)=1/2[G(f-f.)+G*(-f-f.))and the PSD of the waveform isPv(f)=1/4[Pg(f-f.)+Pg(-f-f)]where G(f)=F[g(t)], Pg(f) is the PSD of g(t)Proof: v(t)=Re(g(t)ejoct)=1/2 (g(t)ejoct+g*(t)e-joct)V(f)=1/2F (g(t)ejact)+1/2 F (g*(t)e-jact)

• Bandpass signal’s spectrum complex envelope’s spectrum • Theorem:If a bandpass waveform is represented by: v(t)=Re{g(t)ejωc t} then the spectrum of the bandpass waveform is V(f)=1/2[G(f-fc)+G*(-f-fc)] and the PSD of the waveform is Pv(f)=1/4[Pg(f-fc)+Pg(-f-fc)] where G(f)=F[g(t)], Pg(f) is the PSD of g(t). Proof: v(t)=Re{g(t)ejωc t}=1/2{g(t)ejωc t+g*(t)e-jωc t} V(f)=1/2F{g(t)ejωc t}+1/2F{g*(t)e-jωc t} Spectrum of bandpass signals

We have F(g*(t))=G*(-f)Then V(f)=1/2(G(f-f.)+G*[-(f+f)])The PSD for v(t) is obtained by first evaluating theautocorrelation for v(t)R,(t)==)+ 1/2Re)negligible?But Rg(t)= R;(t)=1/2Re)=1/2 Re(Rg(t) ejoct)Pv(f)-F(R,(t))=1/4[Pg(f-f)+ Pg*(-f-f)]But Pg*(f)= Pg(f),so Pv(f) is real

We have F{g*(t)}=G*(-f) Then V(f)=1/2{G(f-fc)+G*[-(f+fc)]} • The PSD for v(t) is obtained by first evaluating the autocorrelation for v(t). Rv(τ)==} + 1/2Re} negligible? But Rg(τ)= Rv(τ)=1/2Re}=1/2 Re{Rg(τ) ejωc τ} Pv(f)=F{Rv(τ)}=1/4[Pg(f-fc)+ Pg*(-f-fc)] But Pg*(f)= Pg(f),so Pv(f) is real