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Chapter 3: Delta Modulation
Digital Communication Systems 2012 R.Sokullu 1/!
CHAPTER 3
DELTA MODULATION
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Chapter 3: Delta Modulation
Digital Communication Systems 2012 R.Sokullu 2/!
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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Chapter 3: Delta Modulation
Digital Communication Systems 2012 R.Sokullu 3/!
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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Chapter 3: Delta Modulation
Digital Communication Systems 2012 R.Sokullu /!
Illustration of the delta modulation process
4igure 3.22
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Chapter 3: Delta Modulation
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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Chapter 3: Delta Modulation
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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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Chapter 3: Delta Modulation
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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Chapter 3: Delta Modulation
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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Chapter 3: Delta Modulation
Digital Communication Systems 2012 R.Sokullu B/!
Figure 3.23
DM system.
a! Transmitter.
b! "ecei#er.
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Chapter 3: Delta Modulation
Digital Communication Systems 2012 R.Sokullu 10/!
" (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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Chapter 3: Delta Modulation
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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Chapter 3: Delta Modulation
Digital Communication Systems 2012 R.Sokullu 30/!
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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Chapter 3: Delta Modulation
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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 $CM
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Chapter 3: Delta Modulation
Digital Communication Systems 2012 R.Sokullu 32/!
"ecei#er side
" decoder constructs the (uantied error signal
" (uantied 'ersion o% the input is reco'ered yusing the same prediction %ilter as at the t*
" i% there is no channel noise encoded input tothe decoder is identical to the transmitteroutput
" then the recei'er output )ill e e(ual to m[n],di%%ers %rom m[n]y [n] caused y(uantiing the prediction error e[n]-
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Chapter 3: Delta Modulation
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'omparison
" D$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 $CM does not
all suect to (uantiation error
h l d l i
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Chapter 3: Delta Modulation
Digital Communication Systems 2012 R.Sokullu 3/!
Processin) &ain
" Eutput signal+to+noise
ratio ,SRE-" JM2 'ariance o% m
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Chapter 3: Delta Modulation
Digital Communication Systems 2012 R.Sokullu 3!/!
" he processing gain Kp)hen greater than unity
represents the signal+to+noise ratio that is due to thedi%%erential (uantiation scheme.
" 4or a gi'en input message signal JMis %i*ed9 so the
smaller the JGthe greater the Kp.
" his is the design oecti'e o% the prediction %ilter" 4or 'oice signals optimal main ad'antage o% D$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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Chapter 3: Delta Modulation
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Outline
" 3.12 Delta Modulation
Delta Sigma Modulation
" 3.13 #inear $rediction" 3.1 Di%%erential $ulse Code Modulation
" 3.1 da$ti'e Die%ential *ulse &ode
Modulation
Ch t 3 D lt M d l ti
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Chapter 3: Delta Modulation
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
Ch t 3 D lt M d l ti
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Chapter 3: Delta Modulation
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
" $rice A proportionally increased comple*ity
4or same speech (uality ut Lal% the it rate +Computational comple*ity is an order o% magnitude higher
Ch t 3 D lt M d l ti
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Chapter 3: Delta Modulation
Digital Communication Systems 2012 R.Sokullu 3B/!
ADP'M principles
" &llo)s encoding o% speech at 32 k/s re(uires its per
sample
" Fses ada$ti'e uantiationand ada$ti'e $%edi4tion
adapti'e (uantiation uses a time+'arying step 63-Mn n =
Ch t 3 D lt M d l ti
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Chapter 3: Delta Modulation
Digital Communication Systems 2012 R.Sokullu 0/!
" )o possiilities:
adapti'e (uantiation )ith %or)ard estimation
,&4- uses un(uantied samples o% the input
signal to deri'e %or)ard estimates o% 5M[n]6re(uires a u%%er to store samples %or a certain
learning period incurs delay ,N 17 ms %or speech-
adapti'e (uantiation )ith ack)ard estimation,&I- uses samples o% the (uantier output to
deri'e ack)ards estimates o% 5M[n]
Chapter 3: Delta Modulation
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Chapter 3: Delta Modulation
Digital Communication Systems 2012 R.Sokullu 1/!
" &dapti'e prediction in &D$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
Chapter 3: Delta Modulation
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Chapter 3: Delta Modulation
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Figure 3.29
Adapti#e 8uanti-ation 0it% 4ac*0ard estimation
A9+!.
Chapter 3: Delta Modulation
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Chapter 3: Delta Modulation
Digital Communication Systems 2012 R.Sokullu 3/!
Adapti#e prediction 0it% 4ac*0ard estimation AP+!.
Figure 3.30
Chapter 3: Delta Modulation
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Chapter 3: Delta Modulation
'onclusion(
" $CM at 7 k/s and &D$CM at 32 k/s are
internationally accepted standards %or 'oice
coding and decoding.