4.2 Digital Transmission
Outlines
□
□
□
□
Pulse Modulation
Pulse Code Modulation
Delta Modulation
Line Codes
□ Sampling analog information signal
□ Converting samples into discrete pulses
□ Transport the pulses
from source to
destination over physical transmission
medium.
Cont’d...
□ Four (4) Methods
1. PAM
2.
3.
4.
PWM
PPM
PCM
Analog Pulse Modulation
Digital Pulse Modulation
continue…
□ Analog Pulse Modulation
□ Carrier signal is pulse waveform and the
modulated signal is where one of the
carrier signal’s characteristic (either
amplitude, width or position) is changed
according to information signal.
Pulse Amplitude Modulation (PAM)
• The amplitude of pulses is varied in accordance with the
information signal.
• Width & position constant.
Pulse Width Modulation (PWM)
□ Sometimes called Pulse Duration Modulation
(PDM).
□ The width of pulses is varied in accordance
to information signal.
□ Amplitude & position constant.
continue...
Pulse Position Modulation (PPM)
• Modulation in which the temporal positions of the pulses are
varied in accordance with some characteristic of the
information signal.
• Amplitude & width constant.
□ The most common technique for using digital
signals to encode analog data is PCM.
□ Example: To transfer analog voice signals off
a local loop to digital end office within the
phone system, one uses a codec.
□ The pulses are of fixed length and fixed
amplitude
□ PCM is a binary system where a pulse or lack
of a pulse within a prescribed time slot
represents either a logic 1 or a logic 0
condition.
PCM Block Diagram
• Most common form of analog to digital modulation
• Four step process
1. Signal is sampled using PAM (Sample)
2. Integer values assigned to signal (PAM)
3. Values converted to binary (Quantized)
4. Signal is digitally encoded for transmission
(Encoded)
4 Steps Process
PCM Sampling
□ The function of a sampling circuit in PCM
transmitter is to periodically sample the
continually changing analog input voltage
and convert those samples to a series of
constant-amplitude pulses that can more
easily be converted to binary PCM code
□ There are two basic techniques used to
perform the sampling function:
□ Natural sampling
□ Flat-top sampling
Natural Sampling
□ Tops of the sample pulses retain their natural
shape during the sample interval.
□ Frequency spectrum of the sampled output
is different from an ideal sample.
□ Amplitude of frequency components
produced from narrow, finite-width sample
pulses decreases for the higher harmonics
□ Requiring the use of frequency equalizers
Natural Sampling
Flat-top Sampling
□ The most common method used for sampling voice
signals in PCM systems.
□ Accomplish in a sample-and-hold circuit
□ To periodically sample the continually changing
analog input voltage & convert to a series of
constant-amplitude PAM voltage levels.
□ The input voltage is sampled with a narrow pulse
and then held relatively constant until the next
sample is taken.
continue…
□ Sampling process alters the frequency
spectrum & introduces aperture error.
□ The amplitude of the sampled signal
changes during the sample pulse time.
□ Advantages:
□ Introduces less aperture distortion
□ Can operate with a slower ADC
Flat-top Sampling
Sampling rate
□ A process of taking samples of
information signal at a rate of Nyquist’s
sampling frequency.
□ Nyquist’s Sampling Theorem :
The original information signal can be reconstructed at the receiver
with minimal distortion if the sampling rate in the pulse modulation
system equal to or greater than twice the maximum information
signal frequency.
fs >=2 fm (max)
Quantization
□ A process of converting an infinite number of possibilities to a
finite number of conditions (rounding off the amplitudes of
flat-top samples to a manageable number of levels).
□ Analog signals contain an infinite number of amplitude
possibilities. Thus, converting an analog signal to a PCM code
with a limited number of combinations requires quantization.
□ With quantization, the total voltage range is subdivided into a
smaller number of subranges as shown in Table.
□ The PCM code shown in the Table is a 3-bit sign-magnitude
code with 8 possible combinations (4 positive and 4 negative).
□ The leftmost bit is the sign bit (1 = + and 0 = -) and the two
rightmost bits represent magnitude.
continue…
□ Each voltage level has one code assigned to it
except zero volts, which has two codes, 100 (+0)
and 000 (-0).
□ The magnitude difference between adjacent steps
is called the quantization interval or quantum.
continue...
Analog input signal
Sample pulse
PAM signal
PCM code
QUANTIZATION ERROR
□ A difference between the exact value of the
analog signal & the nearest quantization level.
Dynamic Range (DR)
□ The ratio of the largest possible magnitude to the smallest
possible magnitude that can be decoded by the digital-toanalog converter in the receiver.
Vmax
Vmax
DR 

Vmin resolution
DR  2n  1
DR (dB)  20 log( DR )
□ Where
□
□
□
□
DR = absolute value of dynamic range
Vmax = the maximum voltage magnitude
Vmin = the quantum value (resolution)
n = number of bits in the PCM code
Example 1
1. Calculate the dynamic range for a
linear PCM system using 16-bit
quantizing.
2. Calculate the number of bits in PCM
code if the DR = 192.6 dB
Coding Efficiency
□ A numerical indication of how
efficiently a PCM code is utilized.
□ The ratio of the minimum number of
bits required to achieve a certain
dynamic range to the actual number
of PCM bits used.
Coding Efficiency = Minimum number of bits x 100
Actual number of bits
Signal to Quantization Noise Ratio (SQR)
□ The worst-case voltage SQR
SQR(min)
resolution

Qe
□ SQR for a maximum input signal
SQR(max)
R =resistance
(ohm)
v = rms signal
voltage
q = quantization
interval
Vmax

Qe
□ The signal power-to-quantizing noise power ratio
average signal power
SQR( dB)  10 log
average quantizati on noise power
 10 log
v2
R
2
( q 12)
R
 v2 
 10 log  q 2 
 12 
Example 2
1.
2.
Calculate the SQR (dB) if the input signal = 2 Vrms
and the quantization noise magnitudes = 0.02 V.
Determine the voltage of the input signals if the
SQR (max) = 36.82 dB and q =0.2 V.
Companding
• The process of compressing and then expanding.
• The higher amplitude analog signals are compressed
prior to transmission and then expanded in receiver.
• Improving the dynamic range of a communication system.
Companding Functions
Methods of Companding
□ For the compression, two laws are adopted: the -law in US
and Japan and the A-law in Europe.
□ -law
□
Vout 
□ A-law
Vout
Vmax ln( 1  [Vin Vmax ])
ln( 1   )

A Vin Vmax
 Vmax
1  ln A


Vin
1

ln(
A
Vmax )

 1  ln A
Vin 1
0

Vout A
1 Vin

1
A Vout
Vmax= Max uncompressed
analog input voltage
Vin= amplitude of the input
signal at a particular of
instant time
Vout= compressed output
amplitude
A, = parameter define the
amount of compression
□ The typical values used in practice are: =255 and A=87.6.
□ After quantization the different quantized levels have to be
represented in a form suitable for transmission. This is done via
an encoding process.
continue...
μ-law
A-law
PCM Line Speed
□ The data rate at which serial PCM bits are clocked out of the
PCM encoder onto the transmission line.
samples
bits
line speed 
X
second sample
□ Where
□ Line speed = the transmission rate in bits per second
□ Sample/second = sample rate, fs
□ Bits/sample = no of bits in the compressed PCM code
Example 4
□ For a single PCM system with a sample
rate fs = 6000 samples per second and
a 7 bits compressed PCM code,
calculate the line speed.
Virtues & Limitation of PCM
The most important advantages of PCM are:
□ Robustness to channel noise and
interference.
□ Efficient regeneration of the coded signal
along the channel path.
□ Efficient exchange between BT and SNR.
□ Uniform format for different kind of baseband signals.
□ Flexible TDM.
continue…
□ Secure communication through the use of
special modulation schemes of encryption.
□ These advantages are obtained at the cost of
more complexity and increased BT.
□ With cost-effective implementations, the cost
issue no longer a problem of concern.
□ With
the
availability
of
wide-band
communication channels and the use of
sophisticated data compression techniques, the
large bandwidth is not a serious problem.
□ A single-bit PCM code to achieve digital
transmission of analog.
□ Logic ‘0’ is transmitted if current sample
is smaller than the previous sample
□ Logic ‘1’ is transmitted if current sample
is larger than the previous sample
Cont’d…
Operation of Delta Modulation
continue...
□ Analog input is approximated by a staircase function
□ Move up or down one level () at each sample interval (by one
quantization level at each sampling time)  output of DM is
a single bit.
□ Binary behavior
□ Function moves up or down at each sample interval
□ In DM the quantization levels are represented by two
symbols: 0 for - and 1 for +. In fact the coding process is
performed on eq.
□ The main advantage of DM is its simplicity.
Cont’d...
The transmitter of a DM System
The receiver of a DM system
Delta Modulation - Example
DM circuit’s problem
continue…
•Slope overload distortion is due to the fact that the staircase
approximation mq(t) can't follow closely the actual curve of the
message signal m(t ). In contrast to slope-overload distortion,
granular noise occurs when  is too large relative to the local slope
characteristics of m(t). granular noise is similar to quantization noise
in PCM.
•It seems that a large  is needed for rapid variations of m(t) to
reduce the slope-overload distortion and a small  is needed for
slowly varying m(t) to reduce the granular noise. The optimum  can
only be a compromise between the two cases.
•To satisfy both cases, an adaptive DM is needed, where the step
size  can be adjusted in accordance with the input signal m(t).
continue...
□ In summary
□ Slope overload
□ Due to the input analog signal amplitude changes
faster than the speed of the modulator
□ to minimize : the product of the sampling step size and
the sampling rate must be equal to or larger than the
rate of change of the amplitude of the input analog
signal.
□ Granular noise
□ Due to the difference between step size and sampled
voltage.
□ To minimize : increase the sampling rate, decrease the
step size of modulator
DM Performance
□ Good voice reproduction
□ PCM - 128 levels (7 bit)
□ Voice bandwidth 4khz
□ Should be 8000 x 7 = 56kbps for PCM
□ Data compression can improve on this
□ e.g. Interframe coding techniques for video
continue...
□ Adaptive Delta Modulation (ADM)
□ A Delta Modulation system where the step
size of the DAC is automatically varied
depending
on
the
amplitude
characteristics of the analog signal.
□ A well designed ADM scheme can
transmit voice at about half the bit rate of
a PCM system with equivalent quality.
□
Converting standard logic level to a form
more suitable to telephone line transmission.
□
The line codes properties:
1. Transmission BW should be small as
possible
2. Efficiency should be as high as possible
3. Error detection & correction capability
4. Transparency (Encoded signal is received
faithfully)
continue...
□ Six factors must be considered when
selecting a line encoding format;
1.transmission voltage & DC component
2.Duty cycle
3.Bandwidth consideration
4.Clock and framing bit recovery
5.Error detection
6.Ease of detection and decoding
Why Digital Signaling?
□ Low cost digital circuits
□ The flexibility of the digital approach
(because digital data from digital
sources may be merged with digitized
data derived from analog sources to
provide
general
purpose
communication system)
Digital Modulation
□ Using Digital Signals to Transmit Digital Data
□ Bits must be changed to digital signal for transmission
□ Unipolar encoding
□ Positive or negative pulse used for zero or one
□ Polar encoding
□ Uses two voltage levels (+ and - ) for zero or one
□ Bipolar encoding
□ +, -, and zero voltage levels are used
Non-Return to Zero-Level (NRZ-L)
□ Two different voltages for 0 and 1 bits.
□ Voltage constant during bit interval.
□ no transition, no return to zero voltage
□ More often, negative voltage for one value and positive for the
other.
Non-Return to Zero Inverted (NRZ-I)
□ Non-return to zero inverted on ones
□ Constant voltage pulse for duration of bit
□ The polarity of the bit is reversed when a 1 bit is
encountered
□ All subsequent 0s following the 1 are recorded at the
same polarity
Multilevel Binary(Bipolar-AMI)
•
•
•
•
zero represented by no line signal
one represented by positive or negative pulse
one pulses alternate in polarity
No loss of sync if a long string of ones (zeros still a
problem)
• No net dc component
• Lower bandwidth
• Easy error detection
0
1
0
0
1
1
0
0
0
1
1
Pseudoternary
□ One represented by absence of line signal
□ Zero represented by alternating positive and negative
□ No advantage or disadvantage over bipolar-AMI
0
1
0
0
1
1
0
0
0
1
1
Manchester
□ There is always a mid-bit transition {which is used as a
clocking mechanism}.
□ The direction of the mid-bit transition represents the
digital data.
□ 1  low-to-high transition
□ 0  high-to-low transition
□ Consequently, there may be a second transition at the
beginning of the bit interval.
□ Used in 802.3 baseband coaxial cable and CSMA/CD
twisted pair.
Differential Manchester
□ mid-bit transition is ONLY for clocking.
□ 1  absence of transition at the beginning of the bit
interval
□ 0  presence of transition at the beginning of the bit
interval
□ Differential Manchester is both differential and biphase.
[Note – the coding is the opposite convention from NRZI.]
□ Used in 802.5 (token ring) with twisted pair.
□ * Modulation rate for Manchester and Differential
Manchester is twice the data rate  inefficient
encoding for long-distance applications.
Example 5
□ Sketch the data wave form for a bit
stream 11010 using
□ NRZL
□ Bipolar AMI
□ Pseudoternary
□ Manchester
END OF PART 2