digital transmission pulse modulation

8/10/2019 Digital Transmission Pulse Modulation

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EE401B/EE3DTR/EE4DTRDigital Transmission

Pulse Modulation

Dr John A.R. Williams

[email protected]

c 20012008 Dr John A.R. Williams Pulse Modulation p. 1


2/33

Overview

Pulse Modulation Schemes

Pulse Amplitude and Position Modulation

Time Division Multiplexing

Pulse Code Modulation

Quantisation and Companding

Differential and Delta Pulse Code Modulation

Adaptive Modulation Techniques

Subband Coding



3/33

Pulse Modulation Schemes

Pulse PositionModulation(PPM) t

Pulse FrequencyModulation

(PFM) t

t

tPulse Carrier

Message Signal

t

Pulse AmplitudeModulation

(PAM)

t

Pulse WidthModulation

(PWM)



4/33

Natural Sampling

0

t

(t)

W W0

|F( )|

W = 2B W = 2B0

t

(t)

W W0

|F( )|

W = 2B W = 2B

W W0

|F( )|

W = 2B W = 2B

p(t)

00

t

T 2T 3T2T T

1

T Pn

2/T/T

0 2

0

02

0

p(t)

00

t

T 2T 3T2T T

1

T PnPn

2/T/T

0

0 2

02

0

0

02

02

0

2/T

0 2 0 02 0

Fs()

0

t

(t)s

0 T 2T 3T2T T

T

2/T

0 2 0 02 0

2/T

0

0 2 02 0 0 02 02 0

Fs()Fs()Fs()

0

t

(t)s(t)s

0 T 2T 3T2T T

T



5/33

Nyquist Sampling Theorem

1

T0 W

T=1/2W

W 1

T

1

T0 W

T=1/2W

W 1

T

1

T

1

T

1

TW+

1

TWW0 W +

1

TW

T1/2W

W +1

TW

1

TW W

1

TW

Undersampled

A band-limited signal of finite energy, which has no fre-

quency components higher than WHz is completely

described by sampling values of the signal at instantsof time separated by1/(2W)seconds



6/33

Pulse Amplitude Modulation - Flat Topped Sampling

0

Fs( )

T

0

t

(t)s

0

Fs( )Fs( )

TT

0

t

(t)s (t)s

q(t)

0

t

1

0

Q()

-2/ 2/

q(t)

0

t

q(t)

0

t

1

0

Q()

-2/-2/ 2/

t

0

T(t)s

q(t)*

2/T

0 2 0 02 0 0

Fs ( ) Q( )

t

0

T(t)s

q(t)*(t)s

(t)s

q(t)* q(t)*

2/T

0 0 2 02 0 0 02 02 0 0

Fs ( ) Q( )Fs ( )Fs ( ) Q( )



7/33

PAM Demodulation

Sample and Hold Circuit

C R

T

Rs

R sC > TC R

T

Rs

R sC > TC R

T

T

RsRs

R sC T

t

T

input

sample-and-holdoutput

low-pass filteredoutput



8/33

Time Division Multiplexing (TDM)

single communication

channel carrying N

signals:

signal 1

signal 2

signal N

synchronised

commutatorsignal 1

signal 2

signal N

low-pass filters to

band-limit signals

low-pass filters to

recover signals

Time Division Multiplexing Of 2 PAM Signals

t

TT

sTT

sT

s



9/33

TDM Example

A four channel time division multiplexed PAM system has input signals band-

limited as follows:

channel 1: 016 kHz

channel 2: 020 kHzchannel 3: 025 kHz

channel 4: 2530 kHz

If the four channels are sampled at equal time intervals using very short pulses at

the minimum frequency possible, and the TDM signal is low-pass filtered prior totransmission determine

1. The minimum clock frequency and the commutator recycling frequency

2. the minimum cut-off frequency of the LPF consistent with recovery of the

signals after transmission

3. What would be the minimum bandwidth required if the four channels were

frequency division multiplexed using

(a) DSB-AM

(b) SSB



10/33

TDM Example

1. Channel 4 has a maximum frequency = 30 kHz and must,

therefore, be sampled at 60 kHz. This is the maximum frequency

in the set of channels. Hence for the four channels sampled at

equal time intervals, the clock rate=460=240kHz and thecommutator must cycle at 60 kHz

2. For the TDM signal we must have a filter cut-off at half the

maximum frequencyBc=1/(2Ts) =120kHz, andTs=4.17s

3. (a) DSB-AM requires2 (16 + 20 + 25 + 5) =132kHz

(b) SSB requires132/2=66kHz



11/33

PPM and PWM Generation

inputsignal

Sample

and hold

Clock

Sawtooth

Generator

reference level

PWMComparator

reference level

PWMComparator

PPM

Pulse

Generator



inputsignalinputsignal

sawtoothsawtooth

PWMoutputPWMoutput

PPMoutputPPM

output

sumsum



12/33

Pulse Code Modulation

0.0

0.2

0.4

0.6

0.8

1.0

Amplitude

123

45678

9101112131415

0

Quantisationlevel

Binarycode

1111111011011100101110101001

10000111011001010100

0011001000010000

0111 1101 1110 1010 1001 0101 0011 0101 0111

Samplinginstants

sampled signal



13/33

PCM Transmission

PCM Transmitter

analogueto

digital converter

PCM

signal

input(analogue)

signalSampler EncoderQuantiser

Parallelto

serial

converter

NRZ coded PCM signal with 7-bit samples

1011001 1110011 0101010

framing bit

PCM Receiver

Output MessageSignal

DecoderRegenerator Reconstruction

Filter

PCM signal+noise

+distortion

Output MessageSignal

DecoderRegenerator Reconstruction

Filter

PCM signal+noise

+distortion



14/33

PCM Advantages

Digital transmission providesrobustnessagainst noise and

interference

PCM signals can beregeneratedat intermediate repeaters. Modulating and demodulating circuits areentirely digitaloffering

compatibility with VLSI: high reliability and low cost

Signals can be stored in memory;digital signal processingoperationssuch as time scaling can be easily performed

Encryptionusing special codes can allow secure communication

Source codingmay be used to avoid unnecessary repetitions offrequent message



15/33

Quantisation

(t)=f(t)-f (t)

f(t)

q

t

/2

/2

f (t)q

0

0

Error

Magni

tude

0

1

2

3

4

M-3

M-2

M-1

M

M

2

+1M2

V+

2

V

2

True SignalLevel



16/33

Quantisation Noise

Assume all values in the range /2< < /2are equally probable. p() =1/.Then

2

=

1

Z /2

/2

2

d=

1

3

3/2/2 =

2

12

If a signal occupies thefull quantiser range. Peak signal amplitude isM/2giving

(SNRQ)peak=(M/2)2

2/12 =3M2 =322n

(SNRQ)peak=10{log10 3 + 2n log10 2} =4.8 + 6n[dB]

If we have asinusoidal signal, mean signal power is(M/2)2/2and

(SNRQ)mean=10{log10 1.5 + 2n log10 2} =1.8 + 6n[dB]

TheSNRQincreases by 6 dB for each additional bit used in quantisation



17/33

Quantisation Example

What is the quantisation noise for the case where the quantiser always rounds down to

the next lowest level (i.e. the maximum error is).



18/33

Quantisation Example

What is the quantisation noise for the case where the quantiser always rounds down to

the next lowest level (i.e. the maximum error is).If we round down the quantisation error is equiprobable in the range 0


19/33

Companding

A-law compression characteristic

1/A1-1 0

-1/A

Vout

Vin1/A

1-1 0

-1/A

Vout

Vin

Vout= AVin

1 + logeA , 0 |Vin|

1

A (linear region)

=1 + loge(AVin)

1 + logeA,

1

A |Vin| 1, (logarithmic region)

A=87.7in Europe

Vout

Vin

Increasing A

Vout

Vin

Increasing A

0

1/A

2dB {

Vin

SNRQ

WithoutCompanding

0

1/A

2dB {

Vin

SNRQ

WithoutCompanding

0

1/A

2dB {

Vin

SNRQ

WithoutCompanding



20/33

Segmented Companding

640 128 256

512 1024 2048 4096

32

48

64

80

96

112

128

0

Input Level

128 16

64 32

64 16

256 16512 16

1024 16

2048 166 bi ts equiv.

10 bits equiv.

12 bits equiv.

11 bits equiv.

9 bi ts equiv.

8 bi ts equiv.

7 bi ts equiv.



21/33

NICAM

Nearly Instantaneous Companded Audio Multiplex

BitsRange 0

MSB LSB

Range 1Range 2Range 3Range 4

1 2 3 4 5 6 7 8 91011121314

Transmit ted bits

14 bit resolution with 5 ranges represented in 3 bits

1 range setting per block of 32 samples (1 ms)

Ranges packed into 7 bits every 3 blocks (3ms)



22/33

Differential Pulse Code Modulation

If we oversample changes in signal amplitude are small and we can use

fewer bits to quantise.

SampledInput Signal

InputSignal

Range

DifferentialSignalRange

t

t

Ts



23/33

Differential Pulse Code Modulation

DPCM Encoder

Sampler

Predictor

+ Quantiserx(t) xn

xn

+

en en

{ai}

en=xn

p

i=1

aixni

DPCM Decoder

+

Predictor

en

xn

xn

{ai}

nx= en+

p

i=1

ai xni

xnxn =

en+

p

i=1 ai xni

en+

p

i=1 aixni

= qn+p

i=1

ai( xnixni)

i.e. there is an accumulation of quantisation errors at the receiver.



24/33

DPCM Processing Gain

Sampler

Predictor

+ Quantiserx(t) xn

xn

+

en en

{ai}

SNRO=2x

2

E

2E

2

Q

=GPSNRQ

Minimise2Eusing Yule-Walker equations

p

i=1 ai(i j) =(j), j=1,2, . . . ,p

where (n)is the autocorrelation function of the sampled signal sequence xn, whichmay be estimated from the finite set of samples {xn} by

(n) = 1

N

Nn

i=1

xixi+n,n=0,1, . . . ,p

(See Proakis Page 128)



25/33

Practical DPCM

DPCM Encoder

Sampler + Quantiser

Predictor +

x(t) xn +

en en

xnxn

{ai}

en=xnp

i=

1

ai xni

DPCM Decoder

+

Predictor

en

xn

xn= xn+ en

{ai}

To lowpass

Filter

xn= en+p

i=1

ai xni

xnxn =

en+

p

i=1

ai xni

en+

p

i=1

ai xni

= qn

Error at receiver is only the quantisation error.c 20012008 Dr John A.R. Williams Pulse Modulation p. 24


26/33

Improved DPCM

Encoder

Sampler + Quantiser

+Linear Filter

{ai}

Linear Filter{bi}

+

x(t) xn +

en en

xnxn

Decoder

+

+Linear Filter

{ai}Linear Filter

{bi}

en xn To lowpass

Filter

Improve estimate us-

ing linearly filtered past

values of the quantised

error.

xn =

p

i=1

ai xni

+m

i=1

bieni



27/33

Delta Modulation (DM)

DM Encoder

Unit Delayz-1

QuantiserSamplerx t( ) xn en

~xn

~$ ~x xn n= 1

+

-

~en = 1 DM Decoder

Z-1

~en ~ ~$x x en n n= + To lowpassfilter

Ts

t

1 1 0 1 1 0 1 0 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 1 0 1 0 1 1 1

Input Signal ( )f t

StepOverload

A simple practical approach

+

f t( )Comparator

BinaryOutputSignal

Clock

Flip-flop

(Output v)

R

C

R

C

RC Integrator

+V

-V



28/33

Variable Step Size DM

DM Distortion

t

Slope-

overloaddistortion

Granular Noise

x t( )

t

Slope-

overloaddistortion

Granular Noise

x t( )

With Variable Step Size

t

Slope-overloaddistortion

Granular Noisex t( )

Adaptive DM Encoder

QuantiserSampler

Accumulator

x t( ) xn en+

-

~en = 1

~en1

z-1

z-1

To transmitter

n

n1

Adaptive DM Decoder

AccumulatorOutput

LowpassFilter

~en

~en1

z-1

z-1

n

n1



29/33

Slope Overload Distortion Example

Consider a sine wave of frequency fmwith amplitudeAmapplied to a

delta modulator of step size. Show that the slope-overload distortionwill occur if

Am>

2fmTs

whereTsis the sampling period. What is the maximum power that may

be transmitted without slope overload distortion?



30/33

Slope Overload Distortion Example

Consider a sine wave of frequency fmwith amplitudeAmapplied to a

delta modulator of step size. Show that the slope-overload distortionwill occur if

Am>

2fmTs

whereTsis the sampling period. What is the maximum power that may

be transmitted without slope overload distortion?Modulated Wavem(t) =Am cos2fmthas slopedm(t)

dt = 2fmAm sin2fmt.

Maximum average slope reproduced by the delta modulator is/Ts.Therefore require2fm>

Ts

orAm>

2fmTs.

Maximum power is A2m

2 =

2

8f2m

T2

s



31/33

Adaptive Quantisation

000

M(4)

001

M(3)

010

M(2)

011

M(1)

100

M(1)

101M(2)

110

M(3)

111

M(4)

0

-3 -2 -1

1 2 3Input

Output Previous

output

Multiplier

7

2

12

52

32

32

52

12

72

EncoderInput

EncoderOutput

LevelEstimator

LevelEstimator

Quantiser with an adaptive step

N.S. Jayant, Digital Coding of

Speech Waveforms: PCM, DPCM,

and DM Quantizers, Proc IEE, vol62, pp. 611632.

PCM DPCM

2 3 4 2 3 4

M(1) 0.60 0.85 0.80 0.80 0.90 0.90

M(2) 2.20 1.00 0.80 1.60 0.90 0.90

M(3) 1.00 0.80 1.25 0.90

M(4) 1.50 0.80 1.70 0.90

M(5) 1.20 1.20

M(6) 1.60 1.60

M(7) 2.00 2.00

M(8) 2.40 2.40



32/33

Adaptive Prediction

Calculate predictor coefficients from short term estimate of the autocorrelation

function ofxn.

Receiver predictor may compute its own predictor coefficients from signal esti-

mates provided quantisation error is small.

Adaptive Prediction withbackward estimation (APB)

Predictor

Logic foradaptive

Prediction

QuantiserSamplerx t( ) xn en

~en

~xn~$

xn

+

-

Adaptive Differential Pulse-Code Modulation (ADCPM) combines adaptive

quantisation and Prediction.

A standard for speech encoded transmission at 32 kb/s. Standard PCM requires

64 kb/s for speech encoded transmission.



33/33

Adaptive Subband Coding

exploit quasi-periodic nature

of voiced speech permitting

pitch prediction reducing thelevel of prediction error

requiring quantisation

human ear cannot hear noise

below 15 dB below thesignal level in same band

can digitise speech at 16 kb/s

with a quality comparable to

64 kb/s PCM.

FilterBank f or

SubbandAnalysis

Adaptivebi t

assignmentcircuit

Multiplexer

Speech

Signal

To

channel

ADPCM Encoders

FilterBank f orSubbandAnalysis

De-multiplexer

Fromchannel

Output

ADPCM Decoders


digital transmission pulse modulation

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