Sampling,Quantizing and EncodingPCM signal generated from analog signal:three main stepsPCM signalM levelAnalogsamplingencodingsourcequant.clockPCMtransmitterAnalogoutputfilterLPFsamplingdecoderQuantizedPAMPCMreceiver
• PCM signal generated from analog signal:three main steps Sampling,Quantizing and Encoding Analog source sampling M level quant. encoding PCM signal clock PCM transmitter filter sampling decoder LPF Analog output Quantized PAM PCM receiver
Quantizer:M levelOutput:M levelInput:flat-topquant.PAM signaldigital signalOutput voltageM=8levelsInput voltageM=8, n=3 (3bits digital words)
• Quantizer: M level quant. Input:flat-top PAM signal Output:M level digital signal Input voltage Output voltage M=8levels M=8, n=3 (3bits digital words)
.Sampler and encoder:Quantizing levelsW(w(nTs))SamplingQuantizing error*quantizing noise (irreversible)see page 139 figure 3-8 cPCM signal output - serial binary codeThree-bit Gray code for M=8(page 140 table3-1)Mirror image -→ a better anti-noise performance
• Sampler and encoder: • Quantizing error quantizing noise (irreversible) see page 139 figure 3-8 c • PCM signal output serial binary code • Three-bit Gray code for M=8(page 140 table3-1) Mirror image a better anti-noise performance w(t) {w(nTs)} Sampling Quantizing levels
Bandwidth of PCM. Question: what is the spectrum of a PCM signal?From PAM and encoding processes,we known that thebandwidth of a PCM signal will depend on the bit rate andthe pulse shape.Bit rate*analog* sampling rate (≥2B)waveform's bandwidthBit rate+ quality of PCM signalPulse shapePCM signal's PSDCalculation: bit rate R=nf, (M=2n)we will learn that the minimum bandwidth for a PCMwaveform will be:BpCM>≥1/2R
• Bandwidth of PCM: • Question: what is the spectrum of a PCM signal? From PAM and encoding processes,we known that the bandwidth of a PCM signal will depend on the bit rate and the pulse shape. Bit rate sampling rate (≥2B) analog waveform’s bandwidth Bit rate quality of PCM signal Pulse shape PCM signal’s PSD Calculation: bit rate R=nfs (M=2n ) we will learn that the minimum bandwidth for a PCM waveform will be: BPCM≥1/2R
.Effects of noiseThe analog signal, recovered from PCM signal,is corruptedby two kinds of noises:1. Bit error produced by channel's gaussian white noise andimproper channel filtering (ISI)2. Quantizing noiseOne formula for average S/N calculation:(S/N)out=M2/[1+4(M2-1)P.]where M is number of quantized levels ,Pe is the probabilityof bit error in the recovered binary PCM signal.If the system have not bit error,so the noise is caused onlyby the quantification,then we have:(S/N)out=M2
• Effects of noise The analog signal, recovered from PCM signal,is corrupted by two kinds of noises: 1. Bit error produced by channel’s gaussian white noise and improper channel filtering (ISI) 2. Quantizing noise One formula for average S/N calculation: (S/N)out=M2 /[1+4(M2 -1)Pe] where M is number of quantized levels ,Pe is the probability of bit error in the recovered binary PCM signal. • If the system have not bit error,so the noise is caused only by the quantification,then we have: (S/N)out=M2