1358
TRANSACTIONS
IEEE
COMMUNICATIONS,
ON
H. Murakami,Y.Hatori, and H. Yamamoto,“Comparisonbetween
of
DPCM ,and Hadamard transform coding efficiencies for the variation
statistical characteristics of NTSC signals” (in Japanese), Paper Tech.
Group, CS 78-53, IECE Japan, June 1978.
N. Ahmed arid,K.R. Rao, Orthogonal Transformsfor Digital Signal
Processing. New York:Springer-Verlag,1975.
results on the performance of
W.Mauersberger,“Experimental
mismatched quantizers,” IEEE Trans. Irform. Theory, vol. IT-25,
pp. 381-386, July 1979.
J. Max, “Quantizing for minimum distortion,” IRE Trans. Inform.
Theory, vol. IT-6, pp. 7-12, Mar. 1960.
P. A: Wintz and A. J. Kuternback, “Waveform error control in PCM
telemetry,” IEEE Trans. Inform. Theory, vol. IT-14, pp. 650-661,
Sept.1968.
and J. D. Gibson,
“Distribution
of the twoR.C.Reininger
dimensional DCT coefficients for image,” ZEEE Trans. Commun.,
vol. COM-31. June 1983.
Hybrid Adaptive Quantization for Speech Coding
M. E. M. NASR AND C. V.CHAKRAVARTHY
Abstract-This correspondence describes a new quantization technique
called hybrid adaptive quantization (HAQ) that uses instantaneous [l],
[21 as well as syllabic [3] adaptation of the stepsize.Twotypes
of
instantaneousadaptivealgorithmshavebeenused-Jayant’sadaptive
quantizer(JAQ)andtheincrementaladaptivequantizer(IAQ).
Computersimulationshave
tieen performedfor a sine-wave, correlated
(SNR) compuGaussian signal and digitized speech. Signal-to-noise ratio
tation for PCM and DPCM coders indicatesthat the hybrid technique is
the same ratio
superior to the normal adaptive quantizer, when both have
of maximum to minimum step size.
I. INTRODUCTION
Waveform encoding methods based on pulse code modulation (PCM) or differential PCM (DPCM) may employ linear,
nonlinear,oradaptivequantizers
[ 1 ] -[ 31 . Adaptivedelta
modulation (ADM) i s a special case ofa DPCM coder. Adaptive DPCM coders, which use only half the bandwidth needed
by conventional PCM coders, are being standarized for voice
communication. While theexisting1-lawandA-lawcoders
havefixednonuniformquantizers,
ADPCM codersarebased
upon adaptive quantizers.
Adaptive quantization isof two types-instantaneous and
syllabic. The former can change its step size for every sample,
while.in the latter it is much slower (following the envelope
variation in speech). Although instantaneous quantizers have
good attack and decay times, they are prone to
a little more
VOL. COM-32, NO. 12, DECEMBER 1984
quantizing noise, unlike the slower syllabic adaptive systems.
Un et al. [ 4 ] havesuccessfullyemployed
a combination of
both methods for ADM while we have investigated the hybrid
techniquefor PCM and DPCM coders.Themainidea
isas
follows.
Aninstantaneousadaptivequantizerchangesitsstepsize
at each sampling instant, based upon
a certain rule, subject
t o a minimum step size A, and a maximum step size Amax,
resulting in a range factor R = A m a x / & . In an HAQ these
limitsarenotfixed
values,’ but varyproportionally t o t h e
envelope of theinput. If theenvelope is considered t o b e
of A, and
constantovershortperiodsoftime,thevalues
Amax withintheseintervals
will beconstant(butdifferent
from interval to interval).
Anothermethodthat
is somewhatsimilar totheHAQ
(called the“pseudosyllabic”adaptation)hasbeenreported
by Raulln’ et aZ. [ 6 ] , [ 7 1 . In the simplest case the quantizer
can be a linear one with a minimum step size of A,. Whenever
the magnitude 1 B , I of the binary output exceeds a predeterminedvalue, a constantvalue of 256 is fed t o a low-pass
filterwithtransferfunction
H ( z ) = (1 - (511/512)z-l)-’,
and a zero is fed otherwise. The effect is to increase the output
(denoted by S ( n ) , say) by 256 when the threshold is exceeded,
or to reduce it by
a factor of 511/512 otherwise. The step
size A ( n ) i s given by A(?) = A02’(“) where i ( n ) is defined as
the largest integer in [(s(n)/2048)
- 41. This allows the step
size to vary over the range of A, to 2048 A,. It is easy t o see
thatthestepsizecandoubleineightsamples
(1 msfor a
sampling rate of 8 kHz), while the step size reduces by half
in a time that varies between 4 and 16 ms, depending upon the
initial step size.
As an example, a 4 bit quantizer can have 15 values
of B ,
between -7 and +7 (since the implementation reported excludestheall-zerocode).
If thethreshold is selectedas 5,
the filter output
is increasedby256everytime
I E , I 5.
However,whenthestep
size isdoubled,eventhoughthe
threshold is 5 , the absolute value represented by this threshold is doubled. To make the transition smoother, four
nonlinearlawshavebeenused,eachwithdifferentthresholds.
it takes
It must benoted,however,thatduringthetime
i ( n ) t o change by one unit (up or down), the quantizer
will
be the same.
While itseemsto6esimilartothehybridscheme,the
pseudosyllabicsystem is differentforthefollowingreasons.
During the time of eight samples required for step increase or
during the time required for step size decrease, the quantizer
is fixed. On the other hand, in the hybrid scheme, even during
on the instantaneous
this time the step size can change based
algorithm. In fact, if JAQ is used, the step size can double in
just one or two samples. This is particularly efficient in avoiding clipping in PCM or slope overload in DPCM. Likewise, the
timetakento
halve thestepsizewouldbelongerinthe
pseudosyllabic system, and during this time we have the fixed
stepsize. Of the different instantaneous adaptive algorithms
available, we have chosen two for our study-Jayant’s adaptive
quantizer (JAQ) [ 11 and the incremental adaptive quantizer
(IAQ) [2]. PCM and DPCM (single tap predictor) coders have
been
simulated
on a DEC-IO
computer
using
sinusoidal,
correlated
Gaussian
random
signal,
and
digitized
speech
inputs.
In t h e case of the IAQ, the hybrid quantizer offers a substantial increase in dynamic range, while in t h e case of JAQ,
there is not any significant increase. The reasons for and the
implications of this are presented in the concluding section.
>
Paper approved by the Editor for Signal Processing and Communication
Electronics of the IEEE Communications Society for publication without oral
presentation. Manuscript received April 20, 1983; revised
May 4, 1983. This
work was supported in
pan by a fellowship fromthe Government of India and
the Government of Egypt.
M. E. M. NasriswiththeDepartmentofElectricalCommunication
Ehgineering, Indian Institute of Science, Bangalore 560012, India, on leave
from the Faculty of Electronic Engineering, Menoufia University, Menouf,
EgYPt.
C. V. Chakravarthy is withtheDepartment of ElectricalandComputer
Engineering, Louisiana State University, Baton Rouge, LA 70803, on leave
from the Departmentof Electrical and Computer Engineering, Indian Institute ‘The authors thankan anonymous referee for bringing these references to
of Science, Bangalore 560012, India.
their notice and for providing a copy of the CCITT Study Group Report.
0090-6778/84/1200-1358$01.00 0 1984 IEEE
1359
IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. COM-32, NO. 12, DECEMBER 1984
11. QUANTIZER DESCRIPTION
One of the forms of JAQ is shown in Fig. 1. The step size
An of the quantizer (which need not necessarily be uniform)
at the nth sampling time
is
OUTPUT
t
5An/2
I B n P l 1. The HAQ is
realized using the system shown in Fig. 2. The quantizer output is low-passfiltered
toentracttheenvelope,which
is
used to multiply the minimum step size A,. In the simulation
of JAQ [ 1 J , the value of A, used is 0.1 Aopt where Aopt is
the optimum step size for a nonadaptive quantizer
given by
2 ~is the variance and N
the rule of thumb Aopt = 8 ~ / (u2
the number of bits).
Starting with a step size of A,, if the envelope is constant
for t l seconds, then at t = t l , the step size will be
M beingamultiplierdependenton
A n/2
I
-4An
I
I
I
-3An
-2An
-An
I
An
I
I
2%
36,
4A,
INPUT
I
"
t
-5 An11
t
suchthat IT, = t l ( T , beingthesamplingperiod).During
the next sampling time,
if the envelope changes by a factor
P, then the step size for the next sample
is P A ( t , ) and not
A ( t l ) . Thisassumes aninstantaneousresponse.
In practice,
however, the envelope change
will take place in a finite time
(albeitsmall)andduringthetransitionsthestepsizewould
not have stabilized to the optimumvalue.
The syllabic adaptation is achieved as follows. The output
of the quantizer (analog samples)
isrectifiedandfiltered
to
producetheenvelopewhichthenmultipliestheminimum
step size. The filter is a two-pole
LP filter with a 20 ms time
constant.
The adaptation rule for the incremental adaptive quantizer
Fig. 1 . Jayant'sadaptivequantizer.
FULL WAVE
R E C T I F I E R AND
ENVELOPE FILTER
SYLLABIC
CONTROL
INPUT
-
QUANTIZER
=
IIA n - l
An-1
+A,(n)
S T E PS I Z E
if IBn-1 ( > ( 2 N - 1 ) 3 / 4
otherwise.
(3)
A o ( n ) is theminimumstepsizeatthenthsamplinginstant
(=A, if it is not a hybrid quantizer, and =Ao X envelope of
the input at the( n - 1)th instant if it is a hybrid quantizer).
The quantizer schematic was showninFig.2,andFig,4
shows the hardware realization. Both types
of the HAQ have
beenusedfor
PCM andthefamiliarsingle
tappredictor
ADPCM (Fig. 3). Themultipliersusedforthe
J A Q in PCM
and DPCM codersaredifferent,asdiscussedbyJayant
[ 11.
The IAQ is shown in Fig. 5 .
111. SIMULATION AND RESULTS
Figs. 6-10 highlight the performance of the hybrid quantizer.Figs.6and
7 providetheresultsfor
PCM coderswith
sinusoidal and random inputs, respectively, while
Figs. 8-10
arefor DPCM coders,theinputsbeing,respectively,a1020
Hzsinewave,randomnoisebandlimited
to within 300 and
3400Hz,andspeech.Thedigitizedspeechhasasampling
rate of 10 kHz. For speech signals, the segment SNR [ 8 J is
computed. All the values of SNR are computed over 10 000
samples. In thenormaladaptivequantizer,theratio
of the
maximum to minimum step size
islimited t o 6 0 dB. In the
hybrid quantizerthe ratio remains the same but with a difof the largestandsmalleststeps
atany
ference.Theratio
instant is fixed at 100 for the instantaneous adaptation only.
Therefore,whenevertheenvelope
is constant,thisratio
is
100 but the absolute values of the largest and smallest steps
will vary.
Thereisnotmuchdifferencebetweenthe
JAQ andits
A/ D
INSTANTANEOUS
CONTROL
[31 is
A,
-
LOGIC
Fig. 2. Schematic of ahybridadaptivequantizer.
hybridversion.Thereasonforthis
is thattheadaptation
algorithm is ideally suited for very quick changes in the step
size, even when the starting value is grossly suboptimal. This
is too
is notthe case withthe IAQ. If thestepincrement
small, the step size change is too slow. So the SNR degrades.
On theotherhand,
if theincrement is madeproportional
to the envelope (hybrid version) the performance is excellent.
While an ordinary version of JAQ seems enough, the hybrid
version has certain advantages. While the computer simulation
provides a continuum of step sizes, a hardware implementation
has to restrict the values to a finite set, This disadvantage can
be offset to some extent with a hybrid coder.
IV. CONCLUSIONS
A newmethod
of realizing anadaptivequantizer,
called
thehybridadaptivequantizer,hasbeendescribed.Thestep
size adaptation is both instantaneous as well as syllabic-the
firstpartcontrolledbythedigitaloutputandthesecond
partbytheenvelope
of thequantizeroutput.Simulation
results for deterministic, random, and speechsignals have been
obtained in the case of 3 bit and 4 bit PCM and DPCM quantizers.
The
instantaneous
adaptation
algorithms
used
are
(JAQ) and the incremental adapJayant's adaptive quantizer
tive quantizer (IAQ). Although among them there is not much
differenceinperformance,thehybridversionscanoffera
large dynamic range and should prove
to be especially useful
for speech coding.
IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. COM-32, NO. 1 2 , DECEMBER 1984
1360
ENVELOPE
DETECTOR
SYLLABIC 5TEP
SIZE CONTROL
(SINE WAVE INPUT)
HYBRID
VERSION
P C M CODER
QUANTIZER
SAMPLES
.
Xn-9
STEP SIZE
CONTROL LOGIC
c(
-
= P,.Cl,
-40
-30
-20
-10
0
40
30
20
10
INPUT
LEVEL,
dB
Fig. 3. DPCM coder witha single tap predictor.
COMPARATOR
-
Sf H
INCREMENTAL
ADAPTIVE
QUANTIZER
AND ITS
HYBRIDVERSION(SINE
WAVE INPUT)
FF
-t-
PCM
30
CODER
HYBRID
,&-a
-4
K
5 In
4 - - - - - - - -
SIT
.-----___
VI
3 BIT
10
I
I
od
-40
Ill
I
-30
I
-20
I
I
-10
0
I N P U TL E V E L ,
SAR
U/D
CONTROL
I
SAR
;
: DIGITAL/ANALOG
-20
40
-
30
-
40
30
Fig. 6. Comparison of SNR versusinputforsinusoidal
quantizer).
b
DAC
IO
dB
signal (PCM
J A Y A N T ‘ S ADAPTIVE QUANTIZER AND ITS
HYBRID
VERSION
(RANDOM INPUT)
P C M QUANTIZER
w HYBRID
m
S U C C E S S I VAEP P R O X I M A T I ORNE G l S T E R
CONVERTER
Fig. 4. Suggested hardwarerealization scheme forthe HAQ (incremental
version).
OUTPUT
0
t
0’
-40
4
I
-30
-20
-IO
I
0
INPUT
LEVEL,
40
An
I
I
-An
An
2An
I
I
-:An
I
- 3 A- 2n A n
=An
-do
4
-A0
I
3An
4An
-
I
40
I
20
30
dB
INCREMENTAL
ADAPTIVE
QUANTIZER AND I T 5
HYBRID VERSION (RANDOM INPUT)
P C M CODER
HYBRID
’0
INPUT
2o
10
INPUT
L E V E L , dB
Fig. 7. Comparison of SNR versusinputforaGaussianinput(PCM
quantizer.
40
1361
IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. COM-32, NO. 12, DECEMBER 1984
-4
DPCM QUANTIZER
-40
-30
-20
PO
40
0
-10
INPUT
HYBRID
‘1
3o
1
I
Y
20
30
40
01
-40
JAYANT$ ADAPTIVE WANTIZER AND ITS
HYBRID VERSION (SPEECH INPUT)
D P C H CODER
w
HYBRID
I
-30
,
I
- 20
-40
0
20
10
30
40
INPUT L E V E L , dB
L E V E L , dB
IUCREMENTAL ADAPTIVE QUANTIZER AND ITS
HVBRID VERSION (SINE WAVE INPUT)
DPCM CODER
CODD
ER
PCM
-40
-20
-10
0
INPUTLEVEL,
dB
INPUT
LEVEL,
-30
W
Fig. 8. ComparisonofSNRvariationwithinputlevel(sine-wave,DPCM
quantizer).
HYBRID
$0
20
30
40
dB
Fig.10.SNRvariationforspeechsignals(DPCMquantizer).
ACKNOWLEDGMENT
HYBRID VERSION
The authors are grateful to the Computer Centre, I.I.sc.,
for thefacilities provided and to Ms. Bharati Devi of the School
of Automationforproviding
the digitized speech samples.
The first author thanks the Government of India and Government of Egypt for providing a fellowship. The authors thank
t h e reviewers for their suggestions.
CRANDoM INPUT)
DPCM QUANTI2E.R
HYBRID
REFERENCES
-40
-30
-20
-10
0
20
10
30
40
30
40
INPUT LEVEL, dB
INCREMENTAL ADAPTIVE QUANTIZER
HYBRID VERSION
(RANDOM
INPUT)
DPCH
QUANTIZER
30
i.”
01
-40
M
AND ITS
HYBRID
1
-30
~ 2 0 -10
0
INPUTLEVEL,
Fig. 9. Comparisonof
40
20
dB
SNR variationwith
DPCM quantizer).
inputlevel(randominput,
N. S. Jayant, “Adaptive quantization with one work memory,” Bell
Syst. Tech. J., vol.52,pp.1119-1144,Sept.1973.
C. V. Chakravarthy, N.D. Georganas, and S. G . S. Shiva,“An
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M. S. Sodhi, J. Das, and C. V. Chakravarthy, “An adaptive PCM with
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J. L. Flanagan, M.R.Schroeder,
Crochiere, and J.M.Tribolet,“Speechcoding,”
IEEE Trans.
Commun., vol. COM-27, pp. 711-742, Apr. 1979.
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