BSTJ 60: 7. September 1981: Digital Signal Processor: Sub-band Coding. (Crochiere, R.E.)

8.6 MB·English

Digitat Signal Processor:

‘Sub-Band Coding

By FE GROCHIERE
‘omaruscr reson July 8, 1984)

This paper explore the uae of the Hell Laboratoree digital signal
processing integrated eireutt jor digitally encoding speech oF wala
‘ignala based on the sub band coding technique. Sub bond coding
representa a nex! level in ulgrillane rompleity over Bat of latin
differential pudve cate mre, incur ae enprnies pre,
‘and uf has « corresponding adeuntage in performance, We discuss
the detala of recbtime, toe-bont eu hand vvling implementation
‘on the digital signal processor. We then comment om tune this
(oprah cau be etended to mare than to band designs for greater
Dit rate envaprension capablit, In connection with this, ce also
‘ansider sone general suey inculsed in implementing ulin
bignal processing algorithms of Hs fy co the gill signal pw

Digital encoding of apcech and andiv hoe been « topic of lone
standing incerest for purposes of digital communications and digital
storage The efficiency of such encoding wechniques depend stony
fon the degnee to which the bit rale oan be reduced ‘eompressod}
‘rithowsimpuiriny hv uit of Che doe signal. Typiealy igre
fsck is specs etn lo 9 high degre of wedandanes thal ean
To used th reduce this bit pte, Alze. properties of human perception
an house ro nedane che bic eave without impairing che quality of the
‘ened signal

‘To take adwantnge of thea pruperlin, # eomidanable mount of
signal processing is necessars, This, in Tho ge ay of Cause Loche
niques hove enly boca implemented by non rea ime vor sma
Tatu nr wih the aid of highly specalized digital hardware. ‘This

1699
picture ia now rapidly changing, a i exemplified Dy the secu Rell
[aboratores digial signal processing intograved circ. (nse).'* With
‘his device ite possible vo conveniently implement, neal ine signa
proceasing algorithms ufo ts medium nomplenlyhus, a single Da
Incegrated circuit can be ised) simplest any of he sper
fncoding algaithma and multiple nsea can be used for some of the
tne me ith

Te conpenins yopieet il is abown chat the aneeae adaptive
Alfercail ren) encoding algoritam, which ates a bt vate reduction
{neta of approximately to aver conventional logarithmic companded
rox eneneing itr speech, ean be efciensi implomenced on the Ds,
pd that ic ures only about one-quurer of the proces capability uf
the device. In chs paper, we report on continuing efforta towards 3
next level of complexity of encoding techniques on she Ds, Tr pari
sla, we dines the technique of subband coding (suc) Our efforts
Thcus primarily on a twochand mub-band coder denign which demicm
sister the capability of the sb for this class of sgorithine iy
Extension of these sume Lecuiquee, iis uxpeciell nal moze complex
"se designs on the nae lg, feat mote band with greater bi-rate
ompreaiion capability will also be possible and effore mse continuing
in thi direction.

1 THE SUB-BAND CODER ALGORITHM

igure L reviews thy twsie conoxlual sonfiguation for to-band
suv design. The inp cgi ea i aso to he i gal tinea
ost fore und i may be (oprionaly) filtered with » bandpass prefer
forreasons In he dives later. Tae outpu signal xin) chen divided
ino bev exially spaced frequency bands by low-pass and high-pass
fiers, tn) and dyin), respectively, Fach subsbundl gl rece
in sampling rate by a factor of neo. ei Fi the supling rate uf the
input signal, F/2 isthe sampling sto of Ube subband signals, The
fub-ban! signals xn tun vnewded ith anpeia encoder and the
‘ney bite are mul iplexed for storage oF trnsmiston

Ti the receiver, the aub-band signale are decoded end interpolatod
Dal to their orginal campling sates wit the aid of sila low-pass
‘and high.pas Filter The sum ofthe tv interpolated sub-band signals,
“Hin, i Une reconstructed vetson of the input signal xn), (ee 19g. 1

‘This prcessof dividing che signal into sub-bunds poreice each bard
ta be encod with «diferent nnmber uf bile per rape al with =
indapendent adaptive sep.sie in over ca abuain a bester peresived
‘quality, Fur lelephone hand speerh (200 co 3200 Ha aaapled ac kz,
‘the tro-bond technique provides abou. & 9 or 440s advantage wer
AADPOA in the biter range of 24 ys! Tn anneher anudg*" ie at
thet swt Usa the Usa $80 design i use for encoding of

4604 THE REL! SYSTEM TECHNICAL JOURNAL. SEEMBEFT 1981
sem ono enone ees) HES Pom GAPING ch HENAN HER BED eh TL
‘wider bunds (7 3Ff) signals at hierar which ate commensurate
Dll digital iransission sates commonly used fe telephony (oF Gk
Kb/s, The Moonen quality” obeaine from this design i suitable
for applications sh as brnadeast sercces for eve, coterponcence,
puis AM rade wisi fanamsson,

Grewterbil rate vomsressin, for higher quality pexorwance ter the
sam hic rate) over thac of a to-band seheme is posible with more
bhandls.” "his ean be accoroplished, for example by further subdividing
ach of the ta anb-hand signe into tw mone subbands at one
‘quarter of che original sampling rate to produce a our-band she desizn
‘wich equally spaced frequency bands). Altemuvively, designs with
oetavely spaced bands arr possible by siceratively sabeieiing the
lower bands in “sro rutire," Such designs ue ogi exlerion
ofthe torhard apne, and my can ve performance lange
Pup to abaue 8 eb/a over abeCsS lin che renge of 16 be 24 kb) for

siren
Tn the fllowing asetions, we discuss in detail on implementation of
the two-band sie dovign on the na. I Shelion TTT, wt Gest rie

ome ofthe heoreltal sep ive he eesign, pier theatre
Of the quadrature mirear approach tothe flcer bank. ‘The, ip Section
Ty, we mailer sna of the programing aspets of Hh Mein wth
rsp unl show hun Firm one ane ec in he deen ation

1 The qusersture miror eter bank

“An impnacant srl critical aapecr of che sue desig that ofthe Aor
bale ails teraction wi the sung ts nin (sii)
ani the subeenien. xsupling ate iene neapolation) of hese
‘aed sgl The proach weed ia thie desig ie tha ofthe quadrature
amivror Hter bank (apa. ln this section, we wil summarize the
Ise roneepts af che unas and consider e proctical ier desiem- Later
ie Section 44, we will discuss the implemencation of the gue on the

The reduction ofthe aub-band sampling reves is nevossary in order
‘a turintain a minimal overall bit-ta in eating thee. sgnal, This
mpg rae retin imrorinces aise tenia the sub
‘ane signs: For wxaraple, inthe lower band the signal energy inthe
frsuemty range abou F/4 i folded doen inca the range 0 t0 Fe
and appears a aliasing in this signet, a ilostvated by the shaded
eon i Fig. th, Sines, forthe pa band any signal energy
the traqueney range below Fy ie falded upsrard into ica Nyquite Band
F.i4 to F,72. Thismotosl slissing of signal energy between che wrper
fa lower subbands in potnetimies called interband “leakage.” The
amount afleakage that accurs berweencub-bandsis tect dependent

1656 THE BFLY SYST TECIINIGAL JOURNAL, SCPTTWAER 15A1
‘on the degree to which che fers y(n) and Ast) approximate ideal
lowe-paca and high-pass fers, respectively

Inthe reconstruction process the sub-band sampling rates are in
creased by filling in zero valued samples between each pair of sub
band samples. This introduces periodic ropetition of the signal
spectra in the aub-band. For example, in the lower band the signal
energy from 0 to F,/t is symmetrieall folded around the frequency
Fi/4 nto the range of tho upper band. This unwanted signal energy,
teferred to san “image” i filtered ou by the low-pass filter A) #0
the receives, Ths ering operation efecively interpolates the zero
‘valued samples that have been inserted between the sub-band signala
to values thet appropriately reprosoal che desired waveform.” Simi
Iarly, in the upper sub-bare signal wt icuage is reflected to the lower
sub-band and filtered out by the filter ~Ay(n.

‘The degree to which the above innyos ure removed by the fers
Juin) and h(n) He determined by the dere Lo which thes approxi
‘ate ideal low-pass and high-pass filters. Because of the quairavare
Zelationehip of (he sub-batd sia i ve QMPR he remlning eon
onents of the imayis eam bw exactly canceled by the aliasing Urns
introduced in the analie(n he abenceof coding errors) In practice,
{iceanvellatin i abtained down co the level ofthe quantization nose
‘of the coders.

‘To obrain this cancellation property in the qaerz, the fillers At
andl h(a) most be symmetrical finite mpulee response (vt) desiga'*
‘with even mmumbers taps

aim) = Pa)

form <0,
anda

a

‘where W, oven, is the number of taps. The symmetry property implies
that

am) = AAN—1—m), and e2)

whe

Dal) = Aut

mh mae, eb)

‘The qurm further rogutes hal Che fuer in ig. 10 sat the coi
ald

(AY Fal

a

‘which i the miror image relationship af the filters

‘With the above constrains, the aliasing cancellation property tthe
quern can be easly verted * A derivation ia given in the Append
(Az owen from this derivation, the Gers yin) and ln} mua also
ideally satisty the condition
[ater + te =a, a

where He) und Hie) uns he: Fourier transforms of An) and
‘tn), respectively.

"Tho above filter requirement of eg, (0) cannot beet exactly except
when V = 2 nnd when V approwclis infsty, However, itean he very
Slosely approximted for mudest valuer of N Filter designe whieh
satisfy eg, (2a) and approximate the condition of oq. {Al and the
lowpass charaterite can be ctained withthe ait ofan optimization
program, Relerence 1 eavibes 4 procedure hased on the Haoke and
‘Teves optimization algorichm and presence a se: of Hier designs for
wrlues of = 8,12, 18,26, 2,48, and 64. Alo, usefal but Les optimal
esq can be obtained from eonventional Hanning window desizns

‘Figure 2 thows the frequency respnnan characteristics foram
22-Lap iter design tha wax used in he oa nplenentation and Table
T gives the filer coeicienta. Fig. 2a shows the magnitude of Hy(e)
tn H(e"| expressed in dB af a funetion of w and Fig. 2b shows the
mingle of dhe expression

iret]

t6a9 THE BELL SYSTEW TECHNICA! JOURNAL, SEPTEMBER 1461
rm quatirature miro ier

‘Table I—Cocttcen

fay=—opommnea m0 | a4m— oot

ey massa = mee | ka orn

y= norma — aes; | kay = santa
remo =h2u | msi aasserm = AH)

Lrtie) f+ tate)?
express in dP ata fumetion of w. As ean be seem from Fig. 2b, the
requirement of eq, (A) i eatinfied to within « 0125 dB which fe more
‘han satisfactory for good wwe penfurmane. The abo ler design ix
tase un the 2 1 design

"This vonchutes our diseusson ofthe QED conditions and the flor
design. Tn Section 44 we diacuse how the mizor image relationship of
‘sg (8 i aed co advancage in the Os? implementation.

92 The ADPCM covers

“The adaptive citferential eM (ADeca) coders in the two-bandl sc
are baued on Ih algorithms by Curamiskes, Jayanl and Flanagan™
tnd thoy use the oluat frm: of tho step-sige adaption by Guodian
tnd Wilkinson.”

°A detailed description of six skovithm ia given in a companion
caper? Therelor, in thia action we wil unl Briefly outline the fore,
Df the algorithm co Moalfy revs. ptameters and refer the reader
to Ret 6 for speci,

Figure a chows «simplified bloc diagram of the aDrest algorithm.
‘the input tiated) aub-band signal ssenotel as yl). A prediceed
state of this signal, pin). is subleneled from s(a) co produce the
ference signal

io pe co
"This eiference sinal is chen quantized with an sdnptive step size
quantizer to proce the code word Iie) and the decotled diference
signal én)

The stepsie of the quantinar Ain) in adaptively ware wocording to
the relation

tn

lm) = (Xen — DMT cc)

SUBEANDCODNG 1639
eer celia a re cars a acca) ce

where Ain ~ 11 ia the stepsize and Tin ~ 1) isthe eade word atthe
previous ample time n ~The parometar yi nambrr in the vane
ang tyelly, has value of y = 198, used to inereduce a Kner
tremry tn the step-size adapcarion algorithm co mitigece che efeces
chanel ora." "The scale tector M (in) a: a number that depends
fm the code word J¢n). fan outermose pesicive or negeive quantizer
level in uses ac time a ~ La valve of A(.) greater chan one fepically
Io) = 21 e used to ineweane the steprize forthe sample ime mf
loser quancizer mageituce level is used ac time 21, a value of
AC-} Less chan one (vpically Mf(-)= 077) is used to seduee the sie
fae at time n. In this wey. the step size is dynamically varied in ar
flempl to match the eonter of che gunner elmore tn dan of
Ue seve of he ferent signal fe). The vale of AFC ca he
tailored ta modify the edaptstion charactertice of the quantizer
"Topiealy, faster etack (rep-sie increase) and a elower decay (step-
rine decreas) is preferred" for best subjeccve performance,

‘The sum of the decnded diferenee sgeal 20) and Une predictor
signal pin) gives the deceed version of the input mgna, denoted at

Seyi
Fin) = 6) + pint “

W640 THE BELL SYSTEM TECHNICAL JOURNAL, SEPIEMBEH 1981
"isi used in sho aura receiver (ave Fig. sb) to produce the devoded

‘outpt signal: It ha ned ia the ate Irustor fase Pig
senorave the predictor signal according tu the relation
pint = R50 — 11 a

“The prssareter determines the fraction ofthe signal fon 1 hat ie
osu to predict the nest incoming stmple yin Kdesly it should be
‘qual to the sarple-to-ample correlation that exists in the sigmal

For epoch, saupled at 8 kb, ic hat been suggested tha values of
f¢-=117 flower band) and fy ~ 0.45 topper band) are appropriate”
‘The negative corelacion in the upper subband ia hreavse the tre=
quency meals othe spectrin ie inverted inthe decimarion proces of
‘hnegaten. For aslo signal, sampled ac 14 KHe, values of f= 0.28 a
fc= —!182 have been auggestet™ note that fan! fi ave tented sn a8
(aid 9c in Ref. 3h

‘The uoraber of bite per ample used to encode each sub-band i
Atependent on the overall bic rate of the coder. For speech, sampled at
{He choice af its?sarple For the lo hand nnd hese for
the upper band lauds Wo a 2-kbe design, For audio, sampled wt 1
liz a choice of 4 bra/ssmple was used in euch aub-band for the 5
b/s commentary grade coder

33 Prettecing

Tig somesimes desiable in sue coding vo buact-limit che input signal
prior co encoding, For example, in spec x subetomtial sl ul
fignal once’ ay be presenti he frequen range ft 9 10 200 He
‘Ths energy eorributes io an increned stn an Haars
quaetization wine inthe lower subband. I rlephane bane speerh
(200 vo 9200 Fal of inverse, then babd-tiniing she input signal to
Ihis range before encoding removes the signal energy below 200 Lz
‘and sows 3200 He ‘Thi pormie tho wie uf a lower atepsie in he
Uotteas band and, therefore, penviec Tox quantization raise. Rar
audio, asimilar advantage is gained irom prefering by removing low
frequency ham and turntable rimble components in she signal prior
tp encoding

igure 4 shove example of cancade Mer strsctare for a sith
cnder finite imple respec (a) Bilan thas waa se the Be
irwplementation for tia purpose, ‘The vafticients foe « 28 (3200.
HE bands elie Filta desig (assuming an BA. sapling wate)
ave given in Table Il snd the Requeney veqponse for this dosign 12
‘thos in Fig,

Tn he design of aut filters some waution must be observed in
vwinimiing the effects of roundot! meio, iit eyes. and dynamic
i+ Bl dag ae vlc er pt

range canstrsints within Uw lure, Thi cam bie arcomplishe hy
‘aera several rule of chum for pairing and ordering the artung>
tent of poles aad zeroes within the cascade ler structure and als
by wpproprintely seating the siglo apetion to aectin within the
Aller stricture ln enntel the internal dynam range. Further infor
imation un this subject ea be feed Hebe 14 ald 1K In gence
these procedures ate more eres! Tr high-order high @ Gre and
Jess ert for low-order low @ designs

1W, IMPLEMENTING THE SOC ALGORITHM ON THE DSP
‘41 Some geneca! programming cnsidersions

{As cen ftom the abave discussion thore arb a number of dillent
ospeets ta conrider inthe implementation ofan algorithm auch a3 sic
fm the new. In this section, we dhcuss como of chéee fame and pointe
‘out some gontrul proyrimnreng teewigue Mr were wal Priciples
uch ae onalulariation, streams pressing, block processing a dine
ble bulforing il be intreduced. Ts Sections 42 101.3 we discus nore
specifiy hn These principles ave used in the se aottrare, We wll
sssume i the fllowicw discussion thatthe eur is wenorallyGaiar
‘pith the ust eofoware,

"Thy auflvaredevelupment fr the ane and sila signal processing
algortins fs pevatly ship! bye neengnizing che face chat there are
several well-defined operations chet are being performed in the alze
then, suc as filtering, coding, and sampling ral: conversion, By
identifying these opcrutios and modluriing the software around
thom, the prablem aun br subdivided inte w src of smaller pies.

Tobie IICoellciens for siath-order ue bendpase elit Bex
Ta nde sing ee

1642 THERELL SYSTEM TECHINICAL JOUIIMAL, SerTEMBEN! 1261