Download 4.2 Digital Transmission

DIGITAL TRANSMISSION
PART B
1
Review…
PCM Block Diagram
• Most common form of analog to digital modulation (better
noise and interference immunity)
• 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)
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Review…
Types of Quantizer
1. Uniform type : The levels of the quantized amplitude are uniformly spaced.
2. Non-uniform type : The levels are not uniform.
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Review…
Dynamic Range (DR)
□ Ratio of the largest possible
magnitude/smallest possible magnitude.
Vmax
Vmax
DR 

Vmin resolution
DR  2n  1
□ Where
DR (dB)  20 log( DR )
□ DR = absolute value of dynamic range
□ Vmax = the maximum voltage magnitude
□ Vmin = the quantum value (resolution)
□ n = number of bits in the PCM code
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Review…
Review Example..
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
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Review…
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
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Review…
Review Example
Given A PCM system with the following parameters
Maximum analog input frequency = 4kHz.
Maximum decoded voltage at Rx = ±2.55V.
Minimum dynamic range = 46 dB
Determine :
(i) Minimum sample rate. (ans: 8kHz)
(ii) Minimum number of bits used (ans :n=7.63≈8)
(iii) Resolution (ans : 0.01V )
(iv) Quantization error (ans: 0.01V/2=0.005V)
(v) Coding efficiency (ans: (8.63/9)x100%=95.89%)
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Signal to Quantization Noise Ratio (SQR)
□ The worst-case voltage SQR
SQR(min)
resolution

Qe
□ SQR for a maximum input signal
SQR(max)
Vmax

Qe
R =resistance
(ohm)
v = rms signal
voltage
q = quantization
interval
□ The signal power-to-quantizing noise power ratio
average signal power
SQR( dB )  10 log
average quantizati on noise power
 10 log
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v2
R
2
( q 12)
R
 v2 
 10 log  q 2 
 12 
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Example 2
1.
Calculate the SQR (dB) if the input signal = 2 Vrms
and the quantization noise magnitudes = 0.02 V.
2.
Determine the voltage of the input signals if the
SQR = 36.82 dB and q =0.2 V.
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Effect of Non-Linear Coding
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Nonlinear Encoding
□ Quantization levels not evenly spaced
□ Reduces overall signal distortion
□ Can also be done by companding
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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 DR of a communication system.
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Companding Functions
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Method 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

Vmax A
1 Vin

1
A Vmax
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.
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Example 3
□ A companding system with µ = 255
used to compand from 0V to 15 V
sinusoid signal. Draw the characteristic
of the typical system.
□ Draw an 8 level non-uniform quantizer
characteristic that corresponds to the
mentioned µ.
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16
Cont’d...
μ-law
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A-law
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PCM Line Speed
□ Line speed is the data rate at which serial PCM bits are
clocked out of the PCM encoder onto the transmission line.
line speed 
samples
bits
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
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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.
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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.
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Cont’d…
□ 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.
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Time-Division Multiplexing
□ This technique combines time-domain
samples from different message signals
(sampled at the same rate) and transmits
them together across the same channel.
□ The multiplexing is performed using a
commutator (switch). At the receiver a
decommutator (switch) is used in
synchronism with the commutator to
demultiplex the data.
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Cont’d…
□ TDM system is very sensitive to symbol dispersion,
that is, to variation of amplitude with frequency or
lack of proportionality of phase with frequency. This
problem may be solved through equalization of
both magnitude and phase.
□ One of the methods used to synchronize the
operations of multiplexing and demultiplexing is to
organize the multiplexed stream of data as frames
with a special pattern. The pattern is known to the
receiver and can be detected very easily.
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Block diagram of TDM-PCM communication
system
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□ Conventional PCM- multiple bit codes
required to represent the sample value.
□ DM-Uses a single-bit PCM code to
achieve digital transmission of analog
signals.
□ 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
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Cont’d…
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Operation of Delta Modulation
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Cont’d...
□ 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.
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Cont’d...
The transmitter of a DM System
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The receiver of a DM system
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Delta Modulation - Example
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DM circuit’s problem
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Cont’d…
•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).
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Cont’d...
□ 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
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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
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Cont’d...
□ 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.
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