CHAPTER 6
SAMPLING AND ANALOG-TO-DIGITAL
CONVERSION
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Sampling Theorem
Nyquist Rate
Nyquist Interval
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Signal Reconstruction from Uniform Samples
Interpolation: The process of reconstructing a continuous time signal g(t) from its
samples
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Practical Signal Reconstruction (Interpolation)
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Simple interpolation
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Practical Issues in Signal Sampling and Reconstruction
Realizability of Reconstruction Filters
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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.
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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.
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Nonideal Practical Sampling Analysis
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Applications of Sampling Theorem
Pulse Amplitude Modulation (PAM)
Pulse Width Modulation (PWM)
Pulse Position Modulation (PPM)
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Applications of Sampling Theorem
Time Division Multiplexing (TDM)
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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?
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Quantizing
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Nonuniform Quantizing
uLaw
ALaw
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The Compandor
The Compressor and expander together are called the compandor
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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
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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.
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Digital Telephony
T1 carrier system.
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Digital Telephony
T1 system signaling format.
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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.
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Differential Pulse Code Modulation (DPCM)
SNR Improvement: mp, dp
DPCM system: (a) transmitter; (b) receiver.
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Adapative Differential Pulse Code Modulation (ADPCM)
ADPCM encoder uses an adaptive quantizer controlled only by the encoder output bits.
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Vocoders And Video Compression
Linear Prediction Coding
(LPC)
(a) The human speech production mechanism (b) Typical pressure impulses.
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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
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