INFORMATION: ANALOG AND DIGITAL

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INFORMATION ANALOG AND DIGITAL

• David Falconer Halim Yanikomeroglu
• Dept. of Systems and Computer Engineering
• Carleton University

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Topics to be Covered

• Analog (continuous time) signals
• Analog to digital PCM (pulse code modulation)
• Digital transmission

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Analog Signals

• Analog (continuous-time) signals (like speech)
  have a certain bandwidth. Their power spectrum
  describes how their average power is distributed
  with respect to frequency.

Power spectral density (watts/Hz)
High-fidelity speech
Telephone speech (limited by filtering)
Bandwidth
0 1 2 3 4 5
6 7....
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Digital and Analog Signals

• Some signals (like speech and video) are
  inherently analog some (like computer data) are
  inherently digital.
• However both analog and digital signals can be
  represented and transmitted digitally.
• Advantages of digital
• Reduced sensitivity to line noise, temp. drift
  etc.
• Lower maintenance costs than analog.
• Low cost digital VLSI for switching and
  transmission.
• Uniformity in carrying voice, data, video, fax
  etc.
• Better encryption

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Pulse Code Modulation (PCM)

• Key points
• PCM signal is developed by three steps sampling,
  quantizing and encoding.
• Quantizing noise is reduced by using variable
  sized steps. It is independent of line length.

s(t)
s(n?)
011010001...
Filter
Sample at tn? Quantize
Code
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Sampling an Analog Signal

• Sampling theorem The original analog signal can
  be reconstructed if it is sampled at a rate at
  least twice its bandwidth. Reconstruction is by
  filtering sample with a low pass filter.

Sampling Samples
Reconstruction
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Standard PCM in Telephony

• Voice circuit bandwidth is 3400 Hz.
• Sampling rate is 8 KHz (samples are 125 ?s apart.
• Each sample is quantized to one of 256 levels.
• Each quantized sample is coded into a 8-bit word.
• The 8-bit words are transmitted serially (one bit
  at a time) over a digital transmission channel.
  The bit rate is 8X864 Kb/s.
• The bits are regenerated at digital repeaters.
• The received words are decoded back to quantized
  samples, and filtered to reconstruct the analog
  signal.

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Quantization
Uniform Nonuniform
Output signal
Output signal
Input signal
Input signal
The more steps (levels) the less quantization
noise. Nonuniform quantization (e.g. ?-law)
allows a larger dynamic range (important for
speech).
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?-Law Quantization and Coding

• Standardized in North America.
• Based on a logarithmic non-uniform quantizer.
• Range of amplitudes divided into 8 segments, each
  segment with 16 uniformly spaced levels. Segment
  i is double the width of segment i-1.
• 8 bit word 1 bit for sign, 3 bits identify
  segment, 4 bits identify level within segment.
• Can show for n-bit word, signal to quantization
  noise ratio is approx. 6n-10 dB e.g. 38 dB for
  n8 bits.
• Most of the rest of the world uses a related
  logarithmic non-uniformity, called A-law.

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DS1 Format (?-Law Countries)
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Adaptive Differential PCM (ADPCM)

• Allows coding with a lower bit rate (with same
  fidelity) for speech, based on predicting the
  next sample e.g. 8 or 16 or 32 Kb/s.
• More circuits accommodated in the same
  transmission bandwidth.

Coder Decoder
Quant.


Predictor

Predictor
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Regenerative Repeater
Regenerative repeater
Regenerative repeater
Amplifier/ equalizer
Regenerator
Structure of a regenerative repeater
Timing circuit
By appropriate repeater design and inter-repeater
spacing, the effect of occasional bit errors due
to noise can be controlled. Received signal
quality is essentially independent of distance.
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PCM Transmission Formats and Spectra
Power spectra
..... 1 0 1 1 .......
?
Unipolar RZ
0 T 2T 3T -4/T
-1/? -2/T -1/T 0 1/T 2/T 1/? 4/T
Time
Frequency
Unipolar NRZ
0 T 2T 3T 4T
-3/T -2/T -1/T 0 1/T 2/T 3/T
Bipolar NRZ
0 T 2T 3T 4T -4/T
-2/T -1/T 0 1/T 2/T 4/T
Min. bandwidth
Bandlimited
0 T 2T 3T 4T
-1/2T 1/2T
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Multilevel Transmission
1 0 1 1 0 0 0
1
Binary (L2)
4-level L4
0 T 2T 3T
4T
Bit rate
Bandwidth proportional to 1/T for NRZ signals
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Bandwidth Required for Digital Transmission

• required bandwidth is approximately
• (bit rate)/(log2L) for L-level transmission.
• i.e. More levels-gt less bandwidth, but greater
  sensitivity to noise.
• Examples
• 64 Kb/s PCM requires about 64 KHz for binary
  transmission, 32 KHz for 4-level transmission.
• 14.4 Kb/s modem uses a symbol rate 1/T2400 Hz,
  and the equivalent of L32 or 64.

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Channel Capacity

• Shannon channel capacity formula
• Highest possible transmission bit rate R, for
  reliable communication in a given bandwidth W
  Hertz, with given signal to noise ratio, SNR, is
  
• RWlog2(1SNR) bits/s
• R/W 0.332 SNRdB bits/s/Hz
• Assumptions and qualifications
• Gaussian distributed noise added to the signal by
  the channel, highly complex modulation, coding
  and decoding methods.
• In typical practical situations, the above
  formula may be roughly modified by dividing SNR
  by a factor of about 5 to 10.

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Summary

• All information signals can be represented,
  switched, stored and transmitted digitally.
• We have discussed PCM systems and their key
  elements
• sampling
• quantizing
• coding
• digital transmission
• We have discussed the related concepts of
• the telephone set
• bandwidth
• the sampling theorem
• signal to quantization noise ratio
• channel capacity.

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Where to get More Information

• R. Haughton, The Telecommunications Mosaic,
  Vol. 2, (sections II.1, II.2, II.3, II.4), Vol.
  3, (sections I.1, I.2, I.3, I.4)
• E.B. Carne, Telecommunications Primer,
  Prentice-Hall, 1995, Chapters 2,3,4.
• R.L. Freeman, Telecommunications System
  Engineering, (2nd ed.), Wiley, 1989. Chapter 9.
• J. Sklar, Digital Communications, Chapters 2
  and 7