OPTIMIZATION ALGORITHMS FOR ESTIMATING MODULATION SPECTRUM
DOMAIN FILTERS
Pau Paches-Leal

y
,
z
,Richa dC.Rose
y
, and Climen Nadeu
z
y
AT&T Labs-Resea ch, Flo ham Pa k, NJ, USA,
z
Uni . Poli ecnica de Ca alunya, Ba celona, Spain
ABSTRACT
The goal o he wo k desc ib ed in his pap e is o de elop
and e alua e p o cedu es o au oma ic es ima ion o mod-
ula ion sp ec um l e s o compensa e o dis o ions in
he modula ion sp ec um domain. The mo dula ion sp ec-
um (MS) is o en used o desc ib e he ime sequence
o sp ec al pa ame e s (TSSPs) ha a e de i ed om he
sp eechwa e o m, and is hough o be a go o d ep esen a-
ion o many sou ces o a iabili y in speech. These p o-
cedu es will b e used in he con ex o au oma ic sp eech
ecogni ion (ASR) applica ions whe e he e is likely o b e
a signican misma ch in he MS cha ac e is ics ha exis
o sys em aining and e alua ion. Resul s a e p esen ed
desc ibing applica ion o he algo i hm o one ask in ol -
ing an a icially in oduced MS dis o ion and o ano he
ask in ol ing die ences in sp eaking s yles o aining
and es ing. I is shown in he pap e ha hese ech-
niques a e able o comp ensa e o he eec s o a icially
in o duced dis o ions ha appea in es ing. I is also
shown ha a small deg ee o comp ensa ion is ob ained
o sp eaking s yle misma ch, and his esul is compa ed
wi h he measu ed eec s o he sp eaking s yle die ences
in he MS domain.
1. INTRODUCTION
The ime sequence o sp ec al ec o s de i ed om he
sp eech signal can b e ep esen ed by he Mo dula ion Sp ec-
um (MS) [5]. I has been p op osed o use in many ap-
plica ions. These include cha ac e izing mul ipa h dis o -
ions o ccu ing in e e b e an en i onmen s [2], desc ib-
ing he eec s o channel dis o ion and sp ec al es ima-
ion e o s in ASR [5], and desc ibing he eec s o a ying
sp eaking s yles o ASR [5]. When used as a ep esen-
a ion o he long{ e m a e aged spec um o ceps um
pa ame e s in ASR, he MS is dened as he p owe sp ec-
um o he ime sequence o he ea u e ec o s ha a e
inpu o he ecognize . In sp eech ecogni ion ea u e ex-
ac ion, MS l e s ha e b een designed o he pu p ose
o selec i ely emo ing hose p o ions o he modula ion
sp ec um ep esen ing noise o channel dis o ions, and
e aining he p o ion o he MS con aining sp eech[5].
MS l e s a e commonly applied o l e ing he se-
quence o ceps um co eÆcien s and also o compu ing he
ceps um die ence dynamic co eÆcien s. I is imp o an
o no e ha he MS l e s used o b o h he ceps um
and dynamic ceps um coeÆcien s a e gene ally ob ained
empi ically. As a esul , i is o en he case ha MS l-
e s designed o op imize pe o mance o one ask unde
a gi en se o condi ions p o e o be sub op imal when ap-
plied o ano he ask. The au oma ic p o cedu e p esen ed
he e o es ima ing mo dula ion sp ec um l e s is an a -
emp o imp o e sp eech ecogni ion p e o mance unde
highly misma ched ecogni ion / aining scena ios.

This esea chwas conduc ed a AT&T Shannon Labo a-
o y as pa o P.Paches-Leal's Ph.D. hesis wi h he UPC
The pap e is o ganized as ollows. Sec ion 2. desc ibes
he mo dula ion compensa ion algo i hm (MCA) and dis-
cusses implemen a ion issues ela ing o he algo i hm.
In Sec ion 3., he algo i hm is implemen ed on an a i-
cially in o duced dis o ion applied o he es da a. Fi-
nally, in Sec ion 4., he issue o au oma ic comp ensa ion
o sp eaking a e mis{ma ch using he MCA algo i hm is
in es iga ed.
2. MODULATION COMPENSATION
ALGORITHM
The mo dula ion compensa ion algo i hm (MCA) es i-
ma es a se o l e coeÆcien s o maximize he likeli-
ho o d o he l e ed obse a ion sequence wi h esp ec o
a gi en HMM model. The scena io unde which he al-
go i hm is applied is illus a ed by he blo ck diag am in
Figu e 1. The unde lying assump ion in his scena io is
ha condi ions ha migh aec he MS cha ac e is ics
o sp eech du ing ecogni ion may no b e p esen du ing
HMM mo del aining. Discussion o he MCA algo i hm
is p esen ed in his sec ion in wo pa s. Fi s , i is in o-
duced as an ex ension o a class o echniques de elop ed
by Chengal a ayan and Deng o simul aneous es ima ion
o HMM and obse a ion sequence l e pa ame e s [1 ].
Second, he algo i hm is desc ib ed in de ail, along wi h
algo i hmic issues ela ing o he op imiza ion c i e ion
and he o m o he l e s ha a e used in he algo i hm.
DOMAIN SPECIFIC
MODULATION SPECTRAL
SHAPING
T aining
Speech
Tes
Speech
MODULATION
COMPENSATION
ALGORITHM
(MCA)
HMM Model
λ
Es ima ed
Modula ion
Spec um
FIl e
FORWARD−
BACKWARD
TRAINING
Figu e 1. Mo dula ion comp ensa ion algo i hm
(MCA) applied whe e mo dula ion sp ec um dis-
o ions maybe in oduced in es condi ions.
In [1 ], a class o echniques o simul aneous es ima ion
o HMM and obse a ion sequence l e pa ame e s was
de elop ed. This was used only o ob aining die ence
ceps um pa ame e s om he absolu e ceps um. The
comp onen s o a
D
dimensional dynamic ceps um ec o
Y
=
y
1
;:::;y
D
we e compu ed om a s a ic ec o
X
a
ime
acco ding o
Y
=
X
k
=

b
!
k;i;m
X
+
k
;
1


T
(1)
whe e he mo dula ion" l e co eÆcien s
!
k;i;m
a e de-
p enden on s a e
i
and Gaussian mix u e comp onen
m
.
Equa ion 1 was in oduced in o he mo del ees ima ion
equa ions o con inuous Gaussian obse a ion densi y
HMMs and simul aneous ees ima ion o he l e co e -
cien s and he HMM mo del pa ame e s was p e o med.
6 h Eu opean Con e ence on
Speech Communica ion and Technology
(EUROSPEECH’99)
Budapes , Hunga y, Sep embe 5-9, 1999
ISCAA chi e
h p://www.isca-speech.o g/a chi e
Wellekens p op osed a mo e cons ained mo dula ion sp ec-
um l e ees ima ion p o cedu e aimed a op imizing
only he cu {o equency o he MS l e s [7].
Simul aneous es ima ion o hese pa ame e s has he
desi able eec o p o iding a close coupling be ween
mo del es ima ion and ea u e analysis in sp eech ecog-
ni ion. Howe e , b ecause o he coupling o mo del es i-
ma ion, i is unlikely ha he spec al cha ac e is ics o
he l e pa ame e s es ima ed in his way will ac ually
eec any meaning ul s uc u e asso cia ed wi h he MS
o sp eech. The goal in his wo k is o es ima e he MS l-
e pa ame e s sepa a e om he HMM model acili a ing
he scena io depic ed by he blo ck diag am in Figu e 1.
Since he mo del emains xed, MS misma chbe ween u -
e ances used o ain he mo del and he u e ances used
o es ing can b e educed. The MCA algo i hm and i s
ma hema ical p ope ies a e desc ib ed in mo e de ail b e-
low.
The algo i hm es ima es a l e ha , when applied o
he absolu e ceps um co eÆcien s, inc eases he likeliho o d
o he l e ed da a,
Y
!
, wi h esp ec o he HMM model,

. This in heo y could b e accomplished byenume a ing
an ensemble o MS l e s  and choosing he mos likely
l e in he ensemble,
^
~!
= a g max
~!
2

P
(
Y
!
j
~!; 
)
:
(2)
Howe e , in p ac ice i is e y diÆcul o speci y a man-
ageable ensemble o l e s ha would b e sui able o ep-
esen ing an a bi a y se o mo dula ion sp ec um dis-
o ions and i is no clea ha a maximum likeliho o d
c i e ion would b e sui able o selec ing he op imum MS
l e om his ensemble. The algo i hm desc ib ed he e
assumes a ni e impulse esponse l e , whose leng h mus
be chosen, and es ima es he pa ame e s o his l e us-
ing he exp ec a ion maximiza ion (EM) algo i hm. I can
b e applied o l e ing he absolu e ceps um ea u es o
o ob aining he l e pa ame e s used o compu e he dy-
namic ea u es om he absolu e ceps um. The ollowing
discussion will e e sp ecically o he o me case.
Gi en an ini ial HMM mo del,

, and an ini ial
leng h
o he MS l e ,
~!
, his EM based algo i hm maximizes
he exp ec ed alue o he log o he l e ed da a likeli-
hood,
P
(
Y
!
j
~!; 
), wi h esp ec o
~!
. The da a o which
he l e
~!
is applied can be he unl e ed absolu e da a,
X
, o he absolu e da a l e ed wi h an ini ial l e . In
he la e case, he o e all l e ha needs o b e applied
o he es da a so as o educe he MS mis{ma chbe-
ween he unl e ed aining da a and he es da a is he
con olu ion o he ini ial l e and he l e op imized by
he MCA,
~!
. Unless o he wise sp ecied, no ini ial l e
is used and he MCA is s a ed wi h unl e ed da a.
The p o ion o he op imiza ion equa ion ha is dep en-
den on he l e ed da a is gi en by
X
i;m;

;i;m
[
Y

~
x;i;m
]
T


1
x;i;m
[
Y

~
x;i;m
]
;
(3)
whe e

;i;m
is he a p os e io i p obabili yo o ccupying
Gaussian mix u e componen
m
and s a e
i
a ime
. The
quan i ies
~
x;i;m
and


1
x;i;m
in Equa ion 3 a e he HMM
mo del means and a iances o he unl e ed da a,
X
,
and a e no ees ima ed as pa o his p o cedu e. Fo
he pu p oses o his de elopmen ,
Y
in Equa ion 1 can
b e w i en in ec o no a ion as:
Y
= (
X

b
:::
X
+
)
T
(
!

b;i;m
:::!
;i;m
))
T
=
X
+

b
~!
i;m
:
(4)
No e ha , while Equa ion 4 demons a es ha i is p os-
sible o use MS l e s
~!
i;m
, ha a e HMM s a e and mix-
u e comp onen dep enden , his is no done he e. By
subs i u ing he exp ession o
Y
in Equa ion 3 and di -
e en ia ing wi h espec o
~!
, which does no dep end on
i
and
m
,we ob ain
X
l;i;m;

;i;m

X
+

b

T


1
x;i;m
X
+

b
~!
=
X
l;i;m;

;i;m

X
+

b

T


1
x;i;m
~
x;i;m
(5)
Finally,
~!
can b e ob ained by sol ing he ma ix equa ion
gi en by Equa ion 5 which equi es he mo del means and
a iances, he a p os e io i p obabili ies compu ed in he
o wa d{backwa d algo i hm, and he unl e ed obse a-
ions.
While he ab o e p o cedu e can b e i e a ed, using he
es ima ed
~!
ob ained by sol ing Equa ion 5 as inpu o
a ollowing i e a ion, he e a numb e o issues ha mus
b e deal wi h. The  s issue ela es o he ac ha i
is he l e ed da a, as opp osed o he o iginal da a, ha
is inpu o he nex i e a ion o he algo i hm. As a e-
sul , he l e applied o he da a o a gi en i e a ion
mus b e he con olu ion o all he l e s ob ained in he
p eceding i e a ions. As has b een seen, a con olu ion is
also necessa y o he case whe e he MCA p o cedu e is
s a ed wi h da a l e ed wi h an ini ial l e . A second
issue ela es o a i ac s ha a ise due o lack o ene gy
cons ain s in he mo del es ima ion p o cedu e. An em-
pi ical p o cedu e o no malizing l e ene gies be ween
i e a ions is desc ib ed in Sec ion 3..
3. COMPENSATING FOR MS DOMAIN
MISMATCH
The MCA algo i hm was  s applied o a simula ed dis-
o ion. The goal o his  s applica ion was o imple-
men a scena io as depic ed in he block diag am in Fig-
u e 1. The o m o he mo dula ion sp ec um misma ch
was in ended o inco p o a e a lo ose app oxima ion o ex-
is ing MS mo dels o how sp eaking a e a iabili y migh
b e eec ed in he mo dula ion sp ec um domain (e.g. [5]).
These models cha ac e ize he MS o sp eechasha ing a
p eak a app oxima ely ou Hz wi h some a ia ion in he
lo ca ion o ha peak p ossibly esul ing om speaking a e
die ences.
The mo dula ion spec um dis o ion o ok he o m o
an FIR l e o leng h 7 wi h a p eak a 10
Hz
and a s ong
a enua ion o mo dula ion equencies b eyond 20
Hz
. This
l e was ac ually applied o he
aining
u e ances o he
high SNR, noise{ ee TI digi s da abase [4 ]. So he mo du-
la ion sp ec um shaping indica ed in Figu e 1 would ac u-
ally b e he in e se o ha sp ec um. The HMM mo del,

,
was hen ained om he l e ed da a using he o wa d{
backwa d algo i hm. The 8623 digi s ings u e ed bya
p opula ion o adul sp eake s in he aining se o he TI
digi s da abase was used o aining digi mo dels wi h a
mix u e o a mos 16 con inuous Gaussian comp onen s
p e HMM s a e. The TI digi s es se was spli in o a
3306 u e ance de elopmen se , whichwas used as inpu
o he MCA algo i hm, and a 5376 u e ance es se o
e alua ing ASR wo d accu acy.
The inpu s o MCA a e he model and a subse o he
unl e ed de elopmen u e ances and he ou pu is a l-
e ha educes he misma chbe ween he u e ances and
he mo del. Figu e 2 shows he mo dula ion sp ec a o
he aining u e ances and he unl e ed de elopmen
u e ances o ceps al co eÆcien
c
4
. The l e ha was
applied o he aining u e ances is also shown. A sig-
nican misma ch can be obse ed in he MS domain.
The magni ude sp ec um o he MS l e es ima ed us-
ing Equa ion 5 was ound o p o ide a easonably goo d
app oxima ion magni ude sp ec um o he l e used on
0 5 10 15 20
10−1
100Modula ion Spec um o Dimension 4
dB
Hz
ain
es
il e
Figu e 2. Mo dula ion Sp ec a o he T aining U -
e ances and o he Unl e ed De elopmen U -
e ances, along wi h he Spec um o he Fil e
Applied o he T aining U e ances
he aining u e ances. Howe e , since he e is no inhe -
en cons ain on he ceps um ene gy le els in he MCA,
signican misma ch in he ene gy le els o he l e ed
ceps a and he o iginal ceps a can occu . To deal wi h
his, he l e co eÆcien s a e scaled wi h a dimension spe-
cic scale ac o so ha a e age ene gy o he aining and
adap a ion u e ances a e no malized o he same le el.
The es ima ed l e , scaled sepa a ely o each comp onen
o he inpu ceps um ec o , is hen applied o he es
u e ances.
Table 1 displays he ecogni ion p e o mance a e he
MS l e de e mined by he MCA was applied o he es
u e ances. Pe o mance is p esen ed as a unc ion o
he numb e o de elopmen o adap a ion u e ances ha
we e used by he MCA. The algo i hm was implemen ed
he e in a sup e ised mo de wi h he u e ance ansc ip-
ions made a ailable o he MCA. The Table shows ha
when he whole de elopmen se is used o de e mine he
b es l e wi h which o educe he misma ch be ween
ain and es u e ances, wo d accu acy app oaching he
ma ched condi ion can be ob ained. When less da a is
a ailable ( om 60 u e ances h ough jus one), p e o -
mance deg ades g ace ully wi h esp ec o he whole de-
elopmen se and s ill alle ia es mos o he ecogni ion
a e educ ion due o he MS die ences b e ween aining
and es ing. Resul s a e gi en in all cases o he l e
ou pu by he  s i e a ion o MCA, which has leng h
3. Su p isingly, l e s wi h o he leng hs, esul ing ei he
om unning se e al i e a ions wi h a l e leng h equal
o 3, o om cho osing ano he l e leng h (e.g. 5,7o 9)
also gi e goo d p e o mance bu sho o he esul s when
he leng h is 3. A leng h o 3 seems o s ike he igh
balance b e ween he numb e o deg ees o eedom and a
cons ained es ima ion.
Mo dula ion Sp ec um Adap a ion %Wo d
Comp ensa ion U e ances Accu acy
Ma ched - 96.30
Misma ched - 15.04
MCA 3306 92.10
MCA 10 88.78
MCA 1 87.93
Table 1. Resul s o MCA wi h a simula ed dis-
o ion
MCA seems o wo k well o he expe imen s ha we e
done wi h a simula ed dis o ion. MCA was applied o
es ima e he l e applied o he absolu e co eÆcien s, no
dynamic ea u es we e used. The nex sec ion desc ibes
an exp e imen whe e MCA was used o op imize he l e
used o ob ain he del a coeÆcien s.
4. MCA AND SPEAKING RATE
In o de o es MCA in a mo e ealis ic en i onmen , a
da abase con aining sp eech elici ed a mul iple speaking
a es was used [6]. This da abase, e e ed o as DB1,
was eco ded in an anechoic o om wi h a high quali y
mic ophone. I includes sp eech om 22 emale, and 24
male alke s, each o which eco ded 120 sen ences. Bo h
no mal a e and as a e u e ances o each sen ence was
elici ed om each speake . Fas a e sp eechwas elici ed
om each sp eake by asking sp eake s o sp eak sen ences
as apidly as p ossible wi hou g oss misp onouncia ions.
Fo each sp eaking a e, c oss-wo d iphones backed o
o monophones we e ained om he sen ences om 38
sp eake s. The emainde we e ese ed o es ing. Each
sys em had 4903 s a es and o e 28000 Gaussians. In
ecogni ion, each phone may be ecognized ia a iphone
o he co esp onding monophone a any place wi hin a
wo d. All 120 sen ences o all he es sp eake s we e
ecognized. Figu e 3 desc ib es he exp e imen ha was
ca ied ou .
Modula ion Spec um
Fil e
ω
Fas Speaking Ra e:
De elopmen U e ances
λ
S
Speake Dependen
Model
No mal Speaking Ra e:
MODULATION
COMPENSATION
ALGORITHM
Fas Speaking Ra e:
Tes U e ances ASR
FILTER TIME
SEQUENCE OF
CEPSTRUM
PARAMETERS
Figu e 3. MCA and sp eaking a e
The goal was o s udy how well MCA can cop e wi h
sp eaking a e misma ches and up o wha p oin hese can
b e ep esen ed in he mo dula ion sp ec um. The ecog-
ni ion esul s o all 8 es speake s we e analysed. The
u e ances om a single male sp eake whe e mo e d a-
ma ic die ences b e ween as and no mal a e sp eaking
s yles we e obse ed we e selec ed o he exp e imen al
s udy.
Since MCA migh imp o ewo d accu acy by p e o m-
ing sp eake adap a ion, a sp eake adap ed mo del was
ob ained. To do his, he gaussians in he no mal- a e
mo del we e clus e ed in o 4 eg ession classes. On he
 s 60 no mal- a e sen ences, one Maximum Likeliho o d
Linea Reg ession ull ma ix ans o ma ion (MLLR) was
lea ned o each eg ession class [3]. These we e applied
o he means o he no mal- a e no mal- a e mo del, which
esul s in a sp eake adap ed no mal- a e mo del.
This mo del was hen inpu o he MCA along wi h he
 s 60 as sen ences, ega ded as de elopmen o adap-
a ion sen ences. The l e ou pu by MCA was applied
o he 60 las as u e ances. In his case, MCA was used
o op imize he l e used o ob ain he del a ea u es (no
o he dynamic ea u es we e used apa om hem). An-
o he die ence wi h he p e ious expe imen is ha he
l e used o ob ain he del a ea u es o he aining u -
e ances was used as he ini ial l e o MCA. The leng h
o he l e ou pu by each i e a ion was he ini ial model
l e leng h, i.e. 5, plus 2 o each i e a ion. Resul s o
his exp e imen can be ound in Table 2.
Tes Condi ion %Wo d Acc.
Sp eake Indep. No mal Ra e 57.28
Sp eake Adap . (SA) No mal Ra e 80.67
Baseline SA Fas Ra e 61.58
Po oled" MCA Fas Ra e 61.10
Dim. Specic" MCA Fas Ra e 63.96
Table 2. Resul s o MCA wi h die en sp eaking
a es
Two mo des o MCA we e in es iga ed. The  s , e-
e ed o as p o oled MCA" in Table 2, es ima es he MCA
l e co eÆcien s acco ding o he p o cedu e ou lined in
Sec ion 2. The second, e med dimension specic MCA",
es ima es a sepa a e se o MS l e co eÆcien s o each
dimension o he ceps um obse a ion ec o . This ep e-
sen s an ex ension o he MS l e desc ib ed in Equa ion 1
and indep enden ly es ima es l e pa ame e s o op imize
dimension specic ML c i e ion. I is clea om Table 2
ha he MCA yields only a mo des imp o emen in WAC
o e he baseline sys em on he as a e o his ask.
0 5 10 15 20
10−2
10−1
100Modula ion Spec um o Dimension 2
dB
Hz
as
no mal
Figu e 4. Measu ed MS om as and no mal
sp eech u e ances
In o de o ob ain some pe sp ec i e o he deg ee o
which mo dula ion sp ec um based echniques may a -
ec pe o mance o sp eaking a e misma ch, he a e -
age mo dula ion spec um was measu ed o u e ances
wi h die en sp eaking a es. Fo each ceps um com-
p onen , he magni ude o he a e aged modula ion sp ec-
um was compu ed o e 60 sen ences o no mal and as
a e sp eech. Figu e 4 displays he magni ude spec a o
one o he comp onen s o he acous ical ec o . I is clea
om he cu es ha he as a e speech has only sligh ly
mo e ene gy in he highe mo dula ion equencies han
he no mal a e sp eech. This sugges s ha one migh ex-
p ec only small changes in p e o mance using MS domain
echniques o his ask, which supp o s he ai ly mino
imp o emen s ha we e obse ed he e.
5. CONCLUSION
The mo dula ion comp ensa ion algo i hm was p esen ed
as a maximum likeliho o d echnique o es ima ing l e s
o he ime sequence o spec al pa ame e s in o de o
educe misma ch in he mo dula ion sp ec um. The p o ce-
du e was desc ib ed as an ex ension o a class o echniques
de elop ed in [1]. I can be applied o es ima ing MS l-
e s o he absolu e ceps um co eÆcien s o o ob aining
he dynamic ceps um co eÆcien s om he absolu e co-
eÆcien s. Two applica ions o he MCA we e desc ib ed.
The  s applica ion was o a ask whe e a simula ed
mo dula ion sp ec um domain dis o ion was in oduced
du ing es ing. I was shown ha he MCA can eec-
i ely educe misma ch in he MS b e ween aining and
es ing u e ances. In a second applica ion, he MCA was
applied o educing misma ch a ibu able o die ences
in sp eaking a e. The MCA was shown o ha e only a
small impac on p e o mance o his ask. Fu he wo k
is di ec ed owa ds applica ion o he algo i hm o o he
sou ces o a iabili y whe e dis o ions in he mo dula ion
sp ec um a e mo e p onounced.
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