Digital comms

1. Digital Communications - PRELIM
ECE 502
Digital Transmission
djaamora@gmail.com

2. Learning Outcomes
After studying this chapter, you should be able to:
 Compare analog and digital communication techniques and discuss the advantages of each.
 Calculate the minimum sampling rate for a signal and explain the necessity for sampling at
that rate or above.
 Describe the common types of analog pulse modulation.
 Describe pulse-code modulation and calculate the number of quantizing levels, the bit rate,
and the dynamic range for PCM systems.
 Explain companding, show how it is accomplished, and explain its effects.
 Describe the coding and decoding of a PCM signal.
 Describe differential PCM and explain its operation and advantages.
 Describe delta modulation and explain the advantages of adaptive delta modulation.
 Distinguish between lossless and lossy compression and provide examples of each.

3. electronic communications is the transmission, reception, and processing of
information with the use of electronic circuits.
Information is defined as knowledge or intelligence that is communicated (i.e.,
transmitted or received) between two or more points.
djaamora@gmail.com

4. Digital communications
Digital Modulation
Or
Digital Radio
Digital Transmission
require a physical facility between the
transmitter and receiver, such as a metallic
wire pair, a coaxial cable, or an optical fiber
cable.
the carrier facility could be
a physical cable, or it
could be free space.
djaamora@gmail.com
Kurose, J and Ross, K, Computer Networking, 6th ed, ©2013

5. Definition
digital transmission is the transmittal of digital signals between two
or more points in a communications system. The
a physical facility, such as a pair of wires, coaxial cable, or an optical fiber cable,
is required to interconnect the various points within the system.
TRUE OR FALSE:
Digital pulses cannot be propagated through a wireless transmission
system, such as Earth’s atmosphere or free space (vacuum).
djaamora@gmail.com

6. Advantages of Digital Transmission
 noise immunity
 ease of multiplexing,
 ease of processing,
 simpler to measure and evaluate
 transmission errors can be detected and corrected more easily and
more accurately
djaamora@gmail.com

7. Disadvantages of Digital Transmission
 requires significantly more bandwidth
*Bandwidth is one of the most important aspects of any communications system because it is
costly and limited.
 additional encoding and decoding circuitry
 requires precise time synchronization between the clocks in the transmitters
and receivers
 incompatible with older analog transmission systems
djaamora@gmail.com

8. djaamora@gmail.com
PULSE MODULATION
Pulse modulation consists essentially of sampling analog information signals
and then converting those samples into discrete pulses and transporting the
pulses from a source to a destination over a physical transmission medium.

9. PULSE MODULATION
ANALOG DIGITAL
PULSE AMPLITUDE
MODULATION
PULSE POSITION
MODULATION
PULSE DURATION
MODULATION
PULSE CODE
MODULATION
DELTA MODULATION
ADAPTIVE DELTA
MODULATION
Differential PCM

10. djaamora@gmail.com
PULSE WIDTH MODULATION (PWM)
PWM is sometimes called pulse
duration modulation (PDM) or pulse
length modulation (PLM), as the
width (active portion of the duty
cycle) of a constant amplitude pulse
is varied proportional to the
amplitude of the analog signal at the
time the signal is sampled.
Tomasi,Wayne, Advanced Electronic Communication System, 6th ed, © 2014

11. djaamora@gmail.com
PULSE POSITION MODULATION (PPM)
PPM, the position of a constant-
width pulse within a prescribed
time slot is varied
according to the amplitude of the
sample of the analog signal
Tomasi,Wayne, Advanced Electronic Communication System, 6th ed, © 2014

12. djaamora@gmail.com
PULSE AMPLITUDE MODULATION (PAM)
PAM, the amplitude of a
constant width, constant-
position pulse is varied
according to the amplitude of
the sample of the analog
signal.
Tomasi,Wayne, Advanced Electronic Communication System, 6th ed, © 2014

13. djaamora@gmail.com
PULSE CODE MODULATION (PCM)
Alex H. Reeves is credited with inventing PCM in 1937 while working for
AT&T at its Paris laboratories.
PCM is the only digitally encoded modulation technique
The term pulse code modulation is somewhat of a misnomer, as it is not really a type of
modulation but rather a form of digitally coding analog signals.

14. PULSE CODE MODULATION (PCM)

16. djaamora@gmail.com
PCM PROCESS
SAMPLING QUANTIZATION ENCODING
Analog Signal
Time: Continuous
Amplitude: Continuous
Example: 𝑥 𝑡 = 𝑠𝑖𝑛(2𝜋𝑓𝑡)
@ t = 0.1, 0.11, 0.115,……
Discrete Signal
Time: Discrete
Amplitude: Continuous
Example: 𝑥(𝑛) = 𝑠𝑖𝑛(2𝜋𝑓𝑛𝑇𝑠)
@ Ts = 0.1, 0.2, 0.3,……
Digital Signal
Time: Discrete
Amplitude: Discrete
101101

17. djaamora@gmail.com
SAMPLING
Blake, Roy, Electronics Communication System, 2nd ed

18. djaamora@gmail.com
SAMPLING RATE
In 1928, Harry Nyquist showed mathematically that it is possible to
reconstruct a band-limited analog signal from periodic samples, as long as
the sampling rate is at least twice the frequency of the highest-frequency
component of the signal.
If the sampling rate is too low, a form of distortion called aliasing or
foldover distortion is produced
If the sampling rate is too low, a form of distortion called aliasing or
foldover distortion is produced

19. djaamora@gmail.com
Aliasing or Foldover Distortion
Blake, Roy, Electronics Communication System, 2nd ed

20. Example
Find the Nyquist rate and Nyquist interval for the following signals:
𝑖𝑖. ) 𝑚 𝑡 =
1
2𝜋
cos 400𝜋𝑡 cos(1000𝜋𝑡)
𝑖. ) 𝑚 𝑡 =
sin 500𝜋𝑡
𝜋𝑡
𝑓𝑠 = 500𝐻𝑧, 𝑇𝑠 = 2𝑚𝑠𝑒𝑐
𝑓𝑠 = 5000𝐻𝑧, 𝑇𝑠 = 0.2𝑚𝑠𝑒𝑐
cosAcosB =1/2 [cos(A+B)+cos(A-B]
djaamora@gmail.com

21. The codes currently used for PCM are sign-
magnitude codes, where the most significant bit
(MSB) is the sign bit and the remaining bits are
used for magnitude.
Quantization is the process of converting
an infinite number of possibilities to a finite
number of conditions
Assigning PCM codes to absolute magnitudes is
called quantizing
Quantization
Tomasi,Wayne, Advanced Electronic Communication System, 6th ed, © 2014

22. Quantization

26. Quantization and the Folded Binary Code in PCM
The magnitude difference between adjacent steps is called the quantization interval or quantum. This type
of code is called a folded binary code because the codes on the bottom half of the table are a mirror image
of the codes on the top half, except for the sign bit.
The smaller the magnitude of a quantum, the better (smaller) the resolution and the more
accurately the quantized signal will resemble the original analog sample.
Tomasi,Wayne, Advanced Electronic Communication System, 6th ed, © 2014

27. Quantization and the Folded Binary Code
The leftmost bit is the sign bit (1=+ and 0= - ), and the two rightmost bits represent magnitude.
 The 0-V codes each have an input range equal to only one-half a quantum.
n = number of bits in a PCM code, excluding the sign bit
The magnitude of a quantum is also called the resolution.
Tomasi,Wayne, Advanced Electronic Communication System, 6th ed, © 2014

29. Example
Input Signal Subrange (V) Quantization Level 𝒙𝒒 Binary Code
≤ 𝒙 <
≤ 𝒙 <
< 𝒙 <
≤ 𝒙 <

30. Example
Sampled Analog Value 𝒙 0 0.6 0.95 0.95 0.6 0 -0.6 -0.95 -0.95 -0.6 0
Quantized Level 𝒙𝒒
Binary Equivalent Code 𝒊
Quantization error 𝒒𝒆
djaamora@gmail.com
Quantized Level (𝒙𝒒)
= round
𝒔𝒂𝒎𝒑𝒍𝒆 𝒗𝒐𝒍𝒕𝒂𝒈𝒆 (𝒙)
𝒓𝒆𝒔𝒐𝒍𝒖𝒕𝒊𝒐𝒏
maximum quantization error

31. Dynamic Range
The number of PCM bits transmitted per sample is determined by several variables,
including maximum allowable input amplitude, resolution, and dynamic range.
Dynamic Range (DR) is the ratio of the largest possible magnitude to the smallest
possible magnitude (other than 0 V) that can be decoded by the digital-to-analog
converter in the receiver.
djaamora@gmail.com

32. djaamora@gmail.com

33.  The maximum magnitude for the quantization error is equal to one-half a quantum
Quantization Error or Noise
 any round-off errors in the transmitted signal
are reproduced when the code is converted
back to analog in the receiver. This error is
called the quantization error (Qe).
 The quantization error is equivalent to
additive white noise as it alters the signal
amplitude
 quantization error is also called quantization noise (Qn).
djaamora@gmail.com
Tomasi,Wayne, Advanced Electronic Communication System, 6th ed, © 2014

35. Coding Efficiency
 Coding efficiency is a numerical indication of how efficiently a PCM code
is utilized.
 Coding efficiency is the ratio of the minimum number of bits required to
achieve a certain dynamic range to the actual number of PCM bits used.
djaamora@gmail.com

36. Determine the dynamic range for a 10-bit sign-magnitude PCM code.
Determine the minimum number of bits required in a PCM code for a
dynamic range of 80dB. What is the coding efficiency?
For a 12-bit linear PCM code with a resolution of 0.02 V, determine the voltage range that would be
converted to the following PCM codes.
(a ) 1 0 0 0 0 0 0 0 0 0 0 1 b.) 1 0 0 1 0 0 0 0 0 0 0 1

37. Line Codes
 Line Codes are electrical representation of a
binary data stream
Haykin,S., Communication Systems, 4th ed,

38.  Unipolar nonreturn-to-zero (UPNRZ) signaling
In this line code, symbol 1 is represented by transmitting a pulse of
amplitude A for the duration of the symbol, and symbol 0 is represented by
switching off pulse. The line code is also referred to as on-off signaling.
Disadvantages of on-off signaling are the waste of power due to the
transmitted DC level and the fact that the power spectrum of the transmitted
signal does not approach zero at zero frequency.

39. BiPolar nonreturn-to-zero (BPNRZ) signaling
symbola 1 and 0 are represented by transmitting pulses of amplitude +A and –A,
respectively. This line code is relatively easy to generate but its disadvantages is that the power
power spectrum of the signal is large near zero frequency.

40.  UniPolar Return-to-Zero (UPRZ)
Symbol 1 is represented by a rectangular pulse of amplitude A and half-symbol width, and
symbol 0 is represented by transmitting no pulse. An attractive feature of this line code is
the presence of delta functions at 𝑓 = 0, ±1/𝑇𝑏 in the power spectrum of the transmitted
signal, which can be used for bit-timing recovery at the receiver. However, its disadvantages
is that it requires 3 dB more power than polar return-to-zero signaling for the same
probability of symbol errors

41.  BiPolar Return-to-Zero (UPRZ)
This line code uses three amplitude levels. Specifically, positive and negative pulses of equal
amplitude (+A and –A) are used alternate for symbol 1, with each pulse having a half-
symbol width; no pulse is always used for symbol 0. A useful property of BPRZ signaling is
that power spectrum of the transmitted signal has no DC component and relatively
insignificant low-frequency components for the case when symbols 1 and 0 occur with
equal probability.

42.  Split-Phase (Manchester)
symbol 1 is represented by a positive pulse amplitude A followed by a negative pulse of
amplitude –A, with both pulses being half-symbol wide. For symbol 0, the polarities of
these two pulses are reversed. The Manchester code suppresses the DC component and
has relatively insignificantl low-frequency components, regardless of signal statistics.

44. SIGNAL-TO-QUANTIZATION NOISE RATIO
 The maximum quantization noise is half the resolution (quantum value). The
worst possible signal voltage-to-quantization noise voltage ratio (SQR) occurs
when the input signal is at its minimum amplitude
the signal power-to-quantizing noise power ratio (also called signal-to-distortion ratio
or signal-to-noise ratio) is determined by the following formula:

45. LINEAR VERSUS NONLINEAR PCM CODES

46. COMPANDING
 Companding is the process of
compressing and then
expanding.
 With companded systems, the
higher-amplitude analog signals
are compressed (amplified less
than the lower-amplitude signals)
prior to transmission and then
expanded (amplified more than
the lower-amplitude signals) in
the receiver.
 Companding is a means of
improving the dynamic range of a
communications system.

47. ANALOG COMPANDING

48. ANALOG COMPANDING
𝜇 − 𝐿𝑎𝑤
United States and Japan 𝑨 − 𝑳𝒂𝒘
Europe
The most recent PCM systems use an
eight-bit code and a μ=255, A=87.6

51. DIGITAL COMPANDING

52. DIGITAL COMPANDING
The most recent digitally compressed PCM systems use a 12-bit linear PCM code and an
eight-bit compressed PCM code.

53. EXAMPLE
Determine the 12-bit linear
code, the eight-bit
compressed code, the
decoded 12-bit code, the
quantization error, and the
compression error for a
resolution of 0.01V and
analog sample voltages of
(a) +0.053 V, (b) -0.318 V,
and (c) +10.234 V
The segment number in the eight-bit code is determined by counting the number of leading 0s in
the 11-bit magnitude portion of the linear code beginning with the most significant bit. Subtract
the number of leading 0s (not to exceed 7) from 7. The result
is the segment number, which is converted to a three-bit binary number and inserted into
the eight-bit compressed code as the segment identifier.

54. Digital Compression Error

55. PCM LINE SPEED
 Line speed is simply the data rate at which serial PCM bits are clocked out of
the PCM encoder onto the transmission line.
 Line speed is dependent on the sample rate and the number of bits in the
compressed PCM code.
EXAMPLE For a single-channel PCM system with a sample rate fs 6000 samples per second
and a seven-bit compressed PCM code, determine the line speed:

56. DELTA MODULATION PCM
Delta modulation uses a single-bit PCM code to achieve digital transmission of analog signals.
If the current sample is smaller than the previous sample, a logic 0 is transmitted. If the current
sample is larger than the previous sample, a logic 1 is transmitted.

57. two problems associated with delta modulation
Slope overload Granular noise
 happens when the analog input signal
changes at a faster rate than the DAC can
maintain
 The slope of the analog signal is greater than
the delta modulator can maintain and is called
slope overload.
 Increasing the clock frequency and increase
the magnitude of the minimum step size
reduces the probability of slope overload
occurring
 when the original analog input signal has a
relatively constant amplitude, the
reconstructed signal has variations that were
not present in the original signal.
 Granular noise in delta modulation is
analogous to quantization noise in
conventional PCM.
 Granular noise can be reduced by:
 decreasing the step size
 a small resolution is needed

58. ADAPTIVE DELTA MODULATION PCM
Adaptive delta modulation is a delta modulation system where the step size of the DAC is
automatically varied, depending on the amplitude characteristics of the analog input signal.
A common algorithm for an adaptive delta modulator is when three consecutive 1s or 0s
occur, the step size of the DAC is increased or decreased by a factor of 1.5

59. Differential PCM
 Differential pulse code modulation (DPCM) is designed specifically to
take advantage of the sample-to-sample redundancies in typical
speech waveforms.
 With DPCM, the difference in the amplitude of two successive
samples is transmitted rather than the actual sample.
 Because the range of sample differences is typically less than the
range of individual samples, fewer bits are required for DPCM than
conventional PCM.