Chapter Two

1
Chapter Two

• Formatting and Baseband Modulation

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Digital Communication Transformation
3
Formatting and Transmission of Baseband Signals
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Message, Characters, and Symbols
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Formatting Analog Information

• Formatting process
• Transform an analog waveform into a form that is
  compatible with a digital communication system
• Sampling theorem
• A bandlimited signal having no spectral
  components above hertz can be determined
  uniquely by values sampled at
• 
  , where is also called
  the Nyquist rate

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Impulse Sampling (Ideal Case)
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Spectra for Various Sampling Rate
Sampled spectrum (fs gt 2fm)
Sampled spectrum (fs lt 2fm)
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Natural Sampling
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Comparison of Impulse Sampling and Natural
Sampling

• Impulse sampling (Ideal case)
• Natural sampling (A practical way)

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Sample-and-Hold Operation

• Transfer function
• where is the hold-operation and is
  the form of
• Two effects of hold-operation
• The significant attenuation of the higher
  frequency components
• The non-uniform spectral gain
• Post-filtering operation can compensate the
  effects of hold-operation

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Aliasing for Sampling
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Eliminate Aliasing for Higher Sampling
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Aliasing Elimination

• Higher sampling rate
• Pre-filtering the original spectrum so that the
  new maximum frequency is reduced to fs/2 or less
• Post-filtering removes the aliased components
• Both the pre-filtering and the post-filtering
  will result a loss of signal information
• Trade-off is required between the sampling rate
  and cutoff bandwidth
• Engineers version of the Nyquist sampling rate
  is

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Pre-filter Eliminates Alias
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Post-filter Eliminates Alias
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Alias Frequency by Sub-Nyquist Sampling Rate
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Sampling Process (I)

• Without oversampling (sampling rate is the
  Nyquist rate)
• The analog signal passes through a high
  performance analog low-pass filter
• Sampling rate is the Nyquist rate for the
  band-limited signal
• The samples are mapped to a finite list of
  discrete output levels and processed by the
  following digital signal process

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Sampling Process (II)

• With over-sampling (sampling rate is higher than
  the Nyquist rate)
• The analog signal passes through a low
  performance analog low-pass filter
• The pre-filtered signal is sampled at the higher
  Nyquist rate for the band-limited signal
• The samples are mapped to a finite list of
  discrete output levels and processed by a high
  performance digital filter to reduce the
  bandwidth of the digital samples

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Analog Source Description
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Source of Corruption

• Sampling and quantizing effects
• Quantization noise due to round-off or truncation
  error
• Increase the number of levels employed in the
  quantization process
• Quantizer saturation
• AGC can be used to avoid the saturation
• Timing jitter
• Stable clock
• Channel effects
• Channel noise (thermal noise, interference from
  other users)
• Intersymbol interference (ISI)

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Quantization Level
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Signal to Noise Ratio for Quantized Pulse

• Assume the quantization error ,e, is uniformly
  distributed over a single interval q-wide, the
  quantizer error variance is
• The peak power is
• The ratio of signal peak power to average
  quantization error power

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Quantization Samples
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Pulse Code Modulation (PCM)

• Quantize PAM signal into a digital word
• Increase the number of levels
• Reduce the quantization noise
• Increase the number of bits per PCM sequence
• The data rate is thus increased, and the cost is
  a greater transmission bandwidth
• Some communication systems can be tolerable to
  the time delay so that the more quantization
  levels need not more bandwidth (ex outer space
  communication)

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Statistics of Speech Amplitudes
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Uniform and Non-uniform Quantization
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Quantizer Characteristics
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Compression Characteristics
Figure 2.20 Compression characteristics. (a)
µ-law characteristic. (b) A-law characteristic.
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Compression Functions

• m-law compression
• A-law

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Baseband Transmission
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Waveform Representation of Binary Digits

• Binary digits needs to be represented by physical
  waveform

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PCM Waveform Considerations

• DC component
• Eliminate DC energy to enable the system to be ac
  coupled
• Self-clocking
• Some PCM coding schemes aid in the recovery of
  the clock signal
• Error detection
• Bandwidth compression
• Such as multi-level codes
• Differential encoding
• Noise immunity
• Some PCM schemes have better error performance

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Spectral Densities of Various PCM Waveform
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Bits per PCM Word and Bits per Symbol

• PCM word size
• Required number of bits per analog sample for the
  allowable quantization distortion
• For example, we specified the quantization error
  is specified not to exceed a fraction of
  the peak-to-peak analog voltage ,
• Bits per symbol is decided by M-level signal
  transmission

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Quantization Levels and Multi-level Signaling

• Example 2.3
• The information in an analog waveform, with the
  maximum frequency fm3 kHz, is to be transmitted
  over an M-ary PAM system, where the number of
  pulse levels is M16. The quantization distortion
  is specified not to exceed of the
  peak-to-peak analog signal
• What is the minimum number of bits/sample, or
  bits/PCM word that should be used in digitizing
  the analog waveform?
• What is the minimum required sampling rate, and
  what is the resulting bit transmission rate?
• What is the PAM pulse or symbol transmission
  rate?
• If the transmission bandwidth equals 12 KHz,
  determine the bandwidth efficiency for this system

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Correlative Coding

• Transmit 2W symbols/s with zero ISI, using the
  theoretical minimum bandwidth of W Hz, without
  infinitely sharp filters.
• Correlative coding (or duobinary signaling or
  partial response signaling) introduces some
  controlled amount of ISI into the data stream
  rather than trying to eliminate ISI completely
• Doubinary signaling

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Duobinary Decoding

• Example
• Binary digit sequence xk 0 0 1 0 1 1
  0
• Bipolar amplitudes xk -1 -1 1 -1 1 1 -1
• Coding rule ykxkxk-1 -2 0 0 0 2 0
• Decoding decision rule
• If , decide that
• If , decide that
• If , decide opposite of the previous
  decision
• Error propagation could cause further errors

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Precoded Doubinary Signaling

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Duobinary Precoding

• Example
• Binary digit sequence 0 0 1
  0 1 1 0
• Precoded sequence 0 0 1
  1 0 1 1
• Bipolar sequence -1 -1
  1 1 -1 1 1
• Coding rule
  -2 0 2 0 0 2
• Decoding decision rule
• If , decide that
• If , decide that
• Decoded binary sequence 0 1 0 1 1
  0

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Duobinary Equivalent Transfer Function
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Duobinary Transfer Function
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Comparison of Binary with Duobinary Signaling

• Binary signaling assumes the transmitted pulse
  amplitude are independent of one another
• Duobinary signaling introduces correlation
  between pulse amplitudes
• Duobinary technique achieve zero ISI signal
  transmission using a smaller system bandwidth
• Duobinary coding requires three levels, compared
  with the usual two levels for binary coding
• Duobinary signaling requires more power than
  binary signaling (2.5 dB greater SNR than binary
  signaling)