SIGNAL
PROCESSING I
V:
Theo ies and Applica ions
J. L. Lacoume, A. Chehikian,
N.
Ma ín,
and
J.
Malbos (Edi o s)
Else ie Science Publishe s
B.
V.
(No h-Holland)
© EURASIP,
1988
167
ENVELOPE
AND
INSTANTANEOUS
PHASE
IN RESIDUAL REPRESENTATION
A.
Mo eno,
M.A.
Lagu
n
as
Dp o.
Teo ía
de
la
Señal
y
Com
unicaci
ones.
U.P.C.
E.T.S.I.
Telecomunicacion
Apdo .
30.002,
08080
Ba celona,
Spain.
En elope
and
ins an aneous
pha
s e
o
a
eal
s
lgnal
a e
wo
concep s
mainly
asso
c
i.a ed
wl h
modula ion
sys ems.
In
his
pape
is
shown
how
en elope
and
lns an aneous
phase
can
be
applied
in
coding
sys ems.
In
p
a icula
,
he
en elope
o
he
esidual
p o ides
in o ma on
ahnu
pi ch
ilnd
ene gy
o
he
signal
and
can
be
use l
o
p ope ly
codi y
i .
A
pa ame ic
e sion
o
he
en elope
is
aken
om
he
es
ldual
o
a s
ignal
and
his
i.n o ma
ion
ls
used
ln
wo
d
i. e
en
code s:
an
APC
co le
anda
s ochas lcally
exci ed
code
.
In
APC
code
he
esidual
en elope
i.s
used
o
quan
lze
he
p edic
ion
e o
p o iding
s ep
s
ize
and
dynamlc
bU
assignmen
.in o ma ion.
In
s ochas ically
exci ec!
code s,
he
inpu
o
he
syn hesls
il e
is
composecl
by
he
_p oduc
o
he
pa ame ic
en elope
o
he
esidual
mul
ip
li
ed
by
an
ins an aneous
phase
aken
om
a
codebook
o
andom
phases
.
INTRODUCTION
The
cha ac e iza ion
o
he
p edic ion
e o
in
sp
e
ech
coding
is
impo an
o
ge
a
good
syn he
ic
speech
quali y.
In
wa e o m
code s,
as
ADPO!
/1/
,
he
p edic ion
e o
is
quan ized
and
send
o
he
·
ecei e .
In
his
case,
a
p io i
es ima ion
o
he
wa e o m
o
he
p ed
ic
ion
e o
is
use ul
o
quan
ize
i
p o
pe
ly
.
S ochas ically
exci ed
code s
/2/,
by
he
o he
hand,
ep esen s
speec
h
by
means
o
a
ime
a ying
il e
exci ed
by
a
Gaussian
sequence.
A
ime
a ying
il e
is
buil
using
a
sho
delay
il e
which
p o ides
he
onnan s
s
uc u
e
and
a
long
delay
il e ,
(pi ch
il e ),which
p o ides
he
ine
s uc u e
o
he
spec um.
Exci a ion
s e
quence
is
selec ed
om
a
codebook
o
whi e
Gaussian
sequences
by
minimizing
a
pe cep ual
e o
measu emen
.
Long
del
ay
il
e
is
use ul
in
o
iced
egions
bu
du ing
un oiced
egions
has
small
e ec
.
The e o e
i
is
use ul
o
ha e
a
unc ion
which
p ese es
pUch
and
empo al
ene gy
e olu ion
o
he
esidual
in
o de
o
keep
pi ch
in o m
a
ion
in
oiced
egions
and
ene gy
e olu ion
in
all
kind
o
egions.
Some
e o s
ha e
been
made
in
his
sense
a·s
he
sys em
Vec o
Quan ized
Mul ipulse
Code
VQMP
/3/
,
This
code
uses
a
model
whe e
a
sho
delay
il e
i s
exci ed
by
a
signal
This
wo k
has
b
een
pa ially
suppo ed
by
he
CAICYT
g an
2196/84
o
he
Spanish
Go e n-
men .
ob ained
om
a
codebook
o
mul i
pu
lse
like
sequences
,
ha
is
,
only
ew
alues
o
hese
sequences
a e
di e en
o
m
ze o.
Each
sequence
is
mul
i pl
ied
by a
polynomial
weigh ing
un
c ion
whose
coe ici.en s
a e
es ima ed
i n
o de
o
mlnimlze
a
quad a ic
e o
be ween
he
p edic ion
e o
and
he
unc
ion
i sel .
This
unc
ion
is
calcula ed
e e y
5ms
and
discon inui ies
be ween
ames
a ec s
he
qual
i y
o
he
sy
n h
esized
signal.
T
e
en elo
pe
o
he
esidual
s
ignal,
is
an
associa ed
unc ion
which
p ese es
he
a
bo e
men
ioned
ime
e olu
ion
ea u es
o
he
esidual:
pi ch
and
e
ne~gy
.
This
unc ion
possesses
ano he
impo an
ad an age:
he
posi i e
cha ac e
o
he
en elope
allows
o
ob a
in
a
pa
ame
ic
e s
ion
o
he
en
elo
pe,
wi h
a
conside able
da a
educ ion
in
i s
ep esen a
ion.
In
his
pape
l-e
in onna ion
o
he
en elope
is
used
in
wo
di e en
applica ions
in
speech
coding.
Fi s ,
is
p esen ed
how
he
en
el
ope
o
h
e
esidual
can
help
o
quan ize
p ope ly
he
p edic ion
e o
in
an
ADPCM
sys em.
Ene gy
in o ma ion
de i ed
om
he
en elope
a e
used
o
con ol
he
s ep
size
o
he
quan ize
and
o
assign
bi s
dynamically.
Second,
he
en elope
o
he
esidual
is
applied
in
a
low
bi
a e
coding
sys em
whe e
a
ime
a ying
il e
(sho
delay
il e )
is
exci ed
by
a
signal
composed
by
a
pa ame ic
e sion
o
he
en elope
o
he
esidual,
mul
ipl
ied
by
he
cos
ine
o
an
ins an aneous
phase.
lns an aneous
phase
is
chosen
om a
codebook
in
an
analys
is
by
syn
hes
is
loop
in
o
de
o
mi
n
imize
a
pe
cep
ual
we
igh
ing
e o
.