Introduction t Th - IDR

Intro d uctio n t

Th« advantage o f tranam itting analogue s ig n a ls in a d i g i t a l f o r * are w all known and the procaaaae o f co n v e r tin g the analogue s ig n a le In t o a d i g i t a l format or eource encoding techniques have been stud ied in g rea t d e t a i l .

One o f the techniques o f a/ D conversion known as Pulse Code Modulation (PCM) In v o lv in g sam pling q u a n t is in g and coding waa developed q u it e e a rly and communication lin k s u s in g PCM have been in operation f o r a long tim e. W hile PCM was b e in g s t u d i e d , another form of d i g i t a l encoding known as D i f f e r e n t i a l encoding was Invented [C - 9 ], and aa a s p e c ia l oase o f D i f f e r e n t i a l ancodlng

Oeltam odulation (DM) [D-4] waa proposed. Even though adaptive deltam odulation (ADM) re q u ire s M e coder f o r each channel in a m ultiplexed system , two fa c to r s have co n tributed to the grow ing in t e r e s t in the ADM. They a r e , the r e l a t i v e l y low coat o f the encoder and the promise o f good q u a l it y o f transm ission at r e l a t i v e l y lower b i t r a t e s as compared to the PCM.

The ADM encoders d e sc r ib e d in the l i t e r a t u r e have t h e i r own d is a d v a n t a g e s . Some

©1

the im portant drawbacks fo r example are

* f a l l in the output am plitude at the h ig h e r message frequen- d e s i ( l i ) a f a l l in the s ig n a l to n o i s e r a t i o (S K R ) at th e h ig h er input fr e q u e n c ie s * and ( i l l ) a r e l a t i v e l y moderate improvement in the SBR w it h an in c r e a s e in the T ransm ission r a t e . Thus in the ADM eystema an improvement o f only 9 dfl ( s i n g l e in t e g r a t i o n ) o r

15

^dB

Copyright

IIT Kharagpur

(double In t e g r a t io n ) per octave in c r e e s e in the t ra n a a ie a io n r e t * h a . b##n obtained w h ile the SNR in th# PCM incr#a e #e #xp o n #n tia lly w ith th# b i t r a t # .

Th# a ia o f th# pr###nt in v e s t ig a t io n ha# been to d#slgn ADM coder# that would tak# ear# o f or r#aov# soa# o f th# d e fe c t s

■entloned above and thua d#v#lop sy s te a s which ar# b # tt e r and

e f f i c i e n t w hil# # t i l i r e t a in in g th# s l a p l l c l t y o f th # DM tec h n iq u e . Th# in v e s t ig a t io n s hav# lad to th# d#v#lopa#nt of fo u r

d i f f e r e n t syst#ms #ach h aving aoet ap#oial c h a r a c t e r is t ic and perform ance. A ll the ayaten# b e lo n g to the e la a a of encoder#

u s in g Adaptive Q u an tisatio n w it h Backward s s t l a a t io n (AQB) in th#

sens# that th# a da p tiv e atrat#gy i s c o n tro lle d by th# s y s t # » output.

Th# syst#a# hav# b##n c l a s s i f i e d # ith e r on th# b a a is of th#

t#chniqu# o f a d a p ta t io n , th# p#rforasnc# a c h ie v e d , or th# k in d o f approximation in v o lv e d . Thus, the systsas hav# b#sn ca lle d

s a p lit u d # c o n tr o lle d two loop ADM, Slop# C ontro lled two loop ADM, F la t Sp#ctrua ADM and M u l t id ig it ADM s y s t e a s . T h «s « sy st#a# hav#

only on# th in g in coanon, that ia a l l o f th#a us# th# id#a o f a two loop cod#r f o r f u l f i l l i n g th# v ario us r # q u lr# a # n ts»

TWO LOOP ADAPTIVE DELTA MODULATORS

Th# p h ilo so p hy o f th# two loop ADM has b##n based t o son#

#xt#nt on th# two loo p sy stea s proposed w h ich war# d#v#lop#d to r#aov# th # freq uency d is t o r t io n at th# hig h#r end o f th# ao ssa g # band in a DM c o d e r . The two loo p ADM c o n s is t s of s s ia p l# s in g le

DM around w hich an e x tr a fee d b a c k loop c o n t a in in g th# a dap tatio n l o g i c has b##n u s e d . The use o f the fe e d b a c k loops

(ii>

Copyright

IIT Kharagpur

( ( t i l )

has be«n ahown [.C-2] to have s o n * id v a n t a |t i in clu d in g tht uee of a double in t e g r a to r In tha feedback path w hich y ie ld a a higher SNR without the othor a ssociated problems o f s t a b i l i t y and id la channel noise* Thla is achieved by a s k in g the a da p tiv e lo g ic operate only for la rg e r s ig n a ls and by a llo w in g the sy s te a to degen erate into a s in g le in teg ra tio n DM at low input a ig n a la * T h is scheme also avoida tha need fo r a b ia s that must be used to keep the ADH in the i d l i n g c o n d it io n .

Two d if f e r e n t scheaea have been developed fo r o b t a in in g the control s ig n a l which v a r is s the am plitude of the fea d b &c k p ulse in the second feedback loop and thus changss the step s is e * In the a a p lit u d s con trolled two loop AON, the control s i g n a l is developed by d i f f e r e n t i a t i n g , r e c t i f y i n g and f i l t e r i n g the output b i t stream and i t has been shown that t h is c o n tr o l s ig n a l is

in v e r s e ly p ropo rtional to the an p litu d e of th e input s ig n a l* The control s ig n s l v a r ie s ths a a p lit u d s o f the fee d b a c k pulse by

c o n t r o llin g the r e s is t a n c e o f a FET in a d iv i d e r c ir c u it * T h is p ulse output i s then integrated in a d ouble In te g r a t o r and a fte r s u it a b le le v e l adjustm ent, ths reconstructed s ig n a l la fa d back to ths input of the d i f f e r e n t i a l comparator, thereby e o a p le t in g ths second loop* Ths decoder w i l l o f c o u r s e , be Just the fesdb sck path o f the encoder* The c i r c u i t has been ana£yaad by t a k in g

ths input to be a s in u s o id * A r e l a t io n s h ip has baan e s t a b lis h e d batween tha feed back p u ls e a a p l it u d e , tha in p u t am plitude and the norm alised number o f t r a n s it io n s in tha d i g i t a l output par c y c le . Trom t h is r e l a t i o n s h i p , the v a r ia t io n o f SNR over tha input range w ith re sp e c t to th a peak SKR, has been d e r iv e d .

Copyright

IIT Kharagpur

I ( i v )

For • s ia u f o l d a l Input ths SNR o f the l y i t M la the coapanded r « f io o la o f the f o r a

f SNR -

ao

log k < ■■ T ’t-

f a

3 /2

. ( D

v h t rt f r Is the clock r a t # , f is t h « fre q u en cy of th« In p u t ,

k

1

> • constant dapeodant upon tha In t e g r a t o r t l a e constants and tha f a i n o f tha lo o p s . In tha uncowpanded r e g io n , where the s y a t M Is a s l a p i s DM, ths SNR w i l l f a l l w it h tha Input am plitude*

In ths p r a c t ic a l l y ia p le a e n te d s y s t e a , ths a l n g l t l n t i g r a * tor has a pols s t 8 0 0 H s , w h ile ths d oubls In t e g r a t o r has p o lss at 8 0 0 and 1600 Hz w ith a asro at 3 0 0 0 Ha. For these v a lu ta at f r ■ 32 K H s, ths peak SNR i s t h s o r a t lc a lly 3 2 dB f o r a 6 0 0 Ha sinew a r e , and w it h a coapandlng r a t i o o f 0 , 0 3 , ths SNR should b a above 2 6 dB ovsr 35 dB input r a n g e . Tha ex p erim en ta lly aeaaured va lu es show a psak SNR o f 3 0 dB w it h SNR g r e a e r than 2 6 dB ovsr an Input r a n g * o f 3 0 dB* Ths d s c r s a s s In ths dynaalc ranga a r is e s because at h ig h er In p u t le v e la th s SNR la lowered due to the alope overload - a f a c t vldeh was not c o n sid ered i n d e r iv in g the

equation ( l ) . T he depend ence, o f the constant k on the b r e a k - p o in t s , la such t h a t a r e d u c t io n of the in t e g r a to r corner

fr e q u e n c ie s w i l l in c r e a s e the SNRj b u t w i l l r e s u l t in a poorer frequency r e s p o n s e . The v a lu e a used in the experim ental ays tea have been found to b e a good co a p ro a ia e betw een a h ig h SNR and a good fr e q u e n c y r e s p o n s e . Tho speech q u a l i t y a l e o has been found to be good at a b i t r a t a o f 32 K b / a . Aa expected f r o a

fn la the badnwidth &, /*■> */ are the In te g r a t o r b rea k p o in ts and

Copyright

IIT Kharagpur

<*)

tq n , ( l ) , the SNR has baan meaaured and found to improve at a rata o f about

9

d B /o cta v a change In f r «

Tha aaeond method o f o b ta in in g the con trol s ig n a l y la ld a a con trol s ig n a l which la proportional to tha naan input s l o p a

9

and tha aystem haa baan ca lle d tha Slope C ontro llad Two Loop ADM.

Tha control a ig n a l la obtained In tha fo llo w in g manner. Tha

\

d i g i t a l output o f a DM la delayed In a a e rie s o f S h i f t k e g ia t e r e , and the outputo o f theee ara fad to a co in ciden ce d e t e c t o r . Vhen M aucceaaive b i t a o f tha d i g i t a l output are h ig h , tha detector w i l l produce an output which la than f i l t e r e d by a s y l l a b l e f i l t e r of a la rg e time constant to g iv e tha control s ig n a l* T h is s ig n a l is now used to vary th e a n p litu d e o f tha feedback p u ls e , as b e fo r e , but now in a m u lt ip lie r c ir c u it in s te a d o f s d i v i d e r . The re st o f the c ir c u it is s im ila r t o the Amplitude C ontro lled Two Loop ADM.

The SNR o f the system has been shown t o be r _ 5 / s ) i

SNR » 2 0 log

. . (

2

)

w h ich i s s im ila r to e q n . ( i ) except fo r the fa c t o r which Is the a f f e c t i v e frequency o f the input spectrum d efin e d by

2 K t m

aJ to* s(« )d a

2

^jrf

J s (b t ) m

where s(co ) Is the power spectrum o f tha i n p u t . For a s i n u ­ s o i d a l s i g n s ! e q n . (

2

) w i l l bs s im ila r t o e q n . ( t ) .

Copyright

IIT Kharagpur

(V i )

For a 8 0 0 Hi a in ewave, at a clock r a t e o f 32 KHs, the

t h e o r e tic a lly calculated dynaaic raogt la 38 dB (fo r SNR ^ 26 dB) w h ile tha e x p e r ia e n t a lly aeaaured va lu e la 33 dB* I t haa a la o baan aatabllahad that tha numbar o f b it a M, that are to b a chockeda depende upon the eloek r a t a . K eeping the frequency raaponaa aa tha c r i t e r i o n , tha v a lu e of M ■ k y ia ld a good r a a u lt a fo r clock rataa o f 25 Kite and upwards upto 8 0 K H z . Below 25 KHz M - 2 gives a v a s t ly inproved perform ance. Tha a n p litu d a va frequency raaponaa of tha elo p e co n tro lled ayaten la b a tte r than that o f the a a p lit u d e con trolled a y s te n . The SNR lnprovenent ia aga in about 9 dB par octave in c rea se in the clock ro te* SNR aaasurenents fo r a narrow band n o is e s ig n a l have bean nade and tha r a a u lt a are only s l i g h t l y

poorer than tha r a a u lt a fo r a 8 0 0 Hm s in u s o id * Speech t e a t s have been made and tha alopa con trolled ayaten la found to g iv e good q u a l it y o f apeech even at

16

K b /a . But th ia ayaten a t i l l haa tha d e fe c ta o f lower SNR at the higher input fr e q u e n c ie s and no change

in the r a t e of loq>roveaent o f SNR w it h b it r a t e haa baan achieved*

Aa aentio nad abo ve, tha SNR and a a p lit u d e at h ig h er ueasaga freq u e n c ie s is poorer than tha SNR at lower fr e q u e n c ie s even in the alopa co n tro lled two loop ADM* In s i t u a t io n s l i k a t e la a e t r y ,

f a c e l n i l e , e t c * , where i t Is e a a e n t ia l that both a a p lit u d e and SNR r a a a in conatant ovar the a n t lr e aaasage baud* nona o f tha ayataaa d iacu a sed above w i l l work a a t ia f a c t orily* A F la t S p e c t r in ADM haa baan developed w it h t h ia purpoee In v ie w and tha ayaten haa baan daaign ed to o p t ia la e the SNR ovar tha aaaaago b an d . Tha f l a t spectru a ADM la o s a e n t l a l l y a alopa c o n tr o lle d two loop ADM w it h a w d ific a t Io n a * Tha a a p lit u d e o f the feed back pulae la c o n tr o lle d through *a n u l t i p l i e r as b e f o r e , but the o u tp u t , In stea d of b e in g

Copyright

IIT Kharagpur

(vii)

Integ rated i s passed through a second order lowpass f i l t e r w ith a cut o f f frequency equal to the aessa gs bandw idth f ^ * The input s ig n a l and t h is f i l t e r e d s ig n a l ore d if f e r e n c e d in a

d if f e r e n c e a a p l i f i e r and a forward in t e g r a to r is used to saoothen the error s ig n a l* T h is error e ig n s l is the input to the b a s i c DM c ir c u it whose output has bsen used to control the second loop*

The SNR o f the s y s t s a has been shown to be independent o f the s ig n a l frequency* but is found to be lower than that the othc*r two loop ADM system s. The SNR of the f l a t s p e c tr u a ADM can be w ritten as

f

3/2

SNR • 2 0 log It", ;--~ . . ( * * )

( « . » h ' p • *

9

6

t b e in g the In te g r a t o r oorner frequency and k is a const an t.

The SNR o f the p r a c t ic a l l y instrum ented s y s t e a is* at 40 JUfe, the saa e as the SNR o f the slope c o n tr o lle d sy e te a o p eratin g at

32 KHa, but w ith a d iffe r e n c e now that the SNR Is constant over the aessage band* The SNR c h a r a c t e r is t ic s o f t h is sy s te a at kO KHs is a la o s t e q u iv a le n t to that of a 7 b i t PCM. Here a g a in , the SNR In c r e a s e s by 9 dB esch t la e the clock r a t e is doubled*

M u lt id ig it A daptive D e lta a o d u la t lo n i

Even though the SNR has been o p t la ls e d over the taeaaage b a n d , a l b e i t at a h ig h e r b i t r a t e , the r a t a o f In c r e a s e o f the SNR w it h clock r a t e has r e a a in e d unchanged* In order to ob tain a b e t t e r SNR at the eaae b i t r « t e and a l s o t * laprove the r a t e of In c r e a s e o f SNR the a u l t l d i g i t ADM s y s te a [C-3] has besn

Copyright

IIT Kharagpur

( v i i i )

proposed* In t h is aystem, ths error s ig n a l forced between the Input end tha reconetructed s i g n s ! st tha encoder is encoded in an a u x i l i a r y ADM and tranamltted* By t h is proceea an approximate fo ra of the error le a v a ia b le st the decoder and s b e tte r

approxim ation of the input cen be obtslned* T h is p r in c ip le csn be extended fu r th e r such thst the erro r in the e u x i l i s r y coder is coded in another ADM and so on upto N coders* The d l g i t s l streams of s l l coders are in terlesv ed end at th e r e c e iv e r they ere

d em u ltip lex ed , decoded a ep arately and the a nalo g e ig n a ls a r e f i n a l l y added. The o v e ra ll SNR w i l l be the sun of th e SNR o f each co d er, b u t with a d iffe r e n c e * Since the error e ig n a l

occupiea a wide bandwidth it has to b e b an d lim ite d * However, i f we are to reproduce the overload erro rs w e l l , the bandwidth o f the f i l t e r must be s l i g h t l y la rg er than the ae sa a ge b andw idth. Becauee o f the f a c t that the input to the e u x il is r y coder hss s f l a t*

spectrum and i t s bandw idth is more, the SNR o f the a u x i l i a r y coder has been estim ated to be about 9 dB poorer ae compared to the

main c o d e r .

The SNR o f an AIM can b e w r itte n la t h e form

SNR - 2 0 l o g j k , f £ ]

* * , r # w<* ere dependent upon the aystem ussd and o( i s u s u a lly 3 / 2 or 5 / 2 . Prom th le the SNR o f a N- digit ADM the system can be w r it t e n as

.f A

(

8

H R )m . 2 0 N lo g k , (S & ) - 9 (N - 1) . . ( J )

where t R i s the o v a r a ll transm ission r a t e , the clock

Copyright

IIT Kharagpur

I

( i x )

r a t * o f each oo der, and a 9 dB d egrad ation f o r eaoh a u x ilia r y

eodor haa b **n aaauaed* U sing aquation (*») i t haa b#*n ahoi*i that for a p a r t ic u la r t r a n # »ia *io n r a t a f R» tha SNR la maximvm for an optiaum v a iu * o f N given by

"o p t * ( 0 -368 f R ) ( ° ‘ 355 k 1 )l/c( • • ( 6 ) T h ia fu rth er i a p l i e s that t h * o p tia u a c o n d it io n w i l l occur only i f eech in d iv id u a l coder operatee at a ra te d e f i n e d aa the b a e lc p r f f rB where

f R 2 ,7 1 8 ________ (rj\

t au * Z, * \\/M ** '

HB opt ( 0 . 3 5 5 k , )

f r o a Eqn. ( 4 ) the SNR iaproveaent w ith tra n a a ie s io n r a t e can be c a lc u la te d aa

(SN R )N ■ 9N d B /o c ta v e .« (

8

⁾

f o r

0

^{( - 3 /2}

Thus f o r N m 1 ,2 * 3 » •« * the i a p r o v c M n t w i l l b e 9# 1 8 , 27» • • • dB each t ia e fR ia d o u b le d . I t should be reae a b e red that th e SNR at any v a lu e o f f n cannot exceed the v a lu e achieved fo r N ■ N

k opt

I t has b een shown that a bound e x ia t s on the SNR o f the N d i g i t ayetea and t h ia bound haa been shown to b e of the f o r a

f

(S N R )n ^ 5»9n ♦ 9 where n * ~ ia the a o r a a lis e d trans-

■

M is s io n r a t e . O 'N e a l £0-23 haa d e r iv e d the SNR bouade fo r PCM, DPCM and a g e n e r a l p r e d ic t iv e c o d e r . The r e s u l t s are

Copyright

IIT Kharagpur

<*)

SNR*£ 6m ♦ 13*6 5 fo r a P r a d ic t iv * cod«r

6

n ♦ 8 . 5 fo r DPCM

^

6

^{n -}

7 . 3

f o r UO“ PCH

Tha SNR bound la alaoet the aane as fo r DPCM and la b e t t e r than that of PCM eyetem*

An experim ental dual-ADM eyatem has been implemented u s in g s s lo p e c o n tro lled 2 loop ADM aa the b ae ic coder* , The meaoure*

vents on the eyetem show that at 32 K b /a th e ay a tea hae a peak SNR of

33

dB and s SNR g reater than 2 6 dB over an input r a n g * of 38 d B . The SNR v a r ia t io n over the meeeage band ia auob le s s than thst o f th e slop e controlled two loop ADM* The exp erim en tally aeaaured SNR improvement ie 15 d B /o c ta v e change o f b i t r e t e as ag a in s t the expected re ts of

18

d B /o c t a v e . T h s dyaam ic range improvement 1s abo ut 5 dB w h ile the p r e d ic t e d in cre a e e i s

6

^{d B .}

COMPARISONS

1

The v a rio u s systems hsve been instrum ented and tested as d esc r ib e d e a r l i e r . In c o n clu sio n the f o l l o w i n g comparisons can be made w ith other system s. T h s two loop ADM coder I s b e t t e r than most o f the other ADM codere [j-

8

] , and the s lo p e som trolled

two loop ADM i s o n ly s l i g h t l y i n f e r i o r to the Adaptive D i f f e r e n t i a l PCM (ADPCM) [c-

8

^{] .} They are a l s o s u p e rio r t o FCN up to t r a n s *

a l a s ion r a t e a of 7 0 K b / s . The d u a l ADM system o f f e r s s b e t t e r perform ance than ADPCM up to a b i t r a t e of 4 5 K b / s . I t is a ls o soon th at a d ual ADM is no t s u i t s b l e f o r low b i t r a t e w o rkin g, p a r t ic u l a r l y b e lo w

30

K b / s .

Copyright

IIT Kharagpur

(*i)

A ll the t y s t m have beeo teeted in the presence o f channel n o ise* The two loop codere a re found to be h ig h ly

r a e ls t a n t to channel erro rs and good epeech q u a l i t y i s obtained even at error r a t e e of t /2 0 0 * At 16 K b /s i n t e l l i g i b l e speech is ob tained at er ro r r a t e * of 1 /1 0 0 * The d ual ADM has been shown to b e le s e r e s is t a n t to channel errors and beyond a p a r t ic u la r rate i s poorer ae compared to a s in g l e ADM. The speeoh q u a l it y o f the two loop a ysteo haa been found to be o o aparable to o r b e t t e r than the e x i s t i n g aystens on the b a s i s of coaparison w ith speech saa p le s o f other systeos Demonstration records a v a il a b l e along w ith r e f * £ j~

8

^{t G-iQ •}

Copyright

IIT Kharagpur

COMPARISONopTH£ PROPOSEDSCHEMESWITHVAKIOUSDIGITALINCODINGSCHEMES

4»a

• • •

B 4* >

• 0 •

* b • 0 0 4» • 0 0

0 ► ► > 0 > > > *» 4*

fa +* • • • 0 0 0 0 <*4 «H

a -n 4» 4» 4* \ 4» 4» 4* w

B JO « o O S3 o U o •H

«4 0 0 o •o 0 0 o •o

£ s . V. 'N, \ V. V. \

as ** n n a fi fi a fi

T, -H T) •o V ■o V •o T)

W » 1

9s <h o\ CM *\ Os NO

*»

fa fa CM

0 o 1

fa * O

C • tm

• O M

O ^ M

H C 0 >» N CM CM ^r r> J9

CM 1 1 1 i i i 1

fi fa • O O o o o o o

Q 1 f H 0 »“

I H O I 4»

r o « 3 M

u < » i o * 7

o CM

s*0 NO 4»

0 CM 9

■h a. so a CD fi fi n fi fi

8 & A S •o *0 *0 *0 TJ

c c as o r\ •9 ri ao O oo CM 1•

£ j j s a n r\ rs r» r\ n r» -*

oo

40 S3 to a a fi o a fi fi

*¥ b <0 Tl * T> *0 V V

0 « o

• r. ^ o O * rv 00 cn »ry CM

a. tA w n r* r\ n CM r> r» N

o ou

4* V • • • • . 0 0 0 0 0

0 0 V. S \ \ V.

fa 0 fi fi A fi fi fi fO p

.1 • & fi X tt * C S

♦* M

•H • M CM O CM O O CM vO

a) a o r* n r> ir> CM

<0

o >»

fa 4*

0 0

M 8 £

u • x 1 H 0

4* *■4 o o 0 1

e < U l fa

0 o 4» 4*

0 fa B X 6 «4 X

X 4 » X S Q 3 jO P

• a c a fa o i p— \

« < o * 4* • 00

3 e O S >» #l

*» a a • 9 Hr-i xs X i

•* e • 0 a 3 h r- 4» c u l

H 0 0. 0 • C 0 1 ■W e

0 *4 4* O 9 r-n 0 X

1 4* «<UJ H & 9

< cm » cm •

p4 8 * S

X TQ n 0

3 8 . a,

•0 •a ft. u Q 5 Q O

0 A

“ M m M w 00 «*

• CM r> & Ift r» oo

Copyright

IIT Kharagpur