dcs_sampling and quantization

8/8/2019 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

dcs_sampling and quantization

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