dcs_sampling and quantization
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The Chapter includes:
Pulse Amplitude
Modulation Pulse Width Modulation
Pulse PositionModulation
Pulse Code Modulation
PULSE MODULATION
The process of transmitting signals in the form ofpulses (discontinuous signals) by using special
techniques.
Created by C. Mani, Principal, K V No.1, AFS, Jalahalli West, Bangalore
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Analog Pulse Modulation Digital Pulse Modulation
Pulse Amplitude (PAM)
Pulse Width (PWM)
Pulse Position (PPM)
Pulse Code (PCM)
Delta (DM)
Pulse Modulation
Pulse Amplitude Modulation (PAM):
* The signal is sampled at regular intervals such that each sampleis proportional to the amplitude of the signal at that samplinginstant. This technique is calledsampling.
* For minimum distortion, the sampling rate should be more thantwice the signal frequency.
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ANDGate
Pulse ShapingNetwork
FMModulator
AnalogSignal
PAM - FM
Pulses at sampling frequency
HF Carrier Oscillator
PAM
Pulse Amplitude Modulator
Analog Signal
Amplitude ModulatedPulses
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* In this type, the amplitude is maintained constant but the durationorlength orwidth of each pulse is varied in accordance with
instantaneous value of the analog signal.* The negative side of the signal is brought to the positive side byadding a fixed d.c. voltage.
Analog Signal
Width Modulated Pulses
Pulse Width Modulation (PWM or PLM or PDM):
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* In this type, the sampled waveform has fixed amplitude andwidth whereas the position of each pulse is varied as perinstantaneous value of the analog signal.
* PPM signal is further modification of a PWM signal. It haspositive thin pulses (zero time or width) corresponding to thestarting edge of a PWM pulse and negative thin pulsescorresponding to the ending edge of a pulse.
* This wave can befurther amendedby eliminating thewhole positivenarrow pulses.The remainingpulse is calledclipped PPM.
PWM
PPM
Pulse Position Modulation (PPM):
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PAM, PWM and PPM at a glance:
Analog Signal
Amplitude Modulated Pulses
Width Modulated Pulses
Position Modulated Pulses
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Time
Voltag
e
76543210
111110101100
011010001000
Levels
Binary
Codes
Time
Time
V
oltage
0 1 0 1 0 1 1 1 0 1 1 1 1 1 0 1 0 1 0 1 0
Sampling,QuantizationandCoding
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Merits of Digital Communication:1. Digital signals are very easy to receive. The receiver has to just detect
whether the pulse is low or high.
2. AM & FM signals become corrupted over much short distances ascompared to digital signals. In digital signals, the original signal can be
reproduced accurately.
3. The signals lose power as they travel, which is called attenuation. WhenAM and FM signals are amplified, the noise also get amplified. But thedigital signals can be cleaned up to restore the quality and amplified bythe regenerators.
4. The noise may change the shape of the pulses but not the pattern of thepulses.
5. AM and FM signals can be received by any one by suitable receiver. Butdigital signals can be coded so that only the person, who is intended for,can receive them.
6. AM and FM transmitters are real time systems. i.e. they can be received
only at the time of transmission. But digital signals can be stored at thereceiving end.
7. The digital signals can be stored, or used to produce a display on acomputer monitor or converted back into analog signal to drive a loudspeaker.
END
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Digital Communications I:
Modulation and Coding Course
Term 3 2008
Catharina LogothetisLecture 2
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Last time, we talked about:
Important features of digital communication
systems
Some basic concepts and definitions such asas signal classification, spectral density,
random process, linear systems and signal
bandwidth.
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Today, we are going to talk about:
The first important step in any DCS:
Transforming the information source to a form
compatible with a digital system
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EncodeTransmit
Pulse
modulateSample Quantize
Demodulate/
Detect
Channel
Receive
Low-pass
filterDecode
Pulse
waveformsBit stream
Format
Format
Digital info.
Textual
info.
Analog
info.
Textualinfo.
Analog
info.
Digital info.
source
sink
Formatting and transmission of baseband signal
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Format analog signals
To transform an analog waveform into a form
that is compatible with a digital
communication system, the following steps
are taken:
1. Sampling2. Quantization and encoding
3. Baseband transmission
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Sampling
Time domain Frequency domain
)()()( txtxtxs = )()()( fXfXfXs =
|)(| fX)(tx
|)(| fX
|)(| fXs)(txs
)(tx
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Aliasing effect
LP filter
Nyquist rate
aliasing
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Lecture 2 17
Sampling theorem
Sampling theorem: A bandlimited signal
with no spectral components beyond , canbe uniquely determined by values sampled at
uniform intervals of
The sampling rate, is
called Nyquist rate.
Samplingprocess
Analog
signal
Pulse amplitude
modulated (PAM) signal
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Lecture 2 18
Quantization
Amplitude quantizing:Mapping samples of a continuousamplitude waveform to a finite set of amplitudes.
In
Out
Quan
tiz
ed
valu
es
Average quantization noise power
Signal peak power
Signal power to average
quantization noise power
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Lecture 2 19
Encoding (PCM)
A uniform linear quantizer is called Pulse Code
Modulation (PCM).
Pulse code modulation (PCM): Encoding the quantized
signals into a digital word (PCM word or codeword). Each quantized sample is digitally encoded into an lbits
codeword whereL in the number of quantization levels and
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Lecture 2 20
Quantization example
t
Ts: sampling time
x(nTs): sampled valuesxq(nTs): quantized values
boundaries
Quant. levels
111 3.1867
110 2.2762
101 1.3657
100 0.4552
011 -0.4552
010 -1.3657
001 -2.2762
000 -3.1867
PCM
codeword 110 110 111 110 100 010 011 100 100 011 PCM sequence
amplitude
x(t)
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Lecture 2 21
Quantization error
Quantizing error:The difference between the input andoutput of a quantizer )()()( txtxte =
+
)(tx )( tx
)()(
)(
txtx
te
=
AGC
x
)(xqy =
Qauntizer
Process of quantizing noise
)(tx )( tx
)(te
Model of quantizing noise
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Lecture 2 22
Quantization error
Quantizing error: Granular or linear errors happen for inputs within the dynamic
range of quantizer
Saturation errors happen for inputs outside the dynamic
range of quantizer Saturation errors are larger than linear errors
Saturation errors can be avoided by proper tuning of AGC
Quantization noise variance:
2Sat2Lin222 )()(})]({[ +===
dxxpxexqxq E
ll
L
l
l qxpq
)(12
212/
0
22
Lin
=
= Uniform q.12
22
Lin
q=
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Lecture 2 23
Uniform and non-uniform quant.
Uniform (linear) quantizing:
No assumption about amplitude statistics and correlationproperties of the input. Not using the user-related specifications Robust to small changes in input statistic by not finely tuned to a
specific set of input parameters Simple implementation
Application of linear quantizer: Signal processing, graphic and display applications, process
control applications
Non-uniform quantizing: Using the input statistics to tune quantizer parameters
Larger SNR than uniform quantizing with same number of levels Non-uniform intervals in the dynamic range with same quantization
noise variance Application of non-uniform quantizer:
Commonly used for speech
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Lecture 2 24
Non-uniform quantization
It is achieved by uniformly quantizing the compressed signal.
At the receiver, an inverse compression characteristic, called
expansion is employed to avoid signal distortion.
compression+expansion companding
)(ty)(tx )( ty )( tx
x
)(xCy = x
yCompress Qauntize
Channel
Expand
Transmitter Receiver
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Lecture 2 25
Statistics of speech amplitudes
In speech, weak signals are more frequent than strong ones.
Using equal step sizes (uniform quantizer) gives low for weaksignals and high for strong signals.
Adjusting the step size of the quantizer by taking into account the speech statisticsimproves the SNR for the input range.
0.0
1.0
0.5
1.0 2.0 3.0Normalized magnitude of speech signalP
robabili
tyd
ensity
function
qN
S
qN
S
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Lecture 2 26
Baseband transmission
To transmit information through physicalchannels, PCM sequences (codewords) are
transformed to pulses (waveforms). Each waveform carries a symbol from a set of size M.
Each transmit symbol represents bits of
the PCM words.
PCM waveforms (line codes) are used for binary
symbols (M=2).
M-ary pulse modulation are used for non-binary
symbols (M>2).
Mk 2log=
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Lecture 2 27
PCM waveforms
PCM waveforms category:
Phase encoded Multilevel binary
Nonreturn-to-zero (NRZ) Return-to-zero (RZ)
1 0 1 1 0
0 T 2T 3T 4T 5T
+V
-V
+V
0
+V
0
-V
1 0 1 1 0
0 T 2T 3T 4T 5T
+V
-V
+V
-V
+V
0
-V
NRZ-L
Unipolar-RZ
Bipolar-RZ
Manchester
Miller
Dicode NRZ
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Lecture 2 28
PCM waveforms
Criteria for comparing and selecting PCM
waveforms: Spectral characteristics (power spectral density and
bandwidth efficiency)
Bit synchronization capability Error detection capability
Interference and noise immunity
Implementation cost and complexity
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Lecture 2 29
Spectra of PCM waveforms
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Lecture 2 30
M-ary pulse modulation
M-ary pulse modulations category: M-ary pulse-amplitude modulation (PAM)
M-ary pulse-position modulation (PPM)
M-ary pulse-duration modulation (PDM)
M-ary PAM is a multi-level signaling where eachsymbol takes one of the Mallowable amplitude levels,
each representing bits of PCM words.
For a given data rate, M-ary PAM (M>2) requires less
bandwidth than binary PCM. For a given average pulse power, binary PCM is easier
to detect than M-ary PAM (M>2).
Mk 2log=
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2 3
PAM example
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