The document discusses various digital communication techniques including linear vs nonlinear PCM encoding, idle channel noise reduction methods, coding methods like level-at-a-time, digit-at-a-time and word-at-a-time. It also discusses analog companding using A-law and μ-law, digital companding, vocoders, delta modulation, DPCM, intersymbol interference causes and eye patterns.

1. DIGITAL COMMUNICATIONS

2. Linear vs. Nonlinear PCM Codes
- Early systems used linear codes
Linear Encoding
- The accuracy (resolution) for the higher-
amplitude analog signals is the same as for the
lower-amplitude signals, and the SQR for the
lower-amplitude signals is less than for the
higher-amplitude signals.

3. Nonlinear or nonuniform encoding
- If there were more codes for the lower
amplitudes, it would increase the accuracy
where the accuracy is needed. Then, there
would be fewer codes available for the higher
amplitudes, which would increase the
quantization error for the larger-amplitude
signals (decreasing the SQR).
- The step size increases with the amplitude of
the input signal.

4. Linear encoding Nonlinear encoding

5. Idle Channel Noise
• The random thermal noise input to the PAM
sampler when there no analog input signal.
• Converted to a PAM sample just as if it is a
signal
Methods to reduce idle noise channel:
Midtread quantization – the first quantization
interval is made larger in amplitude than the
rest of the steps.

6. Midrise Quantization – the lowest-magnitude
positive and negative codes have the same
voltage range as all the other codes (+ or –
one-half the resolution).

7. Idle channel noise
Uniform code with
midrise quantization
Uniform code with
midtread quantization
Decoded Noise No decoded Noise

8. Coding Methods
• Coding methods used to quantize PAM signal into 2n levels.
Level-at-a-time coding
- Compares the PAM signal to a ramp waveform while a binary
counter is being advanced at a uniform rate.
- When a ramp waveform equals or exceeds the PAM sample,
the counter contains the PCM code.
- Requires a very fast clock if the number of bits in the PCM
code is large.
- Also requires the 2n sequential decisions be made for each
PCM code generated.
- Limited to low-speed applications.
- Nonuniform coding is achieved by using a nonlinear function
as the reference ramp

9. Digit-at-a-time coding
- Determines each digit of the PCM code
sequentially.
- Analogous to a balance where known reference
weights are used to determine an unknown
weight.
- Provide a compromise between speed and
complexity.
- A common kind of digit-at-a-time coder called a
feedback coder, uses a successive approximation
register (SAR).
- the entire PCM code word is determined
simultaneously

10. Word-at-a-time coding
- Flash encoders and are more complex
- More suitable for high-speed applications
- Common type of this uses multiple threshold
circuits.
- Logic circuits sense the highest threshold
circuit sensed by the PAM input signal and
produce the approximate PCM code.
- Impractical for large values of n.

11. - The process of compressing, then expanding.
- The higher-amplitude analog signals are
compressed (less than the lower-amplitude
signals) prior to transmission, then expanded
(more than the smaller-amplitude signals) at
the receiver.

12. 120 dB 120 dB
60 dB
Transmission
Compression Expansion
input output

13. Analog Companding
• Implemented using specially designed diodes
inserted in the analog signal path in the PCM
transmitter prior to the sample-and-hold
circuit.
• 2 methods currently being used that closely
approximate a logarithmic function and are
often called log-PCM codes.
1. A- law
2. μ-law

14. μ - law
• Used in US and Japan
V max ln(1   Vin )
Vout  V max
ln(1   )
Vmax = maximum uncompressed analog signals
Vin = amplitude of the input signal at a particular instant of time
μ = parameter used to define the amount of compression
Vout = compressed output amplitude

15. Example
• For a compression with μ = 255, determine
the gain for the value of Vin: Vmax, 0.75
Vmax, 0.5 Vmax and 0.25 Vmax.

16. A-law
Established by CCIT in Europe to approximate true logarithmic
Companding.
AVin/ V max 1
Vout  V max 0 Vin 
1  ln A V max A
1  ln( AVin/ V max) 1 Vin
Vout  V max  1
1  ln A A V max

17. Digital Companding
- Compression at the transmit end after the
input sample has been converted to a linear
PCM code and expansion at the receive end
prior to PCM decoding

18. Compressed
Analog PCM
Input PAM Linear
Bandpass Sample-and- AD PCM Digital
filter hold circuit converter Compressor
PCM Transmitter
Analog PAM Linear PCM
Output
Bandpass DA Digital
hold circuit
filter converter Expander
PCM Receiver

19. Relative output amplitude
Relative input amplitude

20. Digital companding algorithm for 12-bit-
linear code to 8-bit-compressed code
• The 8-bit compressed code is comprised of a
sign bit, a 3-bit segment identifier, and a 4-bit
magnitude code which identifies the
quantization interval within the specified
segment.
Sign bit 3-bit segment 4-bit quantization
identifier interval
A B C D
1=+ 000 to 111 0000 to 1111
0=-

21. μ255 encoding table
Segment 12-bit linear code 8-bit compressed code
0 s0000000ABCD s000ABCD
1 s0000001ABCD s001ABCD
2 s000001ABCDX s010ABCD
3 s00001ABCDXX s011ABCD
4 s0001ABCDXXX s100ABCD
5 s001ABCDXXXX s101ABCD
6 s01ABCDXXXXX s110ABCD
7 s1ABCDXXXXXX s111ABCD

22. X- bit positions that are truncated during
compression are consequently lost.
A, B, C, D – bits for quantization interval,
transmitted as is.
s – sign bit which is also transmitted as is.
Compression process
1. The analog signal is sampled and converted to a
linear 12-bit sign-magnitude code.
2. The sign bit is transferred directly to the 8-bit
code.
3. The segment is determined by counting the
number of leading 0’s in the 11-bit magnitude
portion of the code beginning with the MSB.

23. 4. Subtract the number of leading 0’s (not to
exceed 7) from 7. The result is the segment
number.
5. The segment number is converted to a 3-bit
binary number and substituted into the 8-bit
code as the segment identifier.
6. The four magnitude bits (A, B, C, D) are the
quantization interval and are substituted into
the least significant bits of the 8-bit
compressed code.

24. • Segments 2 to 7 are subdivided into smaller
subsegments. Each segment has 16
subsegments, which correspond the 16
conditions possible for the bits A, B, C, and D
(0000-1111).
• In segment 2 there are two codes per
subsegment. In segment 3 there are four. The
number of codes per subsegment doubles
with each subsequent segment.

25. μ255 decoding table
8-bit compressed code 12-bit linear code Segment
s000ABCD s0000000ABCD 0
s001ABCD s0000001ABCD 1
s010ABCD s000001ABCD1 2
s011ABCD s00001ABCD10 3
s100ABCD s0001ABCDX100 4
s101ABCD s001ABCD1000 5
s110ABCD s01ABCD10000 6
s111ABCD s1ABCD100000 7

26. Vocoders
• Special voice encoders/decoders
• Used in digitizing speech signals only
• Designed to reproduce only the short-term power
spectrum, and the decoded time waveforms
• Cannot be used in applications where analog signals
other than voice are present such as output signals
from voice band data modems.
• Typically produce unnatural sounding speech are
therefore generally used for recorded information such
as “wrong number” messages, encrypted voice for
transmission over analog telephone circuits, computer
output signals and educational games.

27. Vocoder
• Purpose is to encode the minimum amount of
speech information necessary to reproduce a
perceptible message with fewer bits than
those needed by a conventional
encoders/decoders.
• Used primarily in limited bandwidth
applications

29. Channel Vocoders
• The first channel vocoder developed by
Homer Dudley in 1928.
– Dudley’s vocoder compressed conventional
speech waveforms into an analog signal with a
total bandwidth of approximately 300 Hz.
Present digital vocoders operate at less than 2 kbps.
- use bandpass filters to separate the speech
waveform into narrower subbands.
- each sideband is full-wave rectified, filtered, then
digitally encoded.

30. Channel Vocoder
• The quality of the signal is at the output is
quite poor.
• More advanced channel vocoders operate at
2400 bps and produce a highly intelligible,
although slightly synthetic sounding speech.

31. • The spectral power of most speech energy concentrates at
three or four peak frequencies called formants.
• Determines the location of these peaks and encodes and
transmits only the information with the most significant short-
term components.
• Can operate at lower bit rates and thus require narrow
bandwidths.
• Sometimes have trouble tracking changes in the formants.
• Once the formants have been identified, a formant vocoder
can transfer intelligible speech at less than 1000 bps.

32. • Extracts the most significant portions of speech information
directly from the time waveform rather than from the
frequency spectrum as with the channel and formant
vocoders.
• Produces a time-varying model of the vocal tract excitation
and transfer function directly from the speech waveform.
• At the receive end, a synthesizer reproduces the speech by
passing the specified excitation through a mathematical
model of the vocal tract.
• Provide more-natural-sounding speech than does either
the channel or formant vocoder.
• Encode and transmit speech at between 1.2 and 2.4 kbps.

33. • most popular alternative to PCM
• Uses a single-bit PCM code to achieve digital
transmission of analog signals.
• Rather than transmit a coded representation of
the sample, only a single bit is transmitted
which simply indicates whether that sample is
larger or smaller than the previous sample.
• If the current sample is smaller than the
previous sample, a logic 0 is transmitted, if it is
larger than the previous sample, a logic 1 is
transmitted.

34. DM Transmitter
+
Analog Sample and hold Delta PCM
input
-
Sampling
pulse
Digital-to-analog
converter
(DAC)
Up/down
counter U/D
Clock

35. • The input analog is sampled and converted to a PAM
signal which is compared to the output of the DAC.
• The output of DAC is a voltage equal to the
regenerated magnitude of the previous sample, which
was stored in the up-down counter as a binary number.
• The up-down counter is incremented or decremented
depending on whether the previous is larger or smaller
than the current sample.
• The up-down counter is clocked at a rate equal to the
sample rate. (up-down counter is updated after each
comparison)

36. Ideal operation of DM

37. DM Receiver
Digital-to-analog Recovered
PAM
converter Low-pass filter analog
(DAC) signal
Delta Up/down
U/D counter Clock
PCM

38. 2 problems associated with DM
• Slope Overload
• Granular noise

39. • Slope overload – when the analog input signal
changes at a faster rate than the DAC can keep
up with.
– The slope of the analog signal is greater than the
delta modulator can maintain.
– Increasing the clock frequency reduces the
probability of slope overload occurrences.
– Another way is to increase the magnitude of the
minimum step size.

40. • Granular noise - when the original analog
input signal has a relatively constant
amplitude, the reconstructed signal has
variations that were not present in the original
signal.
– Analogous to quantization noise in conventional
PCM.
– Can be reduced by decreasing the step size.

41. • To reduce the granular noise, a small resolution is
needed, and to reduce the possibility of slope
overload occurring, a large resolution is required.
• Granular noise is more prevalent in analog signals
that have gradual slopes and whose amplitudes
vary only a small amount; slope overload is more
prevalent in analog signals that have steep slopes
or whose amplitudes vary rapidly.

42. • Delta modulation system where the step size
of the DAC is automatically varied depending
on the amplitude characteristics of the analog
input signal.

43. • After a predetermined number of consecutive 1’s
or 0’s, the step size is automatically increased.
• After the next sample, if the DAC output
amplitude is still below the sample amplitude,
the next step is increased even further until
eventually the DAC catches up with the analog
signal.
• The DAC will automatically revert to minimum
step size and thus reduce the magnitude of the
noise error.

44. ADPCM Algorithm
• When 3 consecutive 1’s or 0’s occur, the step
size of the DACs is increased or decreased by a
factor of 1.5.

45. • Designed specifically to take advantage of the
sample-to-sample redundancies in typical
speech waveforms.
• The difference of the amplitude of two
successive samples is transmitted rather than
the actual sample.
• Fewer bits are required than conventional
PCM.

46. DPCM Transmitter
Analog Low-pass + Differentiator
input ADC Encoded
filter (summer)
difference
- sample
Accumulated
signal level
Integrator DAC

47. DPCM transmitter
• The analog input signal is bandlimited to one-
half of the sample rate, then compared to the
preceding accumulated signal level in the
differentiator.

48. DPCM + Hold
DAC Integrator Analog
input Ckt LPF
output
+
Each received sample is converted back to analog,
stored, and then summed with the next sample
received.

49. • All digital carrier systems involve transmission
of pulses through a medium with a finite
bandwidth.
• Practical digital systems utilize filters with
bandwidths that are approximately 30% or
more in excess of the ideal Nyquist
Bandwidth.

50. Output waveform of a bandlimited
communications channel
Secondary lobes are ringing tails

51. Pulse response
sin(T / 2)
f ( )  (T )
T / 2
where :
  2f (rad )
T  pulsewidth(sec)

52. Spectrum of square pulse with
duration 1/T.

53. Nyquist Rate
R = 2B
Where
R = signaling rate (1/T)
B = specified bandwidth

54. Intersymbol Interference (ISI)

55. ISI
• Causes crosstalk
• Energy in the form of spurious responses
from the third and fourth impulses from
one pulse appears during the sampling
instant (T= 0) of another pulse.

56. 4 primary causes of ISI
• Timing inaccuracies – if the rate does not
conform to the ringing frequency designed
into the communications system.
• Insufficient Bandwidth
• Amplitude distortion
• Phase distortion

57. Eye Patterns
• The performance of a digital transmission
systems depends, in part, on the ability to
regenerate the original pulses.
• All waveform combinations are superimposed
over adjacent signaling intervals is called eye
pattern or eye diagram.
• A convenient technique for determining the
effects of degradation.

58. ISI degradation = 20 log (h/H)
Where
H = ideal vertical opening
h = degraded vertical opening

59. Eye diagram setup
Digital Bandlimited
source Channel
V Input
H Input
Symbol
Clock
Oscilloscope

60. Eye Diagram
20 log (90/100) = 0.915 dB ISI degradation