 Analog-to-Digital Conversion

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Analog-to-Digital Conversion
PAM(Pulse Amplitude Modulation) PCM(Pulse Code Modulation)

PAM(Pulse Amplitude Modulation)
Conversion of analog signal to a pulse type signal where the amplitude of signal denotes the analog information Two class of PAM signals Natural sampling (gating) Easier to generate Instantaneous sampling Flat-top pulse More useful to conversion to PCM

PAM with natural sampling
W(t) t Ws(t) t S(t) t Ts Duty Cycle D=/Ts=1/3 W(t) S(t) Ws(t) =W(t)S(t) Analog bilateral switch

Spectrum of PAM with natural sampling
|W(f)| -B B f 1 Spectrum of input analog signal Spectrum of PAM D=1/3, fs=4B BT= 3fs = 12B |Ws(f)| -3fs fs fs B B fs fs fs D=1/3

PAM with flat-top sampling
W(t) t Ws(t) t Ts S(t) t Sample and Hold

Spectrum of PAM with flat-top sampling
|W(f)| -B B f 1 Spectrum of Input Spectrum of PAM /Ts=1/3, fs=4B BT= 3fs = 12B |Ws(f)| -3fs fs fs B B fs fs fs D=1/3

Summary of PAM Require very wide bandwidth Bad noise performance
Not good for long distance transmission Provide means for converting a analog signal to PCM signal Provide means for TDM(Time Division Multiplexing) Information from different source can be interleaved to transmit all of the information over a single channel

PCM(Pulse Code Modulation)
Definition PCM is essentially analog to digital conversion of a signal type where the information contained in the instantaneous samples of an analog signal is represented by digital words in a serial bit stream Analog signal is first sampled at a rate higher than Nyquist rate, and then samples are quantized Uniform PCM : Equal quantization interval Nonuniform PCM : Unequal quantization interval

Why PCM is so popular ? PCM requires much wider bandwidth But,
Inexpensive digital circuitry PCM signal from analog sources(audio, video, etc.) may be merged with data signals(from digital computer) and transmitted over a common high-speed digital communication system (This is TDM) Regeneration of clean PCM waveform using repeater. But, noise at the input may cause bit errors in regenerated PCM output signal The noise performance is superior than that of analog system. Further enhanced by using appropriate coding techniques

LPF BW=B Sampler & Hold Quantizer No. of levels=M Encoder Analog signal Bandlimited Analog signal Flat-top PAM signal Quantized PCM Channel, Telephone lines with regenerative repeater Decoder Reconstruction Signal output

Waveforms in PCM Uniform quantizer Error signals Waveform of signals
PCM signal PCM word

Encoder Usually Gray code is used
Only one bit change for each step change in quantized level Single errors in received PCM code word will cause minimum error if sign bit is not changed In text, NBC(Natural Binary Coding) is used Multilevel signal can be used Much smaller bandwidth than binary signals Requires multilevel circuits

Uniform PCM Let M=2n is large enough Uniform distribution =2Xmax/M x
Distortion x -/ /2

SQNR of PCM Distortion SQNR Let normalized input :

Bandwidth of PCM Hard to analyze because PCM is nonlinear
If sinc function is used to generate PCM , where R is bit rate If rectangular pulse is used , first null bandwidth If fs=2B (Nyquist sampling rate) Lower bound of BW: In practice, is closer to reality

Performance of PCM Quantizer Level, M 2 4 8 16 32 64 128 256 512 1024
2048 4096 8192 16384 32768 65536 n bits M=2n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Bandwidth >nB 2B 4B 6B 8B 10B 12B 14B 16B 18B 20B 22B 24B 26B 28B 30B 32B SQNR|dB_PK 4.8+6n 10.8 16.8 22.8 28.9 34.9 40.9 46.9 52.9 59.0 65.0 71.0 77.0 83.0 89.1 95.1 101.1

PCM examples Telephone communication Voice frequency : 300 ~ 3400Hz
Minimum sampling frequency = 2 x 3.4KHz = 6.8KHz In US, fs = 8KHz is standard Encoding with 7 information bits + 1 parity bit Bit rate of PCM : R = fs x n = 8K x 8 = 64 Kbits/s Buad rate = 64Ksymbols/s = 64Kbps Required Bandwidth of PCM If sinc function is used: B > R/2 = 32KHz If rectangular is used: B = R = 64KHz SQNR|dB_PK = 46.9 dB (M = 27) Parity does not affect quantizing noise but decrease errors caused by channels

PCM examples CD (Compact Disk) For each stereo channel
16 bit PCM word Sampling rate of 44.1KHz Reed-Solomon coding with interleaving to correct burst errors caused by scratches and fingerprints on CD High quality than telephone communication

Homework Illustrative Problems 4.9, 4.10, 4.11, 4.12 Problems 4.14

Nonuniform quantization
Example: Voice analog signal Peak value(1V) is less appears while weak value(0.1V, 20dB down) around 0 is more appears (nonuniform amplitude distribution) Thus nonuniform quantization is used Implementation of nonuniform quantization Compression (Nonlinear) filter PCM with Uniform Quantization Analog Input PCM output

Nonuniform Quantization
Two types according to compression filter -law : used in US See Figure 4.9, Page 155 A-law : used in Europe

Nonuniform Quantization
Compandor = Compressor + Expandor Compressor: Compression filter in transmitter Expander: Inverse Compression filter in receiver -law : SQNR Uniform quantizing: -law: A-law:

Homework Illustrative Problems 4.13, 4.14 Problems 4.17