北京邮电大学：《通信系统原理》课程教学课件（PPT讲稿）第七章 模拟信号的数字化传输（1/2）

·第七章模拟信号的数字化传输7.1 引言模拟信号(指连续波)要在数字通信系统中传输。要解决的几个问题：1．模拟信号的数字化问题：抽样，量化，编码2．多路复用问题：时分多用3．本章的任务：介绍抽样定理，脉冲振幅调制PAM，量化原理IAM介绍两种脉冲调制方式：PCM和增量调制介绍模拟信号的数字传输TDM介绍语音语音及图象的压缩编码概念（了解性）

• 第七章 模拟信号的数字化传输 7.1 引言 模拟信号(指连续波)要在数字通信系统中传输。 要解决的几个问题： 1. 模拟信号的数字化问题：抽样，量化，编码 2. 多路复用问题：时分多用 3. 本章的任务： 介绍抽样定理，脉冲振幅调制PAM，量化原理 介绍两种脉冲调制方式：PCM和增量调制（ M ） 介绍模拟信号的数字传输TDM 介绍语音语音及图象的压缩编码概念（了解性）

Baseband pulse and digital signaling:Introduction:1. How to encode analog waveforms into baseband pulsesignals (sampling)2. How to approximate analog signals with digital signals(quantizing)3. How to process the digital baseband signals so that theirbandwidth is minimizedFour main goals :1. Principle of PCM2.( Spectrum of digital signals)3. (The filtering effects on the digital pulses)4. TDM--time-division-multiplexing

• Introduction: 1. How to encode analog waveforms into baseband pulse signals (sampling) 2. How to approximate analog signals with digital signals (quantizing) 3. How to process the digital baseband signals so that their bandwidth is minimized Four main goals : 1. Principle of PCM 2.( Spectrum of digital signals) 3. (The filtering effects on the digital pulses) 4. TDM-time-division-multiplexing Baseband pulse and digital signaling

·A digital transmission system for analog signal:PCMsignalM levelAnalogsamplingencodingsourcequantclockPCMsignalTransmis-ChannelWc(t)Wout(t)Receiverfiltersion filterfilter Hr(f)H(f)Hc(f)Analog outputnoisefilterLPFsamplingdecoderQuantizedPAM

•A digital transmission system for analog signal: PCM signal Transmis￾sion filter HT(f) Channel filter HC(f) wc(t) Receiver filter HR(f) wout(t) noise Analog source sampling M level quant. encoding PCM signal clock filter sampling decoder LPF Analog output Quantized PAM

Pulse amplitude modulationPAM:Pulse Amplitude ModulationFirst step to digitalize an analog signal PAM:conversion of a time-continuous analog waveform to atime-discrete analog waveformIn sampling theorem,we use the sampling values ws(t) (time-discrete) (sampling from w(t) using sampling impulse or deltafunction train) and (sinx/x) orthogonal function to reproduce theoriginal function w(t) (time-continuous) without error.Here,wewill use another form (looks like sampling impulse) ofwaveform to provide the information necessary to reconstructW(t). Because the pulses are used,we can expect the bandwidth ofPAM waveform to be wider than w(t)

• PAM:Pulse Amplitude Modulation • First step to digitalize an analog signal • PAM:conversion of a time-continuous analog waveform to a time-discrete analog waveform • In sampling theorem,we use the sampling values ws(t) (time￾discrete) (sampling from w(t) using sampling impulse or delta function train) and (sinx/x) orthogonal function to reproduce the original function w(t) (time-continuous) without error.Here,we will use another form (looks like sampling impulse) of waveform to provide the information necessary to reconstruct w(t). • Because the pulses are used,we can expect the bandwidth of PAM waveform to be wider than w(t). Pulse amplitude modulation

w(t) baseband signal (BHz)ws(t) baseband pulses↑pulse samplingFrom sampling theorem,the sampling rate is f≥2B (Nyquistrate).The impulse sampling is:Ws(t)w(t)产Two classes of PAM signalsNatural sampling (gating)Instantaneous sampling (flat-top)

• w(t) baseband signal (BHz) ws(t) baseband pulses pulse sampling From sampling theorem,the sampling rate is fs≥2B (Nyquist rate).The impulse sampling is: Two classes of PAM signals: Natural sampling (gating) Instantaneous sampling (flat-top) t w(t) ws(t)

Natural sampling(gating): Definition:If w(t) is an analog bandlimited waveform(BHz),the PAM signal that uses natural sampling isw,(t)=w(t)s(t)where s(t)=ZII[(t-kT,)/t] and f=1/T,≥2BTheorem:The spectrum for a natural sampling PAM signalw,(t) is:W,(f)=F[ws(t)]=dE(sinnd/πnd)W(f-nf,)where f= Ts,d is the duty cycle of s(t) (d= t/ T,),and W(f) isthe FT of w(t).Proof: Ws(f)=W(f)*S(f)and we have s(t)'s Fourier series:s(t)=cnej2元nfs and cn=d (sin元nd/元nd)

• Definition:If w(t) is an analog bandlimited waveform (BHz),the PAM signal that uses natural sampling is ws(t)=w(t)s(t) where s(t)=∑∏[(t-kTs)/τ] and fs=1/Ts≥2B • Theorem:The spectrum for a natural sampling PAM signal ws(t) is: Ws(f)=F[ws(t)]=d∑(sinπnd/πnd)W(f-nfs) where fs= Ts ,d is the duty cycle of s(t) (d= τ/ Ts),and W(f) is the FT of w(t). Proof: Ws(f)=W(f)*S(f) and we have s(t)’s Fourier series: s(t)=∑cne j2πnfs and cn=d (sinπnd/πnd) Natural sampling(gating)

So:S(f)=F[s(t)]-Zcn8(f-nf,)Ws(f)=W(f)*S(f)=d(sinnd/元nd)W(f-nf,)w(t)s(t)Baseband analog waveformSwitchingwaveform (d-1/3)Ws(t)Resulting PAM signal

So: S(f)=F[s(t)]=∑cnδ(f-nfs) Ws(f)=W(f)*S(f)=d∑(sinπnd/πnd)W(f-nfs) w(t) t Baseband analog waveform s(t) T t s τ Switching waveform (d=1/3) ws(t) t Resulting PAM signal

Generation of natural sampling PAM signal and itsspectrum:Analog bilateral switchw(t)ws(t)s(t)Generation ofPAMClockWs(f)[ W() |d|sin(元tf)/元tfd=1/3fsffB-BMagnitude spectrum of ws(t)Magnitude spectrum of w(t)

• Generation of natural sampling PAM signal and its spectrum: w(t) ws(t) s(t) Clock Analog bilateral switch Generation of PAM f │W(f)│ -B B 1 Magnitude spectrum of w(t) Ws(f) f fs d│sin(πτf)/πτf│ d=1/3 Magnitude spectrum of ws(t)

: For this example with d=1/3,the spectrum is zero forf-±3fs, ±6fs....So the choice of d will infect the resultingspectrum.The null bandwidth is 12B (3f.).So PAM signal sbandwidth is much larger than the bandwidth of theoriginal analog waveform .If f≥2B, no overlap of spectrumAccording to Ws(f),we can use an ideal low-pass filter torecover the original waveform w(t)LPFW(f)d / sin(πtf)/元tf |d=1/3fsfRecovering w(t) from ws(t)

• For this example with d=1/3,the spectrum is zero for f=±3fs ,±6fs ,.So the choice of d will infect the resulting spectrum. • The null bandwidth is 12B (3fs).So PAM signal ‘s bandwidth is much larger than the bandwidth of the original analog waveform . • If fs≥2B, no overlap of spectrum • According to Ws(f),we can use an ideal low-pass filter to recover the original waveform w(t). Ws(f) f fs d│sin(πτf)/πτf│ d=1/3 Recovering w(t) from ws(t) LPF

Demodulation of a natural sampling PAM signalAnalogmultiplierWs(t) PAMCw(t)(Gating)LPFH(f)H(f)Localoscillatorffco-fco

• Demodulation of a natural sampling PAM signal LPF H(f) Local oscillator ws(t) PAM (Gating) Analog multiplier Cw(t) f H(f) -fco fco