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n
ce
o
f
lo
o
k
-
up
-
tab
le
(
L
UT
)
-
ac
ce
s
s
e
s
f
o
llo
w
ed
b
y
s
h
i
f
t
ac
c
u
m
u
la
tio
n
o
p
er
atio
n
s
o
f
t
h
e
L
UT
o
u
tp
u
t.
DA
-
b
ased
co
m
p
u
tatio
n
is
well
-
s
u
ited
f
o
r
FP
G
A
r
ea
lizati
o
n
,
b
ec
au
s
e
t
h
e
L
UT
as
w
e
ll
as
t
h
e
s
h
i
f
t
-
ad
d
o
p
er
atio
n
s
ca
n
b
e
ef
f
icien
tl
y
m
ap
p
ed
to
th
e
L
UT
-
b
ased
FP
GA
lo
g
ic
s
tr
u
ct
u
r
es.
I
n
FIR
f
il
ter
in
g
,
o
n
e
co
n
v
o
l
v
in
g
s
eq
u
en
ce
is
o
b
tain
ed
f
r
o
m
t
h
e
in
p
u
t
s
a
m
p
les
w
h
i
le
th
e
o
th
er
s
eq
u
en
ce
f
r
o
m
t
h
e
f
ix
ed
i
m
p
u
ls
e
r
e
s
p
o
n
s
e
co
e
f
f
icien
ts
o
f
th
e
f
ilter
.
T
h
is
b
eh
a
v
io
r
o
f
FIR
f
ilter
m
a
k
es
it
p
o
s
s
ib
le
to
u
s
e
D
A
-
b
ased
tec
h
n
iq
u
e
f
o
r
m
e
m
o
r
y
-
b
ased
r
ea
lizatio
n
.
I
t
y
ield
s
f
a
s
ter
o
u
tp
u
t
co
m
p
ar
ed
w
it
h
t
h
e
m
u
ltip
lier
-
ac
c
u
m
u
lato
r
-
b
ased
d
esig
n
s
b
ec
au
s
e
i
t
s
to
r
es
t
h
e
p
r
e
-
co
m
p
u
ted
p
ar
tial
r
esu
lts
i
n
t
h
e
m
e
m
o
r
y
ele
m
e
n
ts
[
8
]
,
w
h
ic
h
ca
n
b
e
r
ea
d
o
u
t a
n
d
ac
cu
m
u
lated
to
o
b
tain
t
h
e
d
esire
d
r
esu
l
t.
T
h
e
m
e
m
o
r
y
r
eq
u
ir
e
m
e
n
t o
f
DA
-
b
ased
i
m
p
le
m
e
n
tatio
n
f
o
r
FIR
f
ilter
s
,
h
o
w
e
v
er
,
i
n
cr
ea
s
es
ex
p
o
n
e
n
tiall
y
w
it
h
t
h
e
f
ilter
o
r
d
er
.
DA
w
a
s
f
ir
s
t
in
tr
o
d
u
ce
d
b
y
C
r
o
is
ier
et
al
[
9
]
;
an
d
f
u
r
t
h
er
d
ev
elo
p
ed
b
y
P
eled
an
d
L
u
i
[
1
0
]
f
o
r
ef
f
icien
t
i
m
p
le
m
e
n
tat
io
n
o
f
d
ig
ital
f
ilter
s
.
A
tte
m
p
ts
ar
e
m
a
d
e
to
u
s
e
o
f
f
s
et
-
b
in
ar
y
co
d
i
n
g
[
1
1
]
to
r
ed
u
ce
th
e
R
OM
s
ize
b
y
a
f
ac
to
r
o
f
2
.
An
L
UT
-
les
s
ad
d
er
-
b
ased
D
A
ap
p
r
o
ac
h
h
as
b
ee
n
s
u
g
g
es
ted
b
y
Yo
o
an
d
An
d
er
s
o
n
,
w
h
er
e
m
e
m
o
r
y
-
s
p
ac
e
i
s
r
ed
u
ce
d
at
th
e
co
s
t
o
f
ad
d
iti
o
n
al
ad
d
er
s
[
1
2
]
.
Me
m
o
r
y
-
p
ar
titi
o
n
i
n
g
a
n
d
m
u
ltip
le
m
e
m
o
r
y
-
b
a
n
k
ap
p
r
o
ac
h
alo
n
g
w
i
th
f
le
x
ib
le
m
u
l
ti
-
b
it
d
ata
-
ac
ce
s
s
m
ec
h
an
is
m
s
ar
e
s
u
g
g
e
s
ted
f
o
r
FIR
f
il
ter
in
g
an
d
in
n
er
-
p
r
o
d
u
ct
co
m
p
u
tatio
n
i
n
o
r
d
er
to
r
ed
u
ce
th
e
m
e
m
o
r
y
s
ize
o
f
D
A
-
b
ased
i
m
p
le
m
e
n
tatio
n
[
1
3
]
–
[
1
7
]
.
A
llre
d
et
al
h
av
e
s
u
g
g
e
s
ted
an
e
f
f
ic
ien
t
D
A
-
b
ased
i
m
p
le
m
e
n
tat
io
n
o
f
leas
t
m
ea
n
s
q
u
ar
e
(
L
MS)
ad
ap
tiv
e
f
i
lter
u
s
i
n
g
a
d
ec
o
m
p
o
s
itio
n
o
f
D
A
b
ased
FIR
co
m
p
u
tatio
n
a
n
d
s
u
b
s
e
q
u
en
t
m
e
m
o
r
y
d
ec
o
m
p
o
s
itio
n
[
1
8
]
.
A
ll
th
e
s
e
s
tr
u
ct
u
r
es,
h
o
w
e
v
er
,
ar
e
n
o
t
s
u
itab
le
f
o
r
i
m
p
le
m
e
n
tatio
n
o
f
th
e
FI
R
f
ilter
s
i
n
s
y
s
to
lic
h
ar
d
w
ar
e
s
i
n
ce
t
h
e
p
ar
ti
al
p
r
o
d
u
cts
av
ailab
le
f
r
o
m
t
h
e
p
ar
titi
o
n
ed
m
e
m
o
r
y
m
o
d
u
les
ar
e
s
u
m
m
ed
to
g
et
h
er
b
y
a
n
et
w
o
r
k
o
f
o
u
tp
u
t
ad
d
er
s
.
A
n
e
w
to
o
l
f
o
r
th
e
au
to
m
at
ic
g
e
n
er
atio
n
o
f
h
ig
h
l
y
p
ar
allelize
d
FIR
f
ilter
s
b
ase
d
o
n
P
A
R
O
d
esig
n
m
et
h
o
d
o
lo
g
y
i
s
p
r
esen
ted
in
[
1
9
]
,
w
h
er
e
t
h
e
a
u
th
o
r
s
h
a
v
e
p
er
f
o
r
m
ed
h
ier
ar
c
h
ical
p
ar
tit
io
n
in
g
i
n
o
r
d
er
to
b
alan
ce
th
e
a
m
o
u
n
t o
f
lo
ca
l
m
e
m
o
r
y
w
it
h
e
x
ter
n
a
l c
o
m
m
u
n
i
ca
tio
n
,
an
d
t
h
e
y
h
a
v
e
ac
h
iev
e
d
h
ig
h
er
t
h
r
o
u
g
h
p
u
t
an
d
s
m
aller
late
n
cie
s
b
y
p
ar
tial
lo
ca
lizatio
n
.
A
s
y
s
to
lic
d
ec
o
m
p
o
s
i
tio
n
tec
h
n
iq
u
e
is
s
u
g
g
ested
i
n
a
r
ec
en
t
p
ap
er
f
o
r
m
e
m
o
r
y
-
ef
f
icie
n
t
D
A
-
b
ased
i
m
p
le
m
e
n
tatio
n
o
f
li
n
ea
r
an
d
cir
cu
lar
co
n
v
o
lu
tio
n
s
[
2
0
]
.
I
n
th
is
p
ap
er
w
e
h
a
v
e
ex
ten
d
ed
f
u
r
t
h
er
t
h
e
w
o
r
k
o
f
[
2
0
]
to
o
b
tain
an
ar
ea
-
d
ela
y
-
p
o
w
er
-
e
f
f
icien
t
i
m
p
l
e
m
en
tatio
n
o
f
FI
R
f
ilter
i
n
FP
G
A
p
latf
o
r
m
.
2.
ADAP
T
I
VE
A
L
G
O
RI
T
H
M
S
T
h
er
e
ar
e
m
a
n
y
m
et
h
o
d
s
f
o
r
t
h
e
p
er
f
o
r
m
i
n
g
w
ei
g
h
t
u
p
d
ate
o
f
an
ad
ap
tiv
e
f
il
ter
.
T
h
er
e
is
th
e
w
ie
n
er
f
ilter
,
w
h
ic
h
is
t
h
e
o
p
ti
m
u
m
l
i
n
er
f
ilter
i
n
ter
m
s
o
f
m
ea
n
s
q
u
ar
ed
er
r
o
r
,
an
d
s
ev
er
al
alg
o
r
it
h
m
s
th
a
t
atte
m
p
t
to
ap
p
r
o
x
im
a
te
it,
s
u
ch
as
t
h
e
m
eth
o
d
o
f
s
teep
est
d
e
s
ce
n
t.
T
h
er
e
is
al
s
o
least
-
m
ea
n
s
q
u
ar
e
al
g
o
r
ith
m
,
d
ev
e
lo
p
ed
b
y
W
i
n
d
r
o
w
a
n
d
Ho
f
f
o
r
ig
in
a
ll
y
f
o
r
u
s
e
i
n
ar
ti
f
icial
n
eu
r
al
n
et
w
o
r
k
s
.
Fin
a
ll
y
,
t
h
er
e
ar
e
o
th
er
tech
n
iq
u
e
s
s
u
c
h
as
th
e
r
ec
u
r
s
i
v
e
-
least
s
q
u
ar
e
alg
o
r
ith
m
an
d
th
e
k
al
m
an
f
ilter
.
T
h
e
ch
o
ice
o
f
alg
o
r
ith
m
is
h
ig
h
l
y
d
ep
en
d
en
t
o
n
th
e
s
i
g
n
al
s
o
f
in
ter
e
s
t
an
d
th
e
o
p
er
atin
g
en
v
ir
o
n
m
e
n
t,
as
w
ell
as
t
h
e
co
n
v
er
g
e
n
ce
ti
m
e
r
eq
u
ir
ed
an
d
co
m
p
u
tatio
n
p
o
w
er
av
ai
lab
le.
2
.
1
.
P
r
o
ble
m
Sta
t
e
m
ent
Du
e
to
t
h
e
h
i
g
h
p
er
f
o
r
m
a
n
c
e
r
eq
u
ir
e
m
en
ts
a
n
d
in
cr
ea
s
in
g
co
m
p
le
x
it
y
o
f
D
SP
an
d
m
u
lti
m
ed
ia
co
m
m
u
n
icatio
n
ap
p
licatio
n
s
,
f
ilter
s
w
it
h
lar
g
e
n
u
m
b
er
o
f
t
ap
s
ar
e
r
eq
u
ir
ed
to
in
cr
ea
s
e
th
e
p
er
f
o
r
m
a
n
ce
i
n
ter
m
s
o
f
h
i
g
h
s
a
m
p
li
n
g
r
ate.
As
a
r
esu
lt
t
h
e
f
i
lter
in
g
o
p
e
r
atio
n
s
ar
e
co
m
p
u
tatio
n
all
y
i
n
ten
s
i
v
e
an
d
m
o
r
e
co
m
p
le
x
i
n
ter
m
s
o
f
h
ar
d
w
a
r
e
r
eq
u
ir
em
e
n
t
s
.
T
h
e
FIR
f
i
l
ter
s
p
er
f
o
r
m
th
e
w
e
ig
h
ted
s
u
m
m
atio
n
s
o
f
i
n
p
u
t
s
eq
u
en
ce
s
w
i
th
co
n
s
tan
t
co
ef
f
icie
n
ts
in
m
o
s
t
o
f
t
h
e
s
ig
n
al
p
r
o
ce
s
s
in
g
a
n
d
m
u
l
ti
m
ed
ia
ap
p
licatio
n
s
.
T
h
ese
f
ilt
er
s
ar
e
w
id
el
y
u
s
ed
i
n
v
i
d
eo
co
n
v
o
lu
t
io
n
s
f
u
n
ctio
n
s
,
s
ig
n
al
p
r
ec
o
n
d
itio
n
i
n
g
an
d
o
th
er
co
m
m
u
n
icatio
n
ap
p
licatio
n
s
.
T
h
e
d
ec
r
ea
s
e
in
co
m
p
u
tatio
n
al
co
m
p
lex
i
t
y
ca
u
s
es
th
e
i
n
cr
ea
s
e
in
th
e
p
er
f
o
r
m
an
ce
,
i
n
ter
m
s
o
f
s
p
ee
d
,
ar
ea
an
d
p
o
w
er
.
Hi
g
h
s
p
ee
d
,
lo
w
ar
ea
a
n
d
p
o
w
er
e
f
f
i
cien
t
co
n
s
cio
u
s
d
esi
g
n
tech
n
i
q
u
es
in
So
C
i
n
cl
u
d
e
ef
f
o
r
t
s
at
al
l
le
v
el
o
f
ab
s
tr
ac
ti
o
n
.
O
n
e
w
a
y
to
e
f
f
icie
n
tl
y
i
n
co
r
p
o
r
ate
h
ig
h
p
er
f
o
r
m
a
n
ce
d
esig
n
tec
h
n
iq
u
e
i
s
to
i
m
p
le
m
e
n
t I
P
co
r
es [
4
]
.
T
h
ese
co
r
es h
av
e
f
o
llo
w
i
n
g
m
aj
o
r
ad
v
an
tag
e
s
.
•
R
eu
s
ab
ilit
y
a
cr
o
s
s
d
esig
n
s
•
R
ed
u
ctio
n
o
f
th
e
d
es
ig
n
ef
f
o
r
t
•
S
h
o
r
ter
ti
m
e
to
m
ar
k
et.
T
h
e
d
is
ad
v
an
tag
e
o
f
FIR
f
ilt
er
s
is
th
at
th
e
y
r
eq
u
ir
e
h
ig
h
o
r
d
e
r
.
T
h
e
h
ig
h
o
r
d
er
d
em
an
d
s
m
o
r
e
h
ar
d
w
ar
e,
ar
ea
an
d
p
o
w
er
co
n
s
u
m
p
tio
n
.
T
o
m
in
i
m
ize
th
e
s
e
p
ar
am
eter
s
,
o
u
r
g
o
al
is
to
i
m
p
l
e
m
e
n
t
an
e
f
f
ici
e
n
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4864
IJ
R
E
S
Vo
l.
5
,
No
.
2
,
J
u
l
y
201
6
:
1
2
4
–
12
6
123
h
ig
h
o
r
d
er
f
ilter
i
n
d
ig
ital
s
y
s
te
m
s
.
B
y
t
h
e
r
ed
u
ctio
n
o
f
ar
ith
m
etic
i
n
ter
m
s
o
f
m
u
ltip
lier
s
,
o
u
r
g
o
al
is
to
r
ed
u
ce
th
e
p
ar
a
m
eter
s
n
a
m
el
y
,
h
ar
d
war
e,
ar
ea
an
d
p
o
w
er
.
T
h
is
i
s
u
l
ti
m
ate
g
o
al
o
f
th
e
i
m
p
le
m
e
n
ta
tio
n
o
f
a
n
e
f
f
icien
t
FIR
f
ilter
an
d
h
e
n
ce
D
A
al
g
o
r
ith
m
is
u
s
ed
f
o
r
i
m
p
le
m
en
tatio
n
o
f
h
ig
h
o
r
d
er
FIR
f
ilter
.
FIR
f
il
ter
is
in
co
r
p
o
r
ated
w
it
h
a
M
AC
u
n
i
t.
T
h
e
p
u
r
p
o
s
e
o
f
MA
C
u
n
it
i
s
to
m
u
l
tip
l
y
t
h
e
i
n
p
u
t
w
it
h
c
o
n
s
ta
n
t
co
ef
f
icie
n
ts
,
to
s
h
i
f
t
an
d
th
e
n
to
ad
d
th
e
m
.
T
h
is
p
r
o
ce
s
s
is
r
ep
ea
ted
u
n
t
il
all
p
ar
tial
p
r
o
d
u
cts
p
r
o
d
u
c
e
t
h
e
o
u
tp
u
t
a
f
ter
ac
cu
m
u
lat
io
n
.
I
t
i
n
cr
ea
s
es
th
e
h
ar
d
w
ar
e
co
m
p
lex
i
t
y
b
ec
a
u
s
e
a
s
i
m
p
le
m
u
lt
ip
lier
cir
cu
itr
y
i
s
u
s
ed
.
T
h
e
id
ea
is
to
s
o
m
e
h
o
w
b
y
p
as
s
o
r
r
ep
lace
th
e
m
u
ltip
l
y
a
n
d
s
h
i
f
t
o
p
er
atio
n
s
w
it
h
les
s
co
m
p
le
x
o
p
e
r
atio
n
s
.
Di
s
tr
ib
u
ted
r
ith
m
etic
(
D
A
)
A
l
g
o
r
ith
m
ca
n
b
e
u
s
ed
to
r
ep
lace
MA
C
u
n
i
t.
T
h
e
DA
A
l
g
o
r
ith
m
ac
t
u
all
y
u
s
es
lo
o
k
u
p
tab
le
f
o
r
s
to
r
in
g
co
n
s
tan
t
co
ef
f
icie
n
ts
.
So
th
e
u
s
e
o
f
lo
o
k
u
p
tab
les
r
ed
u
ce
s
th
e
h
ar
d
w
ar
e
co
m
p
le
x
it
y
a
n
d
h
en
ce
t
h
e
n
e
w
d
e
s
ig
n
is
m
o
r
e
ef
f
ic
ien
t
in
ter
m
s
o
f
les
s
ar
ea
,
m
o
r
e
s
p
ee
d
an
d
lo
w
p
o
w
er
co
n
s
u
m
p
tio
n
.
FIR
f
i
lter
r
ef
er
en
ce
co
r
e
u
s
e
s
a
s
i
m
p
le
MA
C
u
n
i
t.
W
e
h
av
e
r
ep
lace
d
MA
C
u
n
it
i
n
FI
R
f
ilter
r
ef
e
r
en
ce
co
r
e
w
it
h
D
A
A
l
g
o
r
ith
m
.
I
n
th
is
s
t
u
d
y
,
p
er
f
o
r
m
a
n
ce
o
f
R
e
f
er
en
ce
C
o
r
e
w
it
h
Si
m
p
le
M
A
C
an
d
r
ef
er
e
n
ce
co
r
e
w
i
th
D
A
is
co
m
p
ar
ed
.
3.
I
NT
RO
D
UCT
I
O
N
O
F
DIS
T
RIB
UT
E
D
AL
G
O
R
I
T
H
M
Dis
tr
ib
u
ted
ar
i
th
m
etic
is
a
b
it
le
v
el
r
ea
r
r
an
g
e
m
en
t
o
f
a
m
u
lt
ip
l
y
ac
cu
m
u
late
to
h
id
e
th
e
m
u
ltip
licatio
n
s
.
I
t
is
a
p
o
w
er
f
u
l
tec
h
n
iq
u
e
f
o
r
r
ed
u
ci
n
g
t
h
e
s
ize
o
f
a
p
ar
allel
h
ar
d
w
ar
e
m
u
ltip
l
y
-
ac
c
u
m
u
late
th
at
is
w
el
l
s
u
ited
to
FP
GA
d
esig
n
s
.
I
t
ca
n
also
b
e
ex
t
en
d
ed
to
o
th
er
s
u
m
f
u
n
ctio
n
s
s
u
c
h
as
co
m
p
le
x
m
u
ltip
lies
,
Fo
u
r
ier
tr
a
n
s
f
o
r
m
s
an
d
s
o
o
n
.
I
n
m
o
s
t
o
f
t
h
e
m
u
ltip
l
y
ac
cu
m
u
late
ap
p
licatio
n
s
in
s
i
g
n
al
p
r
o
ce
s
s
in
g
,
o
n
e
o
f
t
h
e
m
u
ltip
lican
d
s
f
o
r
ea
ch
p
r
o
d
u
ct
is
a
co
n
s
tan
t.
T
h
e
DA
tar
g
ets
t
h
e
p
r
o
d
u
cts
o
f
s
u
m
s
w
h
ic
h
co
v
er
all
f
ilter
i
n
g
ap
p
licatio
n
an
d
f
r
eq
u
e
n
c
y
tr
a
n
s
f
er
f
u
n
ctio
n
s
.
D
A
u
s
es
L
o
o
k
-
Up
T
ab
le
(
L
UT
)
w
h
ic
h
s
to
r
es
th
e
co
n
s
tan
t
co
ef
f
ic
ien
t
s
o
f
FIR
Fil
ter
.
T
h
e
s
ize
o
f
L
o
o
k
-
Up
T
ab
le
(
L
UT
)
in
DA
al
g
o
r
ith
m
is
2
,
w
h
er
e
k
i
s
t
h
e
n
u
m
b
er
o
f
f
ilter
tap
s
.
W
h
en
n
u
m
b
er
o
f
tap
s
i
n
cr
e
ases
,
L
UT
g
r
o
w
s
-
e
x
p
o
n
en
t
ial
l
y
.
B
y
u
s
i
n
g
o
f
f
s
e
t
B
in
ar
y
C
o
d
e
(
OB
C
)
,
th
e
s
ize
o
f
th
e
L
UT
ca
n
b
e
r
ed
u
ce
d
.
T
h
is
is
v
er
y
ef
f
icie
n
t
i
n
ter
m
s
o
f
le
s
s
h
ar
d
w
ar
e
a
n
d
m
o
r
e
s
p
ee
d
Ma
n
y
D
SP
ap
p
lic
atio
n
s
r
eq
u
ir
ed
FIR
w
h
ic
h
h
a
v
in
g
M
A
(
U
n
it
m
u
ltip
lier
an
d
ad
d
ac
cu
m
u
lato
r
)
,
r
ep
lacin
g
M
AC
w
i
th
L
UT
-
B
a
s
ed
D
A
alg
o
r
it
h
m
h
av
i
n
g
p
o
w
er
,
e
f
f
icien
c
y
a
n
d
les
s
ar
e
a
u
s
a
g
e.
P
r
o
p
o
s
ed
DA
alg
o
r
it
h
m
is
h
ar
d
w
ar
e
ef
f
icie
n
t
f
o
r
VL
SI
an
d
FP
G
A
,
b
u
t
L
UT
-
L
e
s
s
OB
C
is
e
f
f
icie
n
t
o
n
l
y
f
o
r
cu
s
to
m
VL
SI
[
5
]
.
W
e
h
a
v
e
u
s
ed
D
A
f
o
r
m
u
lt
ip
lier
le
s
s
ar
ch
i
tectu
r
e
in
FP
G
A
.
Fo
r
D
A
b
ased
o
n
lo
o
k
-
u
p
tab
le
h
av
i
n
g
co
n
s
ta
n
t
co
ef
f
icie
n
t
a
n
d
ch
a
n
g
i
n
g
v
ar
iab
le,
o
n
e
n
ee
d
s
to
d
esig
n
a
h
ig
h
l
y
e
f
f
icien
t
FI
R
in
d
ig
ita
l
s
i
g
n
al
p
r
o
ce
s
s
in
g
.
DA
ca
n
b
e
u
s
ed
f
o
r
h
ig
h
o
r
d
er
f
ilter
.
T
h
er
e
ar
e
t
w
o
te
h
n
iq
u
e
s
u
s
ed
in
D
A
a
lg
o
r
it
h
m
,
o
n
e
o
f
w
h
ich
is
p
ar
allel
d
is
tr
ib
u
ted
an
d
th
e
o
th
er
is
s
er
ial
d
is
tr
ib
u
ted
[
6
]
.
T
h
e
DSP
FIR
f
ilter
f
u
n
c
tio
n
s
ar
e
u
s
ed
i
n
telec
o
m
m
u
n
icatio
n
s
(
e.
g
.
T
elec
o
m
m
i
n
B
io
m
ed
ical
Si
g
n
a
l
P
r
o
ce
s
s
in
g
C
o
m
m
u
n
icatio
n
,
W
i
r
eless
s
atellite
an
d
I
m
ag
e
p
r
o
ce
s
s
i
n
g
)
w
h
ic
h
ar
e
p
er
f
o
r
m
ed
e
f
f
icien
tl
y
.
T
h
e
m
u
ltip
lier
s
i
n
M
AC
u
n
it
o
f
m
an
y
D
SP
f
u
n
ctio
n
s
h
av
e
m
o
r
p
o
w
er
an
d
ar
ea
r
eq
u
ir
e
m
e
n
t
s
.
T
h
er
e
ar
e
t
w
o
tec
h
n
iq
u
es
in
th
is
r
e
s
p
ec
t
w
h
ich
ar
e
m
u
ltip
lier
le
s
s
.
On
e
o
f
t
h
e
m
is
C
o
n
v
er
s
io
n
b
ased
,
in
w
h
ich
co
e
f
f
icien
ts
o
f
f
ilter
s
ar
e
co
n
v
er
ted
i
n
to
n
u
m
e
r
ic
r
ep
r
esen
tatio
n
.
T
h
e
s
ec
o
n
d
is
b
ased
o
n
L
UT
w
h
ic
h
s
to
r
es
p
r
e
-
co
m
p
u
ted
co
ef
f
icien
ts
v
alu
e
s
o
f
FI
R
f
i
lter
s
.
T
h
e
L
UT
in
D
A
alg
o
r
ith
m
u
s
es
m
o
r
e
m
e
m
o
r
y
.
[
7
]
.
4.
B
UIL
DI
NG
B
L
O
CK
O
F
F
I
R
RE
F
E
R
E
NC
E
CO
R
E
T
h
e
ex
is
ti
n
g
co
r
e
m
a
y
b
e
i
m
p
l
e
m
en
ted
u
s
i
n
g
th
e
m
ai
n
co
m
p
o
n
en
t
s
w
h
ic
h
ar
e
g
i
v
e
n
b
elo
w
:
•
C
o
u
n
ter
•
C
o
n
tr
o
ller
•
X
s
a
m
p
le
v
alu
e
m
e
m
o
r
y
(
X
-
R
A
M)
•
B
co
ef
f
icie
n
t
m
e
m
o
r
y
(
B
-
R
o
m
)
•
B
eta
an
d
g
a
m
m
a
r
eg
i
s
ter
•
M
u
ltip
l
y
-
ac
c
u
m
u
lato
r
(
MA
C
)
•
R
o
u
n
d
in
g
•
O
u
tp
u
t
s
a
m
p
le
(
Y
-
R
eg
i
s
ter
)
T
h
e
m
ai
n
co
m
p
o
n
e
n
ts
o
f
t
h
e
co
r
es
ca
n
b
e
ea
s
ily
r
ec
o
g
n
ized
f
r
o
m
th
e
to
p
o
f
m
o
d
u
le
of
t
h
e
co
r
e.
T
h
e
b
lo
ck
d
iag
r
a
m
o
f
t
h
e
ex
is
ti
n
g
d
ir
ec
t f
o
r
m
o
f
FIR
f
ilter
co
r
e
is
[
8
]
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
R
E
S
I
SS
N:
2
0
8
8
-
8708
V
LS
I
Desig
n
a
n
d
C
o
mp
a
r
is
o
n
o
f D
A
a
n
d
LM
S
B
a
s
ed
R
ec
o
n
fig
u
r
a
b
le
F
I
R
F
ilter
(
P
.
Hem
a
n
th
ku
ma
r
)
124
Fig
u
r
e
1
.
B
lo
ck
d
iag
r
a
m
o
f
T
OP
m
o
d
u
le
o
f
th
e
FI
R
Fil
ter
5.
I
M
P
L
E
M
E
NT
AT
I
O
N
O
F
F
I
R
F
I
L
T
E
R
USI
N
G
DA
FIR
f
ilter
h
as
1
6
-
tap
s
.
E
ac
h
ta
p
co
n
s
is
t
s
o
f
1
6
f
ilter
co
ef
f
ici
en
ts
w
it
h
1
6
-
b
it
i
n
p
u
t
d
ata
w
i
d
th
.
W
h
il
e
d
esig
n
in
g
FIR
f
ilter
w
it
h
D
A
,
th
ese
co
ef
f
icie
n
ts
ar
e
o
r
d
er
ed
in
a
lo
ok
-
u
p
tab
le.
T
h
is
is
o
w
in
g
to
th
e
f
ac
t
t
h
a
t
th
ese
co
ef
f
icie
n
ts
ar
e
co
n
s
ta
n
ts
.
T
h
e
lo
o
k
-
u
p
tab
le
g
r
o
w
s
e
x
p
o
n
en
t
iall
y
w
h
e
n
t
h
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ith
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r
ith
m
a
n
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it
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h
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u
p
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le.
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th
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p
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o
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n
t
u
p
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t
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n
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m
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ter
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r
s
u
p
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s
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ter
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th
e
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o
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Fil
ter
in
f
u
t
u
r
e
th
i
s
tech
n
iq
u
e
ca
n
b
e
u
s
ed
.
RE
F
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NC
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w
.
x
il
in
x
.
c
o
m
.
[3
]
N.
S
a
n
k
a
ra
y
y
a
,
K.
Ro
y
,
D.
Bh
a
tt
a
c
h
a
r
y
a
,
“
A
l
g
o
rit
h
m
s
f
o
r
L
o
w
P
o
w
e
r
a
n
d
Hig
h
S
p
e
e
d
F
IR
f
il
ter
Re
a
li
z
a
ti
o
n
Us
in
g
Diff
e
r
e
n
ti
a
l
Co
e
ff
icie
n
ts”
,
A
n
a
lo
g
a
n
d
Dig
i
tal
S
ig
n
a
l
P
ro
c
e
ss
in
g
,
IEE
E
T
ra
n
s
a
c
ti
o
n
s
,
v
o
l,
4
4
(
6
)
,
p
p
.
4
8
8
-
4
9
7
,
1
9
9
7
.
[4
]
A
.
T
.
Erd
o
g
a
n
,
M.
Ha
sa
n
a
n
d
T.
A
rsla
n
,
“
Al
g
o
rit
h
mic
lo
w
p
o
we
r
FIR
c
o
re
s
”
,
c
ircu
it
s
a
n
d
s
y
ste
m
s,
IEE
E
p
ro
c
e
e
d
in
g
s,
v
o
l
1
5
0
,
p
p
.
1
5
5
-
1
6
9
,
2
0
0
3
.
[5
]
He
e
jo
n
g
y
o
o
a
n
d
Da
v
id
V
.
A
n
d
e
rso
n
,
“
Ha
rd
w
a
re
e
ff
icie
n
t
d
istrib
u
ted
a
rith
me
ti
c
a
rc
h
it
e
c
tu
re
fo
r
h
i
g
h
o
r
d
e
r
d
ig
it
a
l
fi
lt
e
rs
”
,
A
c
o
u
stics
,
S
p
e
e
c
h
,
a
n
d
S
ig
n
a
l
P
ro
c
e
ss
in
g
,
2
0
0
5
.
P
ro
c
e
e
d
in
g
s.
(ICA
S
S
P
'
0
5
)
.
IEE
E
,
v
o
l
5
,
p
p
.
1
2
5
-
1
2
8
,
2
0
0
5
.
[6
]
W
a
n
g
se
n
,
T
a
n
g
Bin
a
n
d
Zh
u
Ju
n
,
“
Distrib
u
ted
a
rit
h
m
e
ti
c
f
o
r
F
IR
f
il
te
r
d
e
si
g
n
o
n
F
P
G
A
”
,
C
o
m
m
u
n
ica
ti
o
n
s,
Circu
it
s an
d
S
y
ste
m
s
,
2
0
0
7
.
ICC
CA
S
2
0
0
7
.
IEE
E
,
p
p
.
6
2
0
-
6
2
3
,
2
0
0
7
.
[7
]
P
a
tri
c
k
L
o
n
g
a
a
n
d
A
li
M
iri
,
“
Are
a
e
ff
icie
n
t
FI
R
fi
lt
e
r
d
e
si
g
n
o
n
F
PGAs
u
sin
g
d
istri
b
u
te
d
a
rit
h
me
ti
c
”
,
S
y
m
p
o
siu
m
o
n
sig
n
a
l
p
ro
c
e
ss
in
g
a
n
d
in
f
o
rm
a
t
io
n
tec
h
n
o
lo
g
y
,
IEE
E
p
ro
c
e
ss
in
g
,
p
p
.
2
4
8
-
2
5
2
,
2
0
0
6
.
[8
]
M
u
h
a
m
m
a
d
A
k
h
tar
k
h
a
n
a
n
d
A
.
T
.
Rrd
o
g
a
n
,
“
Pa
ra
me
ter
ize
d
a
n
d
p
ro
g
r
a
mm
a
b
le
l
o
w
p
o
we
r
so
ft
FIR
fi
lt
e
rin
g
IP
c
o
re
s
”
,
P
r
o
c
e
e
d
in
g
s
o
f
th
e
4
th
W
S
EA
S
In
tern
a
ti
o
n
a
l
Co
n
f
e
re
n
c
e
o
n
S
ig
n
a
l
P
ro
c
e
ss
in
g
,
Co
m
p
u
tati
o
n
a
l
G
e
o
m
e
t
r
y
&
A
rti
f
icia
l
V
isio
n
,
2
0
0
4
.
[9
]
P
.
K.
M
e
h
e
r,
S.
Ch
a
n
d
ra
se
k
a
ra
n
a
n
d
A
.
Am
ir
a
,
“
F
P
G
A
r
e
a
li
z
a
ti
o
n
o
f
F
IR
f
il
ters
b
y
e
ff
icie
n
t
a
n
d
f
lex
ib
le
s
y
ste
m
iz
a
ti
o
n
u
si
n
g
d
istri
b
u
te
d
a
r
it
h
m
e
ti
c
”
,
IEE
E
T
ra
n
s
a
c
ti
o
n
s o
n
S
ig
n
a
l
Pro
c
e
ss
in
g
,
v
o
l.
5
6
,
p
p
.
3
0
0
9
-
3
0
1
7
,
2
0
0
8
.
[1
0
]
D.
J.
A
ll
re
d
,
H.
Yo
o
,
V
.
Krish
n
a
n
,
W
.
Hu
a
n
g
a
n
d
D.V
.
A
n
d
e
rso
n
,
“
L
M
S
a
d
a
p
ti
v
e
f
il
ters
u
sin
g
d
istri
b
u
ted
a
rit
h
m
e
ti
c
f
o
r
h
ig
h
th
r
o
u
g
h
p
u
t
”
,
IEE
E
T
ra
n
sa
c
ti
o
n
s o
n
Circ
u
it
s
a
n
d
S
y
ste
ms
,
v
o
l,
5
2
,
p
p
,
1
3
2
7
-
1
3
3
7
,
2
0
0
5
.
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