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Chapter 3: Delta Modulation

Digital Communication Systems 2012 R.Sokullu 1/!

CHAPTER 3

DELTA MODULATION

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Outline

" 3.12 Delta Modulation

Delta Sigma Modulation

" 3.13 #inear $rediction" 3.1 Di%%erential $ulse Code Modulation

" 3.1! &dapti'e Di%%erential $ulse Code

Modulation

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3.12 Delta Modulation

" Definition:Delta Modulation is a techni(ue)hich pro'ides a staircase appro*imation

to an o'er+sampled 'ersion o% the message

signal ,analog input-.

" sampling is at a rate higher than the y(uist

rate aims at increasing the correlation

et)een adacent samples simpli%ies

(uantiing o% the encoded signal

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Digital Communication Systems 2012 R.Sokullu /!

Illustration of the delta modulation process

4igure 3.22

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Digital Communication Systems 2012 R.Sokullu !/!

Principle Operation

" message signal is o'er+sampled

" di%%erence et)een the input and the

appro*imation is (uantied in t)o le'els + 5/+6" these le'els correspond to positi'e/negati'e

di%%erences

" pro'ided signal does not change very rapidlythe appro*imation remains )ithin 5/+6

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Assumptions and model

8e assume that:

" m(t)denotes the input message signal

" m(,t- denotes the staircase appro*imation" m[n] = m(nTs), n = +/-1, +/-2 denotes a

sample o% the signal m(t)at timet=nTs9 )here

Sis the sampling period" then

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Digital Communication Systems 2012 R.Sokullu ;/!

" )e can e*press the asic principles o% the delta

modulation in a mathematical %orm as %ollo):

< = < = < 1= ,3.!2-

e n m n m n

= sgn, < =- ,3.!3-e e n=

< = < 1= < = ,3.!-

m n m n e n= +

error signal

(uantied

out ut

(uantied

error signal

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Digital Communication Systems 2012 R.Sokullu >/!

Pros and cons

" Main ad'antage simplicity

" Sampled 'ersion o% the message is applied to a

modulator ,comparator9 (uantier9accumulator-

" delay in accumulator is ?unit delay@ A one

sample period ,+1-

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Digital Communication Systems 2012 R.Sokullu B/!

Figure 3.23

DM system.

a! Transmitter.

b! "ecei#er.

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" (uantier includes a hard+

limiter )ith an input+output

relation a scaled 'ersion o%the signum %unction

" accumulator produces the

appro*imation m[n] ,%inal

result- at each step yadding either 56 or 6

" A tracking input samples y

one step at a time-!!.3,

=/!

Figure 3.28

DP'M system.

a! Transmitter.

b! "ecei#er.

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Digital Communication Systems 2012 R.Sokullu 2B/!

Details(

" Ilock scheme is 'ery similar to DM

" (uantier input

H< = < = < = ,3.;-e n m n m n=

< = < = < = ,3.;!-e n e n n= +

H< = < = < = ,3.;7-

m n m n e n= +

" (uantier output may e e*pressed as:

" prediction %ilter output may e e*pressed as:

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H< = < = < = < = ,3.;;-m n m n e n n= + +

% )e sustitute 3.;! into 3.;7 )e get:

sum is e(ual to input

sample

< = < = < = ,3.;>-m n m n n= +

uantied input o% the

prediction %ilter +

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Details cont5d

" m[n]is the (uantied 'ersion o% the input sample m[n]

" so9 irrespecti'e o% the properties o% the prediction %ilter the(uantied sample m[n] at the prediction %ilter input di%%ers

%rom the original sample m[n])ith the (uantiation error[n].

" % the prediction %ilter is good9 the variance of the predictionerrore[n])ill e smaller than the variance ofm[n]

" his means that i% )e make a 'ery good prediction %ilter,adust the numer o% le'els- it )ill e possile to produce aquantization error with a smaller variance than if the inputsample m[n]is quantized directly as in standard $CM

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"ecei#er side

" decoder constructs the (uantied error signal

" (uantied 'ersion o% the input is reco'ered yusing the same prediction %ilter as at the t*

" i% there is no channel noise encoded input tothe decoder is identical to the transmitteroutput

" then the recei'er output )ill e e(ual to m[n],di%%ers %rom m[n]y [n] caused y(uantiing the prediction error e[n]-

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'omparison

" D$CM and DM

D$CM includes DM as a special case

Similarities

" suect to slope+o'erhead and (uantiation error Di%%erences

" DM uses a 1+it (uantier

" DM uses a single delay element ,ero prediction order-

" D$CM and $CMoth DM and D$CM use %eedack )hile $CM does not

all suect to (uantiation error

h l d l i

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Processin) &ain

" Eutput signal+to+noise

ratio ,SRE-" JM2 'ariance o% m

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Digital Communication Systems 2012 R.Sokullu 3!/!

" he processing gain Kp)hen greater than unity

represents the signal+to+noise ratio that is due to thedi%%erential (uantiation scheme.

" 4or a gi'en input message signal JMis %i*ed9 so the

smaller the JGthe greater the Kp.

" his is the design oecti'e o% the prediction %ilter" 4or 'oice signals optimal main ad'antage o% D$CM

o'er $CM is /n +11 dI

" &d'antage e*pressed in terms o% it rate ,its-

1 it A7 dI o% (uantiation noise ,ale 3.3!9 p 1B>- So %or %i*ed SR9 sampling rate > kL DC$M pro'ides

sa'ing o% >+17 k/s ,1 +2 its per sample- $CM

Ch 3 D l M d l i

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Outline

" 3.12 Delta Modulation

Delta Sigma Modulation

" 3.13 #inear $rediction" 3.1 Di%%erential $ulse Code Modulation

" 3.1 da$ti'e Die%ential *ulse &ode

Modulation

Ch t 3 D lt M d l ti

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Digital Communication Systems 2012 R.Sokullu 3;/!

3.16 Adapti#e Di,,erential P'M

" $CM %or speech coding o% 7 k/s re(uires highchannel and)idth

" some applications ,secure transmission o'er radio

channel lo) capacity-" re(uires speech coding at lo) it rates ut preser'ing

acceptale %idelity ,not 7 k/s $CM ut 329 179 >etc-

" possile using special coders that utilie statisticalcharacteristics o% speech signals and properties o%hearing


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Digital Communication Systems 2012 R.Sokullu 3>/!

Desi)n O47ecti#es

" 1. Remo'e redundancies %rom speech signals

" 2. &ssign a'ailale its to encode non+redundant parts

o% speech signal in an e%%icient )ay

" Standard $CM is at 7 k/s can e reduced to 329179 > or e'en k/s

" $rice A proportionally increased comple*ity

4or same speech (uality ut Lal% the it rate +Computational comple*ity is an order o% magnitude higher


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Digital Communication Systems 2012 R.Sokullu 3B/!

ADP'M principles

" &llo)s encoding o% speech at 32 k/s re(uires its per

sample

" Fses ada$ti'e uantiationand ada$ti'e $%edi4tion

adapti'e (uantiation uses a time+'arying step 63-Mn n =


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" )o possiilities:

adapti'e (uantiation )ith %or)ard estimation

,&4- uses un(uantied samples o% the input

signal to deri'e %or)ard estimates o% 5M[n]6re(uires a u%%er to store samples %or a certain

learning period incurs delay ,N 17 ms %or speech-

adapti'e (uantiation )ith ack)ard estimation,&I- uses samples o% the (uantier output to

deri'e ack)ards estimates o% 5M[n]


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" &dapti'e prediction in &D$CM

adapti'e prediction )ith %or)ard estimation,&$4- uses un(unatied samples o% the input

signal to calculate prediction coe%%icients

disad'antages similar to &4

adapti'e prediction )ith ack)ard estimation

,&$I- uses samples o% the (uantier output and

the prediction error to compute predictor

coe%%icients logic %or adapti'e prediction algorithm %or updating predictor coe%%icients


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Figure 3.29

Adapti#e 8uanti-ation 0it% 4ac*0ard estimation

A9+!.


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Adapti#e prediction 0it% 4ac*0ard estimation AP+!.

Figure 3.30


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'onclusion(

" $CM at 7 k/s and &D$CM at 32 k/s are

internationally accepted standards %or 'oice

coding and decoding.

Documents

commsys-2-2012-3 (1)