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C H A P T E R 6 SAMPLING AND ANALOG-TO-DIGITAL CONVERSION

C H A P T E R 6 SAMPLING AND ANALOG-TO-DIGITAL CONVERSION. Sampling Theorem. Nyquist Rate. Nyquist Interval. Signal Reconstruction from Uniform Samples. Interpolation: The process of reconstructing a continuous time signal g(t) from its samples.

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C H A P T E R 6 SAMPLING AND ANALOG-TO-DIGITAL CONVERSION

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  1. C H A P T E R 6 SAMPLING AND ANALOG-TO-DIGITAL CONVERSION ELCT 332 Fall 2011 1

  2. Sampling Theorem Nyquist Rate Nyquist Interval ELCT 332 Fall 2011 2

  3. Signal Reconstruction from Uniform Samples Interpolation: The process of reconstructing a continuous time signal g(t) from its samples ELCT 332 Fall 2011 3

  4. Practical Signal Reconstruction (Interpolation) ELCT 332 Fall 2011 4

  5. Simple interpolation ELCT 332 Fall 2011 5

  6. Practical Issues in Signal Sampling and Reconstruction Realizability of Reconstruction Filters ELCT 332 Fall 2011 6

  7. Practical Issues in Signal Sampling and Reconstruction The Treachery of Aliasing Aliasing effect. (a) Spectrum of a practical signal g(t). (b) Spectrum of sampled g(t). (c) Reconstructed signal spectrum. (d) Sampling scheme using antialiasing filter. (e) Sample signal spectrum (dotted) and the reconstructed signal spectrum (solid) when antialiasing filter is used. ELCT 332 Fall 2011 7

  8. Maximum Informaiton Rate A maximum of 2B independent pieces of information per second can be transmitted, error free, over a noiseless channel of bandwidth B Hz (a) Non-band limited signal spectrum and its sampled spectrum G( f ). (b) Equivalent low-pass signal spectrum Ga( f ) constructed from uniform samples of g(t) at sampling rate 2B. ELCT 332 Fall 2011 8

  9. Nonideal Practical Sampling Analysis ELCT 332 Fall 2011 9

  10. Applications of Sampling Theorem Pulse Amplitude Modulation (PAM) Pulse Width Modulation (PWM) Pulse Position Modulation (PPM) ELCT 332 Fall 2011 10

  11. Applications of Sampling Theorem Time Division Multiplexing (TDM) ELCT 332 Fall 2011 11

  12. Pulse Code Modulation (PCM) Natural binary code (NBC) Binary digit (bit) For a audio signal with a bandwidth about 15kHz, the signal is not affected if all the above 3400 Hz are suppressed. If sampled at a rate of 8000 samples per second, and each sample is finalized quantized into 256 levels, the telephone signal requires how many binary pulses per second? ELCT 332 Fall 2011 12

  13. Quantizing ELCT 332 Fall 2011 13

  14. Nonuniform Quantizing uLaw ALaw ELCT 332 Fall 2011 14

  15. The Compandor The Compressor and expander together are called the compandor ELCT 332 Fall 2011 15

  16. Examples: Transmission Bandwidth and the Output SNR A signal m(t) band-limited to 3kHz is sampled at a rate 33.333% higher than the Nyquist rate. The maximum acceptable error in the sample amplitude (the maximum quantization error) is 0.5% of the peak amplitude mp. The quantized samples are binary coded. Find the minimum bandwidth of a channel required to transmit the encoded binary signal. If 24 such signals are time-division-multiplexed, determine the minimum transmission bandwidth required to transmit the multiplexed signal. Nyquist rate RN=6000Hz Sampling rate RA=8000Hz L=200 N=8, CM=24*64000/2=0.768MHz ELCT 332 Fall 2011 16

  17. Exponential Increase of the Output SNR A signal m(t) of bandwidth B=4kHz is transmitted using a binary companded PCM with μ=100. Compare the case of L=64 with the case L=256 from the point of view of transmission bandwidth and the output SNR. ELCT 332 Fall 2011 17

  18. Digital Telephony T1 carrier system. ELCT 332 Fall 2011 18

  19. Digital Telephony T1 system signaling format. ELCT 332 Fall 2011 19

  20. Differential Pulse Code Modulation (DPCM) By estimating the value of the kth sample m[k] from a knowledge of several previous sample values. We transmit the difference between m[k] and its predicted value. More band efficient, and better SNR Line Predictor Transversal filter (tapped delay line) used as a linear predictor. ELCT 332 Fall 2011 20

  21. Differential Pulse Code Modulation (DPCM) SNR Improvement: mp, dp DPCM system: (a) transmitter; (b) receiver. ELCT 332 Fall 2011 21

  22. Adapative Differential Pulse Code Modulation (ADPCM) ADPCM encoder uses an adaptive quantizer controlled only by the encoder output bits. ELCT 332 Fall 2011 22

  23. Vocoders And Video Compression Linear Prediction Coding (LPC) (a) The human speech production mechanism (b) Typical pressure impulses. ELCT 332 Fall 2011 23

  24. LPC Models Analysis and synthesis of voice signals in an LPC encoder and decoder. Video Compression: MPEG NTSC TV in digital form 45-120 Mbit/s------- 1.5-15Mbit/s HDTV in digital form 800 Mbit/s------- 19.39Mbit/s ELCT 332 Fall 2011 24

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