I
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Adv
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I
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Dig
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1.
I
NT
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D
UCT
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p
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as
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tellig
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AI
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ch
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ter
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s
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ar
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th
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ch
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r
eq
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ir
es
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eth
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th
at
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el
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n
ar
tific
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r
al
n
etwo
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s
(
ANNs)
,
lear
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id
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d
b
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a
co
s
t
f
u
n
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at
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e
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th
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d
if
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er
en
ce
b
etwe
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p
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ed
icte
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an
d
ac
tu
al
o
u
tco
m
es.
R
ed
u
ci
n
g
th
is
co
s
t
f
u
n
ctio
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is
ce
n
tr
al
to
im
p
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m
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d
el
ac
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.
I
n
o
th
er
w
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r
d
s
,
AI
lear
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in
g
is
th
e
co
s
t
s
tr
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f
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r
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p
tim
izin
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a
cy
cle.
T
h
u
s
,
th
e
lim
itatio
n
s
to
m
ak
in
g
th
is
co
s
t
f
u
n
ctio
n
s
m
all
ar
e
as
f
o
llo
ws
.
T
h
e
m
ai
n
p
r
o
b
lem
with
th
e
co
s
t
f
u
n
ctio
n
r
ep
r
esen
tatio
n
an
d
its
en
h
an
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m
en
t
is
th
e
d
ef
in
it
io
n
o
f
th
e
ter
m
:
th
e
h
ig
h
e
r
th
e
co
s
t
f
u
n
ctio
n
,
th
e
m
o
r
e
in
f
o
r
m
atio
n
th
e
ANN
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2
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s
tr
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ly
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o
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f
th
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co
s
t
f
u
n
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n
in
cr
ea
s
es.
AI
d
ev
elo
p
s
th
e
am
o
u
n
t
o
f
av
ail
ab
le
in
f
o
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m
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n
.
I
t
g
ets
ch
allen
g
in
g
to
in
c
r
ea
s
e
th
e
ANN
s
tr
u
ctu
r
e.
T
h
e
co
s
t
f
u
n
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s
h
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u
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d
b
e
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s
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to
h
elp
co
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p
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AI
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r
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in
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with
m
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l
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ities
.
T
h
e
f
o
ll
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w
in
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p
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in
a
c
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s
t
f
u
n
cti
o
n
[
1
]
–
[
3
]
.
Dee
p
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s
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s
u
b
s
tan
tial
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t
o
f
th
e
g
lo
b
al
m
in
im
u
m
,
th
e
c
o
s
t
f
u
n
ctio
n
f
ir
s
t
-
o
r
d
er
s
u
b
o
r
d
in
ate
is
u
s
ed
in
Mo
m
en
tu
m
,
an
d
th
e
r
esear
ch
e
r
ad
d
ed
th
e
en
tire
b
o
u
n
d
ar
y
.
Giv
en
th
e
c
o
s
t
f
u
n
ctio
n
o
f
t
h
e
f
ir
s
t
s
u
b
s
id
iar
y
,
th
e
M
o
m
en
tu
m
tech
n
iq
u
e
is
al
s
o
an
ac
ce
s
s
ib
le
s
tr
ateg
y
.
T
h
e
p
r
im
ar
y
s
u
b
o
r
d
in
ate
r
esu
lts
f
r
o
m
b
o
u
n
d
ar
y
lear
n
in
g
ca
r
r
ied
o
u
t
b
y
t
h
e
in
cr
ea
s
ed
m
o
d
el
b
o
u
n
d
ar
ies.
I
n
an
y
ca
s
e,
lear
n
in
g
ca
n
p
r
o
ce
ed
s
o
m
ewh
at
d
ep
en
d
i
n
g
o
n
th
e
n
ewly
ad
d
e
d
co
s
t
f
u
n
ctio
n
f
ir
s
t
s
u
b
s
id
iar
y
wh
ile
th
e
co
s
t
f
u
n
ctio
n
f
ir
s
t
s
u
b
o
r
d
in
ates
ar
e
ze
r
o
.
T
h
e
m
o
s
t
m
em
o
r
a
b
le
s
u
b
s
id
iar
y
o
f
th
e
co
s
t
f
u
n
ctio
n
h
as
b
ee
n
in
cl
u
d
ed
;
l
ea
r
n
in
g
c
o
n
tin
u
es
as
it
p
r
o
g
r
ess
es,
an
d
af
ter
it
is
f
in
is
h
ed
,
y
o
u
will
n
o
t
h
av
e
m
ad
e
th
e
p
r
o
g
r
ess
y
o
u
co
u
ld
r
eq
u
ir
e
to
b
e
ab
le
to
;
m
eth
o
d
s
f
o
r
ad
d
r
ess
in
g
th
is
p
r
o
b
le
m
in
clu
d
e
alter
in
g
th
e
lear
n
in
g
r
ate
an
d
in
clu
d
in
g
an
ex
tr
a
s
tep
.
T
h
e
Mo
m
en
tu
m
te
ch
n
iq
u
e
h
as
b
ee
n
g
i
v
en
v
er
s
at
ile
p
r
o
p
er
ties
.
T
h
is
is
a
s
ch
o
lar
ly
p
a
p
er
b
ased
o
n
t
h
e
Mo
m
en
t
u
m
a
p
p
r
o
ac
h
with
th
e
ex
p
a
n
s
io
n
o
f
a
v
er
s
atile
tr
ait,
wh
ich
is
a
s
tag
e
in
th
e
g
r
ea
t
n
ess
o
f
th
e
co
s
t
f
u
n
ctio
n
ch
a
n
g
es
with
its
b
o
u
n
d
ar
y
.
T
h
e
Mo
m
en
t
u
m
tech
n
i
q
u
e
f
ab
r
icate
s
a
s
tag
e
s
ize
g
iv
en
th
e
co
s
t
f
u
n
ctio
n
n
ea
r
a
p
r
ac
tical
co
s
t
f
u
n
cti
o
n
with
n
eg
lig
ib
le
wo
r
th
.
M
o
r
e
s
p
ec
if
ic
th
o
u
g
h
ts
an
d
tech
n
iq
u
es
ar
e
ca
n
v
ass
ed
f
r
o
m
to
p
to
b
o
tto
m
i
n
th
e
tex
t.
T
h
e
co
n
v
er
g
en
ce
o
f
t
h
e
b
o
u
n
d
a
r
ies
is
ch
ar
ac
ter
ized
in
th
is
tech
n
iq
u
e.
T
o
o
v
er
c
o
m
e
th
ese
lim
itatio
n
s
,
th
is
wo
r
k
p
r
o
p
o
s
es th
e
in
teg
r
atio
n
o
f
ad
ap
tiv
e
d
ig
ital f
ilter
s
in
to
d
ee
p
lear
n
in
g
ar
ch
itectu
r
es.
B
y
m
er
g
in
g
f
ilter
in
g
o
p
er
atio
n
s
with
th
e
lear
n
in
g
lay
er
s
,
th
e
m
o
d
el
lev
er
ag
es
th
e
ad
ap
tiv
e
p
r
o
p
e
r
ties
o
f
in
f
in
ite
im
p
u
ls
e
r
esp
o
n
s
e
(
I
I
R
)
an
d
f
in
ite
im
p
u
ls
e
r
esp
o
n
s
e
(
FIR)
f
ilter
s
to
ac
ce
ler
ate
tr
ain
in
g
,
m
in
im
ize
er
r
o
r
r
ate
s
,
an
d
r
ed
u
ce
co
m
p
u
tatio
n
al
b
u
r
d
e
n
.
T
h
is
in
teg
r
atio
n
all
o
ws
th
e
s
y
s
tem
to
ad
ap
ti
v
ely
ad
ju
s
t
weig
h
ts
wh
ile
p
r
eser
v
in
g
m
em
o
r
y
ef
f
icien
cy
,
o
f
f
er
in
g
a
p
r
o
m
is
in
g
d
ir
ec
tio
n
f
o
r
im
p
r
o
v
in
g
n
eu
r
al
n
etwo
r
k
p
er
f
o
r
m
an
ce
in
co
n
s
tr
ain
ed
e
n
v
ir
o
n
m
en
t
s
.
Fig
u
r
e
1
s
h
o
ws
a
s
ch
em
a
tic
d
iag
r
am
o
f
t
h
e
ad
ap
tiv
e
d
ee
p
lear
n
in
g
tech
n
i
q
u
e.
Fig
u
r
e
1
.
Sch
em
ati
c
d
iag
r
am
o
f
th
e
ad
a
p
tiv
e
d
ee
p
lear
n
in
g
t
ec
h
n
iq
u
e
Sev
er
al
o
p
tim
izatio
n
alg
o
r
ith
m
s
,
s
u
ch
as
Mo
m
en
tu
m
,
r
o
o
t
m
ea
n
s
q
u
ar
e
p
r
o
p
ag
atio
n
(
R
MSPr
o
p
)
,
an
d
Ad
am
,
h
av
e
b
ee
n
wid
ely
ad
o
p
ted
t
o
im
p
r
o
v
e
th
e
co
n
v
er
g
en
ce
p
r
o
p
e
r
ties
o
f
d
ee
p
lear
n
in
g
.
W
h
ile
th
ese
m
eth
o
d
s
ad
ju
s
t
lear
n
in
g
r
ates
ad
ap
tiv
ely
an
d
m
itig
ate
v
an
is
h
in
g
o
r
ex
p
l
o
d
in
g
g
r
ad
ien
ts
,
th
ey
d
o
n
o
t
d
ir
ec
tly
ad
d
r
ess
th
e
s
tr
u
ct
u
r
al
in
e
f
f
ici
en
cies
o
f
n
eu
r
al
n
etwo
r
k
s
,
s
u
ch
as
r
e
d
u
n
d
an
t
weig
h
ts
an
d
h
ig
h
f
ilter
o
r
d
e
r
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ad
v
Ap
p
l Sci
I
SS
N:
2252
-
8
8
1
4
I
n
crea
s
in
g
th
e
efficien
cy
o
f
d
e
ep
lea
r
n
in
g
p
erfo
r
ma
n
ce
u
s
in
g
a
d
a
p
tive
filt
ers
(
S
u
a
d
K
h
a
ir
i Mo
h
a
mme
d
)
777
Mo
r
eo
v
er
,
th
e
in
teg
r
atio
n
o
f
a
d
ap
tiv
e
d
ig
ital
f
ilter
s
,
w
h
ich
a
r
e
well
estab
lis
h
ed
i
n
s
ig
n
al
p
r
o
ce
s
s
in
g
f
o
r
t
h
eir
ab
ilit
y
to
m
an
ag
e
d
y
n
am
ic
in
p
u
ts
with
m
in
im
al
r
eso
u
r
ce
s
,
h
as
n
o
t
b
ee
n
s
u
f
f
icien
tly
ex
p
l
o
r
ed
in
d
ee
p
lear
n
in
g
f
r
am
ewo
r
k
s
.
T
h
is
g
a
p
m
o
ti
v
ates
th
e
in
v
esti
g
atio
n
o
f
h
y
b
r
id
ar
ch
itectu
r
es
th
at
co
m
b
in
e
th
e
lear
n
in
g
ca
p
ab
ilit
ies o
f
n
eu
r
al
n
etwo
r
k
s
with
th
e
ef
f
icien
cy
o
f
ad
a
p
tiv
e
f
ilter
s
.
T
o
ad
d
r
ess
th
ese
lim
itatio
n
s
,
t
h
is
s
tu
d
y
in
tr
o
d
u
ce
s
a
h
y
b
r
id
f
r
am
ewo
r
k
th
at
m
er
g
es
ad
ap
tiv
e
d
ig
ital
f
ilter
s
with
d
ee
p
lear
n
in
g
m
o
d
els.
B
y
em
b
e
d
d
in
g
f
ilter
o
p
e
r
atio
n
s
in
to
th
e
n
etwo
r
k
ar
ch
i
tectu
r
e,
th
e
s
y
s
tem
ac
h
iev
es
ac
ce
ler
ated
tr
ain
in
g
,
r
ed
u
ce
d
e
r
r
o
r
r
ates,
an
d
lo
wer
co
m
p
u
tatio
n
al
b
u
r
d
en
,
wh
ile
m
ain
tain
in
g
m
o
d
el
ac
cu
r
ac
y
.
T
h
e
a
d
ap
tiv
e
b
e
h
av
i
o
r
o
f
th
e
f
ilter
s
en
ab
les
ef
f
icie
n
t
weig
h
t
ad
ju
s
tm
en
t
an
d
im
p
r
o
v
ed
u
tili
za
tio
n
o
f
m
em
o
r
y
r
eso
u
r
ce
s
,
m
ak
in
g
th
em
well
-
s
u
ited
f
o
r
en
v
ir
o
n
m
e
n
ts
with
lim
ited
h
ar
d
war
e
ca
p
ab
ilit
ies.
T
h
e
m
ain
co
n
tr
ib
u
tio
n
s
o
f
th
is
p
a
p
er
ca
n
b
e
s
u
m
m
ar
ized
:
i)
A
n
o
v
el
h
y
b
r
id
f
r
a
m
ewo
r
k
is
p
r
o
p
o
s
ed
th
at
i
n
teg
r
ates
ad
a
p
tiv
e
I
I
R
d
ig
ital
f
ilter
s
with
d
ee
p
lear
n
in
g
m
o
d
els to
en
h
a
n
ce
ef
f
icie
n
cy
an
d
r
ed
u
ce
weig
h
t c
o
m
p
lex
ity
.
ii)
T
h
e
p
r
o
p
o
s
ed
ar
c
h
itectu
r
e
is
d
esig
n
ed
an
d
im
p
lem
e
n
ted
u
s
in
g
MA
T
L
AB
/
Simu
lin
k
,
with
d
etailed
v
alid
atio
n
p
r
o
v
id
e
d
th
r
o
u
g
h
s
im
u
latio
n
ex
p
er
im
en
ts
.
iii)
T
h
e
p
er
f
o
r
m
an
ce
o
f
th
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
is
co
m
p
ar
e
d
ag
a
in
s
t
co
n
v
en
tio
n
al
FIR
an
d
I
I
R
d
ig
ital
f
ilter
s
,
d
em
o
n
s
tr
atin
g
im
p
r
o
v
em
en
ts
i
n
m
ea
n
s
q
u
a
r
e
er
r
o
r
(
MSE
)
,
ef
f
icien
cy
,
an
d
weig
h
t r
e
d
u
ctio
n
.
iv
)
T
h
e
p
r
ac
tical
im
p
licatio
n
s
o
f
th
e
m
o
d
el
a
r
e
an
aly
ze
d
f
o
r
r
ea
l
-
wo
r
l
d
ap
p
licatio
n
s
s
u
ch
as
s
ig
n
al
p
r
o
ce
s
s
in
g
,
I
o
T
d
ev
ices,
a
n
d
r
eso
u
r
ce
-
lim
ited
em
b
e
d
d
ed
AI
s
y
s
tem
s
.
2.
DIGIT
AL
F
I
L
T
E
R
S ID
E
AS
T
h
e
p
r
i
n
cip
al
p
iece
o
f
an
y
co
r
r
esp
o
n
d
en
ce
s
y
s
tem
is
s
i
g
n
al
h
a
n
d
lin
g
.
Dea
lin
g
with
th
is
is
an
u
n
q
u
esti
o
n
a
b
le
n
ee
d
to
av
o
id
u
n
f
o
r
t
u
n
ate
s
ig
n
s
.
I
n
f
o
r
m
ati
o
n
ca
n
b
e
d
ea
lt
with
th
r
o
u
g
h
s
ig
n
al
-
tak
in
g
ca
r
e,
b
o
th
s
tr
aig
h
tf
o
r
wa
r
d
an
d
d
i
g
i
tal.
Mo
r
e
u
n
m
is
tak
ab
le
f
lex
i
b
ilit
y
an
d
b
etter
p
r
ec
is
io
n
co
n
tr
o
l
ar
e
g
iv
en
b
y
s
tate
-
of
-
th
e
-
ar
t sig
n
als th
at
s
tan
d
ap
ar
t
f
r
o
m
ess
en
tial sig
n
m
an
ag
em
en
t.
Fil
ter
s
ar
e
u
s
ed
to
co
p
e
with
th
e
s
ig
n
.
W
h
en
it
co
m
es
to
h
a
n
d
lin
g
c
r
u
d
e
in
d
icato
r
s
,
d
i
g
ital
f
ilter
s
ar
e
cr
u
cial.
Dig
ital
s
ig
n
s
ar
e
s
tr
u
ctu
r
es
th
at
u
s
e
m
ath
em
atica
l
co
m
p
u
tatio
n
s
to
alter
a
ce
r
tain
q
u
ality
o
f
a
n
ex
am
in
e
d
,
d
is
cr
ete
-
tim
e
s
i
g
n
al
[
4
]
.
T
h
e
r
e
ar
e
n
u
m
er
o
u
s
leg
itima
te
way
s
to
a
s
s
es
s
a
d
ig
ital c
h
an
n
el'
s
p
o
ten
tial.
Fu
r
th
er
m
o
r
e
,
p
lan
s
m
ay
i
n
clu
d
e
a
v
ar
iety
o
f
d
is
ce
r
n
in
g
s
tr
ateg
ies.
T
h
ese
tech
n
iq
u
es
ar
e
al
way
s
u
s
ed
as
th
e
b
asis
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o
r
ch
an
n
el
d
et
ail
.
T
h
e
s
im
p
lest
m
eth
o
d
f
o
r
d
ea
lin
g
with
f
ilter
s
is
to
f
ig
u
r
e
o
u
t
h
o
w
th
ey
wo
u
ld
r
esp
o
n
d
to
o
b
v
io
u
s
en
tr
ies,
s
u
ch
as
in
s
p
ir
atio
n
.
B
y
co
m
b
in
in
g
o
n
e
d
ata
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et
with
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o
th
er
,
th
e
ch
a
n
n
el'
s
r
esp
o
n
s
e
ca
n
th
en
b
e
in
f
er
r
e
d
f
r
o
m
o
th
e
r
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m
p
o
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ite
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icato
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s
.
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y
co
m
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i
n
in
g
o
n
e
d
ata
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et
with
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o
th
er
,
th
e
ch
an
n
el'
s
r
esp
o
n
s
e
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n
th
en
b
e
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er
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ed
f
r
o
m
o
th
e
r
co
m
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o
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ite
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icato
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s
.
I
n
th
is
au
d
it,
v
ar
io
u
s
f
ilter
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u
ch
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ass
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ass
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ig
h
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p
ass
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ilter
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h
av
e
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ee
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u
s
ed
to
in
s
p
ec
t th
e
ex
ec
u
tio
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o
f
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ig
ital c
h
an
n
els.
At
th
e
ch
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n
el
r
esu
lts
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e
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o
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s
es o
f
v
ar
io
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s
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ig
ital f
ilter
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to
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o
r
th
r
ee
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ted
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o
u
n
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ig
n
als
wer
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s
er
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ed
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lo
t
ted
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d
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lay
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m
en
tio
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e
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r
ev
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o
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s
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ec
tio
n
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is
s
tu
d
y
aim
s
to
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et
er
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in
e
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eth
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ig
ital
f
ilter
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ar
e
m
o
r
e
e
f
f
ec
ti
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e.
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o
ac
co
m
p
lis
h
th
is
g
o
al,
th
e
v
ar
io
u
s
lim
its
o
f
d
i
g
ital
f
ilter
s
ar
e
an
ticip
ated
to
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e
o
p
tim
ized
to
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h
ig
h
d
eg
r
ee
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im
its
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s
u
ch
as
s
tag
e
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ea
ctio
n
,
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u
n
ch
d
elay
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r
iv
e
r
ea
ctio
n
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o
s
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lo
ts
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s
ize
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ea
ctio
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,
s
tag
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d
ef
e
r
r
al,
a
n
d
s
tep
r
ea
ctio
n
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h
a
v
e
s
im
p
li
f
ied
th
e
r
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lts
an
d
id
en
tifie
d
th
e
m
o
s
t
co
m
m
o
n
co
n
clu
s
io
n
.
T
h
e
I
I
R
B
u
tter
wo
r
t
h
ch
an
n
el
was
u
s
ed
to
g
et
a
n
o
v
er
p
o
wer
in
g
o
u
tco
m
e.
W
h
e
n
n
ar
r
o
win
g
an
d
s
tag
e
r
ea
cti
o
n
ar
e
co
m
b
in
ed
,
B
u
tter
wo
r
t
h
f
ilter
s
ar
e
cr
ea
ted
.
B
ec
au
s
e
th
er
e
is
n
o
s
tr
ea
m
in
th
e
p
ass
an
d
s
to
p
g
ath
er
in
g
s
,
t
h
is
is
o
cc
asio
n
ally
r
ec
o
m
m
en
d
ed
as
a
m
ax
im
ally
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el
ch
an
n
el.
T
h
e
B
u
tter
wo
r
th
ch
a
n
n
el
h
as
a
p
r
etty
ex
ten
s
iv
e
im
p
r
o
v
em
e
n
t
f
r
ag
m
e
n
t
to
r
ea
c
h
its
lev
el
f
r
o
m
th
e
p
ass
b
an
d
to
th
e
s
to
p
b
an
d
.
T
h
e
B
u
tter
wo
r
th
ch
a
n
n
el
f
r
a
m
ewo
r
k
ass
ess
m
en
ts
ar
e
m
o
r
e
p
r
o
m
in
e
n
t
an
d
less
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itical
th
an
o
th
er
ch
an
n
el
ty
p
es.
I
t
is
im
p
o
s
s
ib
le
to
co
m
p
ar
e
B
u
tter
wo
r
th
f
ilter
s
'
tr
an
s
ien
t
an
d
ad
eq
u
ac
y
p
r
o
p
er
ties
[
4
]
.
I
n
co
r
p
o
r
atin
g
t
h
ese
p
lan
n
ed
r
ed
ir
ec
tio
n
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in
to
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tu
al
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d
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en
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icial
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ec
u
tio
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is
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o
th
er
cr
u
cial
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alu
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c
o
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ce
r
n
.
All
th
e
p
r
o
p
ag
atio
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s
with
r
esu
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o
r
t
esti
n
g
d
if
f
er
e
n
t
cu
to
f
f
p
o
in
ts
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av
e
b
ee
n
b
r
o
k
e
n
d
o
wn
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d
u
p
h
eld
u
s
in
g
th
e
f
ilter
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esig
n
an
d
an
aly
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is
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FDA
)
d
ev
ice
in
MA
T
L
AB
.
A
p
r
ac
tical
d
ev
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f
o
r
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ep
ar
atin
g
s
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u
n
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ig
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als
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ted
.
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tio
n
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o
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s
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o
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th
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tim
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-
in
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ar
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T
I
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d
ir
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t
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in
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ia
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f
ilter
s
.
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ilter
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p
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d
th
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co
ef
f
icien
ts
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em
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c
o
n
s
tan
t
o
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tim
e.
T
im
e
-
s
h
if
tin
g
an
d
ad
ap
tab
le
f
ilter
s
ar
e
co
n
s
id
er
ed
in
th
e
f
o
llo
win
g
s
eg
m
en
ts
.
T
h
e
f
ilter
c
o
r
r
elat
io
n
b
etwe
e
n
th
e
en
ter
e
d
a
n
d
r
esu
lts
o
v
er
tim
e
ca
n
b
e
s
h
o
wn
u
s
in
g
th
e
ap
p
r
o
ac
h
in
g
tim
e
o
r
r
ec
u
r
r
en
ce
ar
ea
ap
p
r
o
ac
h
es
[
5
]
–
[
1
0
]
.
Usi
n
g
a
weig
h
ted
m
i
x
tu
r
e
o
f
th
e
d
ata
a
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p
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test
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th
e
d
if
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er
en
tiatio
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co
n
d
itio
n
illu
s
tr
ates
th
e
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f
ec
t
o
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a
d
is
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ete
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tim
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ilter
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F
o
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s
tan
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th
e
(
1
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m
ay
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e
th
e
d
is
tin
g
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h
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c
o
n
d
itio
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f
o
r
a
f
ir
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-
r
eq
u
est f
ilter
.
(
)
=
.
(
−
1
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+
(
)
(
1
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2
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1
5
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2
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I
n
th
is
ca
s
e,
th
e
f
ilter
'
s
r
esu
lt
i
s
(
)
an
d
th
e
f
ilter
p
ar
a
m
eter
s
o
f
th
e
f
ilter
-
in
p
u
t
s
am
p
les
ar
e
(
)
.
T
h
e
ac
tiv
ity
o
f
im
p
u
ls
e.
I
t
ca
n
b
e
d
e
p
icted
b
y
h
o
w
th
e
f
ilter
r
esp
o
n
d
s
to
an
im
p
u
ls
e
p
ie
ce
o
f
in
f
o
r
m
atio
n
.
I
n
s
am
p
les in
s
tan
t a
t
=
0
,
f
o
r
in
s
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ce
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th
e
f
ee
d
b
ac
k
th
at
th
e
f
ilte
r
f
r
o
m
co
n
d
itio
n
(
1
)
to
an
im
p
u
ls
e
in
p
u
t is
s
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o
wn
in
(
2
)
.
(
)
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(
2
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Als
o
,
f
o
r
=
0
,
1
,
2
,
3
,
…
4
,
let
(
−
1
)
=
0
,
an
d
(
)
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=
1
,
,
2
,
3
,
4
.
T
h
e
im
p
u
ls
e
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ctio
n
ad
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e
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t
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n
s
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tes
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e
s
ig
n
to
ad
d
r
ess
th
e
r
esp
o
n
s
e
o
f
a
d
ir
ec
t
f
ilter
to
a
wav
ef
o
r
m
.
T
h
e
in
f
o
b
ea
t
e
n
er
g
izes
th
e
f
ilter
at
ea
ch
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ec
u
r
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r
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F
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t
h
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elate
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tr
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s
f
er
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u
n
ctio
n
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s
ze
r
o
s
an
d
p
o
les.
T
h
e
r
atio
o
f
th
e
i
n
f
o
r
m
atio
n
p
r
o
d
u
ce
d
b
y
th
e
r
ela
tio
n
to
th
e
ch
an
g
es
o
f
th
e
c
h
an
n
el
s
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r
e
is
th
e
ex
ch
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g
e
p
o
wer
o
f
a
co
m
p
u
ter
c
h
an
n
el,
o
r
(
)
as in
(
3
)
.
(
)
=
(
)
(
)
(
3
)
Fo
r
ex
am
p
le,
t
h
e
tr
an
s
f
er
f
u
n
c
tio
n
o
f
a
f
ir
s
t
-
o
r
d
e
r
d
ig
ital f
ilt
er
is
d
eter
m
in
ed
as
in
(
4
)
.
(
)
=
−
−
1
(
4
)
A
v
al
u
ab
le
to
o
l
f
o
r
d
eter
m
i
n
in
g
a
f
ilter
'
s
b
eh
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io
r
is
its
p
o
le
-
ze
r
o
r
ep
r
esen
tatio
n
.
As
s
tated
in
s
eg
m
en
t,
th
e
X
p
o
les
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d
ze
r
o
s
s
er
v
e
as
th
e
f
u
n
d
am
en
tal
b
ases
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o
r
th
e
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en
o
m
in
ato
r
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d
n
u
m
er
ato
r
o
f
th
e
tr
an
s
f
er
f
u
n
ctio
n
,
r
esp
ec
tiv
ely
.
T
h
e
r
ec
u
r
r
e
n
ce
r
ea
ctio
n
o
f
a
f
ilter
d
em
o
n
s
tr
ates h
o
w
it a
lter
s
th
e
s
u
f
f
icien
cy
o
f
th
e
en
ter
e
d
wav
ef
o
r
m
'
s
r
ep
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ts
with
a
p
e
r
io
d
.
On
e
m
ig
h
t
d
eter
m
in
e
a
f
ilter
'
s
r
ep
ea
t
r
ea
ctio
n
as
f
o
llo
ws
b
y
ap
p
ly
in
g
th
e
Fo
u
r
ier
tr
an
s
f
o
r
m
o
n
th
e
f
ilter
'
s
im
p
u
ls
e
r
ea
ct
io
n
o
r
b
y
ess
en
tially
s
u
b
s
titu
tin
g
th
e
r
e
p
lace
m
en
t
v
ar
iab
le
ej
ω
f
o
r
th
e
z
v
ar
iab
le
z
=
ej
ω
in
th
e
z
-
tr
an
s
f
er
f
u
n
ctio
n
as
in
(
5
)
.
T
h
u
s
,
th
e
co
n
s
tr
u
ctio
n
d
ia
g
r
a
m
o
f
th
e
d
ir
ec
t
-
f
o
r
m
FIR
f
ilter
is
p
r
esen
ted
in
Fig
u
r
e
2
[
1
1
]
–
[
2
4
]
.
Ad
d
itio
n
ally
,
t
h
e
in
ter
n
al
s
tr
u
ctu
r
e
d
iag
r
a
m
o
f
a
tim
e
-
in
v
ar
ian
t f
ilter
,
w
h
ich
is
g
iv
en
b
y
(
1
)
,
is
s
h
o
wn
in
Fig
u
r
e
3
[
1
2
]
.
(
)
=
(
)
(
)
(
5
)
A
p
o
ly
n
o
m
ial
r
atio
in
th
e
v
a
r
iab
le
co
u
ld
b
e
u
s
ed
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ca
s
ca
d
e
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o
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m
at
r
ep
r
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tatio
n
o
f
th
e
f
ilter
tr
an
s
f
er
f
u
n
ctio
n
in
r
elatio
n
(
6
)
.
(
)
=
1
(
)
2
(
)
(
6
)
Su
ch
th
at
ev
e
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y
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ze
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o
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a
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er
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ee
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f
ilter
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e
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p
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ess
ed
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)
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n
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ld
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e
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ep
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ted
as in
(
7
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.
1
(
)
=
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(
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Fu
r
th
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o
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e
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s
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e
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ec
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iv
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ilter
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ig
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t b
e
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eter
m
in
ed
as in
(
8
)
.
2
(
)
=
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1
−
∑
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=
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(
8
)
Fig
u
r
e
2
.
C
o
n
s
tr
u
ctio
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d
iag
r
a
m
o
f
th
e
FIR f
ilter
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ad
v
Ap
p
l Sci
I
SS
N:
2252
-
8
8
1
4
I
n
crea
s
in
g
th
e
efficien
cy
o
f
d
e
ep
lea
r
n
in
g
p
erfo
r
ma
n
ce
u
s
in
g
a
d
a
p
tive
filt
ers
(
S
u
a
d
K
h
a
ir
i Mo
h
a
mme
d
)
779
Fig
u
r
e
3
.
C
o
n
s
tr
u
ctio
n
d
iag
r
a
m
o
f
th
e
p
o
le
-
ze
r
o
I
I
R
f
ilter
3.
DE
E
P
L
E
A
RNING
T
E
CH
N
I
Q
UE
S
On
e
o
f
th
e
p
r
in
cip
le
s
th
at
co
n
ce
n
tr
ates
o
n
d
is
tin
g
u
is
h
in
g
co
u
n
ter
f
eit
p
ictu
r
es
u
tili
zin
g
AI
was
d
ir
ec
ted
b
y
s
cien
tis
ts
;
th
ey
r
ec
o
m
m
en
d
e
d
a
f
ac
tu
al
m
eth
o
d
o
l
o
g
y
f
o
r
d
ig
ital
p
ictu
r
e
f
r
au
d
a
ck
n
o
wled
g
m
en
t
b
y
b
r
ea
k
in
g
d
o
wn
d
is
p
ar
ities
in
im
ag
e
q
u
alities
.
Sin
ce
th
en
,
o
t
h
er
AI
-
b
ased
tech
n
iq
u
es,
in
cl
u
d
in
g
d
ee
p
lear
n
in
g
s
ch
em
es
lik
e
r
ec
u
r
r
en
t
n
eu
r
al
n
etwo
r
k
s
(
R
NNs),
h
av
e
b
ee
n
d
ev
elo
p
ed
to
r
ep
licate
f
ak
e
im
ag
es.
As
s
ee
n
i
n
Fig
u
r
e
4
[
1
4
]
–
[
2
8
]
,
a
f
ee
d
-
f
o
r
war
d
ce
r
eb
r
u
m
n
etwo
r
k
with
at
least
o
n
e
h
id
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e
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lay
er
a
n
d
a
f
ee
d
b
ac
k
cir
cle
is
a
d
is
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n
tin
u
o
u
s
n
etwo
r
k
.
Fig
u
r
e
4
.
A
f
ee
d
-
f
o
r
war
d
R
N
N
n
etwo
r
k
with
in
ter
n
al
lay
er
s
As
d
is
p
lay
ed
in
Fig
u
r
e
4
,
th
e
f
ee
d
b
ac
k
m
ig
h
t
b
e
au
to
n
o
m
ic,
th
at
is
,
t
h
e
co
n
s
eq
u
en
ce
o
f
th
e
ac
tiv
ity
o
f
th
e
s
till
u
n
k
n
o
wn
b
y
its
tech
n
iq
u
e
f
o
r
p
r
ep
ar
in
g
.
T
h
e
f
ee
d
b
ac
k
cir
cu
its
in
clu
d
e
th
e
u
tili
za
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n
o
f
p
o
s
tp
o
n
ed
u
n
it
p
ar
ts
in
a
f
ew
lo
ca
les,
p
r
o
m
p
tin
g
a
n
o
n
-
s
tr
aig
h
t,
u
n
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e
way
o
f
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n
d
u
ct,
as
a
b
r
illi
a
n
t
f
r
am
ewo
r
k
wo
u
ld
b
e
s
u
p
p
o
s
ed
to
h
a
v
e
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o
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t
u
n
its
.
Dif
f
er
en
t
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o
r
ts
m
ig
h
t
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o
n
tr
ast
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th
e
te
ch
n
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e
o
f
in
war
d
co
n
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tin
g
.
Ho
wev
er
,
th
e
y
ac
co
m
p
lis
h
a
s
im
ilar
o
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jectiv
e
an
d
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h
iev
e
a
s
im
ilar
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u
tc
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m
e,
wh
ich
is
ap
p
ly
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g
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eiter
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n
.
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ce
R
NNs
h
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e
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ter
n
al
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em
o
r
y
,
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ey
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o
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ld
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l
with
en
ter
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eq
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en
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s
o
f
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ar
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le
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th
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n
d
s
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ld
ly
elem
en
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.
R
eg
ar
d
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g
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e
R
NN
alg
o
r
ith
m
'
s
s
tr
u
ctu
r
e
s
h
o
wn
in
Fig
u
r
e
4
,
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n
e
m
ay
id
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tify
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e
r
ec
u
r
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an
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tim
estam
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as
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lts
,
′
.
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af
ter
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ar
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Xt
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:
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.
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e
n
etwo
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th
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ter
ed
s
am
p
les,
tim
estam
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estam
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,
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ec
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r
s
iv
ely
.
W
ith
th
e
ac
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f
u
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et
t
o
ta
n
h
an
d
th
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e
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ter
ed
s
eq
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e
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ce
xt
−
1
o
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th
e
r
ec
u
r
r
en
t
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n
it
ot
−
2
ap
p
lied
,
t
h
e
r
esu
ltan
t
v
ec
to
r
x
′
t
is
ca
lcu
l
ated
u
s
in
g
(
9
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
8
1
4
I
n
t J Ad
v
Ap
p
l Sci
,
Vo
l.
1
5
,
No
.
2
,
J
u
n
e
2
0
2
6
:
7
7
5
-
789
780
′
=
(
′
,
−
1
+
′
)
,
−
1
=
ℎ
(
.
−
1
+
.
−
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+
ℎ
)
(
9
)
W
h
er
e
′
,
,
,
an
d
ar
e
n
etwo
r
k
co
m
p
o
n
e
n
ts
ar
e
ac
h
iev
ed
with
r
ep
etitio
n
wh
en
th
e
n
etwo
r
k
u
s
es
th
e
tr
ain
in
g
r
esu
lts
to
co
m
p
a
r
e
w
ith
th
e
in
p
u
ts
to
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em
em
b
e
r
w
h
at
it
h
as
lear
n
ed
alo
n
g
th
e
p
r
ev
io
u
s
s
tep
s
.
T
h
is
m
ea
n
s
th
at
th
e
n
etwo
r
k
lear
n
s
in
th
e
lo
n
g
ter
m
th
r
o
u
g
h
s
h
o
r
t
-
ter
m
p
r
e
d
ictio
n
s
[
7
]
–
[
1
0
]
,
[
1
3
]
.
4.
RE
L
AT
E
D
S
T
UDI
E
S
Star
tin
g
f
r
o
m
th
e
p
r
esen
tatio
n
o
f
AI
,
ANN
h
a
v
e
b
ee
n
o
n
a
m
eteo
r
ic
ascen
t
[
4
]
.
E
m
er
g
in
g
n
eu
r
al
s
tr
u
ctu
r
es,
p
r
e
p
ar
in
g
s
y
s
tem
s
,
an
d
g
i
g
an
tic
in
f
o
r
m
atio
n
a
u
th
o
r
ities
co
n
s
tan
tly
p
u
s
h
th
e
b
est
in
class
in
n
u
m
er
o
u
s
ap
p
licatio
n
s
in
d
ee
p
lear
n
in
g
o
f
c
o
m
p
licated
m
o
d
els.
T
h
ese
ar
e
p
r
esen
tly
,
to
s
o
m
e
d
eg
r
ee
,
cr
ed
ited
to
q
u
ick
ad
v
a
n
ce
m
en
ts
in
th
ese
p
r
o
ce
d
u
r
es
a
n
d
h
ar
d
war
e
in
n
o
v
atio
n
.
No
n
et
h
eless
,
th
e
in
v
esti
g
atio
n
o
f
ANN
r
u
d
im
en
ts
d
o
es
n
o
t
f
o
llo
w
s
im
ilar
n
etwo
r
k
s
[
5
]
.
O
n
e
o
f
t
h
e
m
o
s
t
well
-
k
n
o
wn
ANN
d
esig
n
s
f
o
r
th
e
PC
m
o
d
el
is
a
lack
o
f
p
er
ce
p
tio
n
o
f
its
f
u
n
d
am
e
n
tal
s
u
b
tleties
d
u
e
to
s
p
ec
if
ic
f
ascin
atin
g
,
u
n
ex
p
lain
ab
le
p
ec
u
liar
ities
to
b
e
n
o
ted
.
T
ests
h
av
e
s
h
o
wn
t
h
at
m
in
o
r
i
n
f
o
r
m
atio
n
ch
a
n
g
e
s
ca
n
in
f
lu
en
ce
e
x
ec
u
tio
n
,
a
p
h
en
o
m
e
n
o
n
k
n
o
wn
as
ill
-
d
is
p
o
s
ed
m
o
d
els
[
7
]
.
I
t
i
s
p
lau
s
ib
le
th
at
p
o
r
tr
ay
als
ar
e
u
n
id
en
tifia
b
le.
Ho
wev
e
r
,
c
o
n
v
o
lu
tio
n
al
n
etwo
r
k
s
em
p
h
atica
lly
ac
ce
p
t
th
at
th
er
e
ar
e
th
in
g
s
.
T
h
ese
h
az
ar
d
s
co
m
p
el
r
esear
ch
o
n
n
e
u
r
al
n
etwo
r
k
ac
tiv
ity
an
d
n
etwo
r
k
u
p
g
r
a
d
es,
f
o
r
ex
am
p
le,
im
p
r
o
v
e
d
n
e
u
r
o
n
in
tr
o
d
u
c
tio
n
,
b
u
ild
i
n
g
d
esig
n
s
ea
r
ch
,
an
d
f
itti
n
g
c
y
cles.
AI
[
8
]
will
b
en
ef
it
f
r
o
m
e
f
f
o
r
ts
to
co
m
p
r
eh
en
d
th
e
p
r
o
p
er
ties
o
f
in
tellig
en
t
alg
o
r
ith
m
s
an
d
d
e
v
elo
p
m
o
r
e
p
r
ec
is
e
an
d
tr
u
s
two
r
th
y
m
o
d
els.
As
a
r
esu
lt,
th
e
s
tu
d
y
o
f
ANN
s
i
s
ar
g
u
ab
ly
th
e
m
o
s
t
r
ec
en
t
ar
ea
o
f
k
n
o
wled
g
e.
I
t
also
d
e
v
elo
p
s
i
n
to
leg
itima
te
m
u
ltid
is
cip
lin
ar
y
r
esear
ch
th
at
b
r
in
g
s
to
g
eth
e
r
ex
p
e
r
ts
,
s
o
f
twar
e
en
g
in
ee
r
s
,
b
io
l
o
g
is
ts
,
m
ath
em
atician
s
,
an
d
p
h
y
s
icis
ts
.
So
m
e
o
f
th
e
o
d
d
b
eh
av
io
r
s
o
f
AN
Ns
wer
e
co
n
s
is
ten
t
wit
h
n
o
is
y
f
r
am
es,
wh
ich
wer
e
g
en
er
ally
v
er
y
s
en
s
itiv
e,
n
o
n
lin
ea
r
,
an
d
h
ar
d
to
p
r
ed
ict.
An
aly
zin
g
th
e
m
an
y
n
etwo
r
k
s
co
n
n
ec
ted
b
y
th
e
n
eu
r
al
n
etwo
r
k
,
t
h
e
co
n
f
o
u
n
d
in
g
cy
cles,
a
n
d
th
ei
r
co
n
n
e
ctio
n
s
to
th
e
o
t
h
er
n
etwo
r
k
s
,
s
u
ch
as
th
e
v
ar
io
u
s
n
etwo
r
k
s
,
is
th
e
f
u
n
d
a
m
en
tal
d
esig
n
o
f
co
m
p
lex
n
etwo
r
k
s
(
C
N)
.
Fo
r
ex
am
p
le,
th
e
n
eu
r
al
n
etwo
r
k
o
f
th
e
C
a
en
o
r
h
a
b
d
itis
eleg
a
n
s
wo
r
m
h
as
b
ee
n
d
em
o
n
s
tr
ated
to
e
x
h
i
b
it
th
e
litt
le
wo
r
ld
C
.
N.
p
h
en
o
m
en
a
[
7
]
.
T
h
e
av
er
ag
e
r
eticu
lar
im
p
r
o
v
em
e
n
t
o
f
th
e
ce
r
eb
r
u
m
s
tem
[
2
0
]
,
c
o
r
tical
ass
o
ciatio
n
ex
am
in
atio
n
s
[
1
9
]
,
an
d
en
ce
p
h
alo
g
r
a
p
h
y
ac
co
u
n
ts
[
8
]
ar
e
ex
am
p
les
o
f
co
m
p
ar
ativ
e
to
p
o
lo
g
ical
q
u
alities
o
b
s
er
v
ed
in
h
u
m
an
m
in
d
n
etw
o
r
k
s
.
N
u
m
e
r
o
u
s
a
p
p
r
o
a
c
h
e
s
h
av
e
b
e
e
n
u
s
e
d
to
w
o
r
k
o
n
t
h
e
in
i
t
i
al
g
r
ad
i
e
n
t
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1
2
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4
.
1
.
Co
ntr
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f
t
he
s
t
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T
h
is
s
tu
d
y
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th
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f
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lear
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r
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f
r
am
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k
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ap
tiv
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I
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d
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f
ilter
s
in
to
n
eu
r
al
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etwo
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k
ar
ch
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p
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id
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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v
Ap
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I
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N:
2252
-
8
8
1
4
I
n
crea
s
in
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th
e
efficien
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d
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in
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p
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p
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filt
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(
S
u
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mme
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5.
M
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tag
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,
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iii)
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