‫دانشکده مهندس ی کامپیوتر‬
‫ارتباطات داده (‪)40-883‬‬
‫مدوالسیون پالس‬
‫نیمسال ّ‬
‫دوم ‪92-93‬‬
‫افشین ّ‬
‫همتیار‬
Pulse Modulation
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Introduction
Sampling Process
Pulse-Amplitude Modulation
Other forms of Pulse Modulations
Bandwidth-Noise Trade-off
Quantization Process
Pulse-Code Modulation
Noise Consideration in PCM Systems
Time-Division Multiplexing
Digital Multiplexers
Virtues, Limitations, and Modifications of PCM
Linear Prediction
Differential PCM
Adaptive Differential PCM
Delta Modulation
2
Introduction
Continuous-Wave Modulation:
Some parameter (amplitude, phase, or frequency) of a
sinusoidal carrier wave is varied continuously in accordance
with the message signal.
Analog Pulse Modulation:
Some parameter (amplitude, duration, or position) of each
pulse (in a periodic pulse train) is varied in a continuous
manner in accordance with the corresponding sample value
of the message signal.
(Information transmission in analog form, but transmission at discrete times.)
Digital Pulse Modulation:
The message signal is represented in a form that is discrete in
both time and amplitude, thereby permitting its transmission
in digital form as a sequence of coded pulses.
3
Sampling Process (1)
fs = 2W
Ts = 1/(2W)
4
Sampling Process (2)
Sampling theorem:
A band-limited signal of finite energy, which has no
frequency components higher than W Hertz,
1) is completely described by specifying the values of the
signal at instants of time separated by 1/(2W) seconds.
2) may be completely recovered from a knowledge of its
samples taken at the rate of 2W samples per second.
fs < 2W
fs > 2W
5
Pulse Amplitude Modulation (1)
6
Pulse Amplitude Modulation (2)
Reconstruction filter 
Aperture effect:
Flat-top samples  Amplitude distortion and T/2 delay
Equalizer

7
Other forms of Pulse Modulation
Modulating signal

Carrier Pulse

Pulse Duration Modulation 
(Pulse Width Modulation)
Pulse Position Modulation 
8
Bandwidth-Noise Trade-off (1)
PPM is the optimum form of analog pulse modulation,
and has similar noise performance as FM:
1) Both systems have a figure of merit proportional to the square
of the transmission bandwidth normalized with respect to the
message bandwidth.
2) Both systems exhibit a threshold effect as the signal-to-noise
ratio is reduced.
Can we produce a trade-off better than a square law?
Yes, by Digital Pulse Modulation .
9
Bandwidth-Noise Trade-off (2)
A basic form of DPM is Pulse Code Modulation:
• Discrete in both time and amplitude.
• Transmission of the message signal as a sequence of
coded binary pulses.
• The effect of channel noise at the receiver output can be
reduced to a negligible level simply by making the average
power of the transmitted binary PCM wave large enough
compared to the average power of the noise.
Two fundamental processes are involved in the generation of a
binary PCM wave:
1) Sampling: Discrete-time representation of the message signal
2) Quantization: Discrete –amplitude representation of the message signal
Possibility to realize an exponential law for the bandwidthnoise trade-off.
10
Quantization Process (1)
midtread
midrise
11
Quantization Process (2)
Quantization Noise
12
Quantization Process (3)
Quantization Noise


(SNR)O Increases
exponentially with
the number of bits.
13
Quantization Process (4)
Example: Sinusoidal Modulating Signal

L (levels)
R (bits)
SNR (dB)
256
8
49.8
1024
10
61.8
4096
12
73.8
16384
14
85.8
65536
16
91.8
14
Pulse Code Modulation (1)
Basic Elements
15
Pulse Code Modulation (2)
Quantization (Compression & Expansion)
μ Law
A Law
Typical used values: μ = 225 , A = 87.6
16
Pulse Code Modulation (3)
Line Codes:
Unipolar NRZ

Polar NRZ

Unipolar RZ

Bipolar RZ
(AMI)

Manchester
(Split Phase)

17
Pulse Code Modulation (4)
Line Codes:
Unipolar NRZ 
Unipolar RZ

 Polar NRZ
 Bipolar RZ
Manchester 
18
Pulse Code Modulation (5)
Line Codes:
Unipolar NRZ

DC component and thus waste of DC power
Nonzero spectrum near zero frequency
Lack of synchronization
Polar NRZ

High spectrum near zero frequency
Lack of synchronization
Unipolar RZ

DC component and high Spectrum near zero frequency
Need for more power than Polar NRZ and twice bandwidth
Good for timing recovery
Bipolar RZ

No DC component
Low spectrum near zero frequency
(if equal probability for “1”s and “0”s)
Good for timing recovery
Manchester

No DC component
Low spectrum near zero frequency
(regardless of signal statistics)
Very good for timing recovery
Twice bandwidth
19
Pulse Code Modulation (6)
Differential Encoding
20
Pulse Code Modulation (6)
Regeneration:
1) Channel noise and interference  Wrong decisions  Bit errors
2) Deviation of spacing between received pulses  Jitter  Distortion
Decoding: Generating a pulse the amplitude of which is the
weighted sum of all the pulses in the code word.
Filtering: Low-pass reconstruction filter whose cutoff frequency
is equal to the message bandwidth.
21
Noise Considerations in PCM Systems (1)
Two major sources of Noise:
Channel Noise
• Is introduced anywhere between the transmitter output and
the receiver input.
• Always present, once the equipment is switched on.
Quantization Noise
• Is introduced in transmitter and is carried all the way along
to the receiver output.
• Is signal-dependent. It disappears when the message signal is
switched off.
Measure for fidelity of PCM transmission:
Average probability of symbol error  Bit Error Rate (BER)
22
Noise Considerations in PCM Systems (2)
Error Threshold:
Eb/N0
(dB)
4.3
Pe
10-2
Time between errors
(Bit Rate = 105 bps)
10-3 Second
8.4
10-4
10-1 Second
10.6
10-6
10 Seconds
12
10-8
20 Minutes
13
10-10
1 Day
14
10-12
3 Months
Eb/N0: The ratio of the transmitted signal energy per bit,
to the noise spectral density.
23
Time-Division Multiplexing
Block Diagram of TDM System
24
Digital Multiplexer
1
1
2
Multiplexer
High-speed
Transmission
Line
2
Demultiplexer
N
Data Sources
T1 Digital Hierarchy
DS0:
64
Kbps
DS1:
1.544 Mbps
DS2:
6.312 Mbps
DS3: 44.736 Mbps
DS4: 274.176
Mbps
DS5: 560.160
Mbps
N
Destinations
one voice channel
(twenty four DS0) {(1+24x8)x8 KSamples/Sec}
(four DS1)
(seven DS2)
(six DS3)
(two DS4)
25
Virtues, Limitations and Modifications of PCM (1)
Advantages:
1) Robustness to channel noise and interference
2) Efficient regeneration of the coded signal along the
transmission path.
3) Efficient exchange of increased channel bandwidth for
improved signal-to-noise ratio, obeying an exponential law.
4) A uniform format for the transmission of different kinds of
baseband signals, hence their integration with other forms of
digital data in a common network.
5) Comparative ease with which message sources may be
dropped or reinserted in a time-division multiplex system.
6) Secure communication through the use of special modulation
scheme or encryption.
26
Virtues, Limitations and Modifications of PCM (2)
Limitations:
1) Increased system complexity
>> Cost effective fashion using VLSI
2) Increased channel bandwidth
>> Availability of wideband channels (satellite, fiber optics)
>> Data compression techniques
Modifications:
1) Differential PCM
2) Adaptive Differential PCM
(DPCM)
(ADPCM)
27
Linear Prediction
(Finite-duration Impulse Response (FIR) Discrete-time Filter)
Linear
Adaptive
Prediction
28
Differential Pulse Code Modulation
Transmitter
Receiver
29
Adaptive Differential Pulse Code Modulation
Adaptive Quantization
with:
• Forward estimation (AQF)
• Backward estimation (AQB)
AQB
Adaptive Prediction
with:
• Forward estimation (APF)
• Backward estimation (APB)
APB
30
Delta Modulation (1)
• Sampling at higher rates
• One bit for each sample
31
Delta Modulation (2)
Transmitter
Receiver
32
Delta Modulation (3)
Slope Overload
Required condition:
(for no overload)
33
Delta Modulation (4)
Delta-Sigma
Modulation
• Simplification of the receiver
• Pre-emphasis of low-frequency content of the input signal
• Increasing correlation between adjacent samples
 reduction the variance of the error signal
34