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Analog-to-Digital Conversion

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)

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Analog-to-Digital Conversion

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

  2. 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

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

  4. |W(f)| 1 f |Ws(f)| -B B D=1/3 -3fs -2fs -fs -B B fs 2fs 3fs Spectrum of PAM with natural sampling • Spectrum of input analog signal • Spectrum of PAM • D=1/3, fs=4B • BT= 3fs = 12B

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

  6. |W(f)| 1 |Ws(f)| f D=1/3 -B B -3fs -2fs -fs -B B fs 2fs 3fs Spectrum of PAM with flat-top sampling • Spectrum of Input • Spectrum of PAM • /Ts=1/3, fs=4B • BT= 3fs = 12B

  7. 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

  8. 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

  9. 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

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

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

  12. 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

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

  14. SQNR of PCM • Distortion • SQNR • Let normalized input :

  15. Bandwidth of PCM • Hard to analyze because PCM is nonlinear • Bandwidth of PCM • 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

  16. 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

  17. 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

  18. 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

  19. Homework • Illustrative Problems • 4.9, 4.10, 4.11, 4.12 • Problems • 4.14

  20. PCM with Uniform Quantization Compression (Nonlinear) filter Analog Input PCM output 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

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

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

  23. Homework • Illustrative Problems • 4.13, 4.14 • Problems • 4.17

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