Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
6, N
o
. 3
,
Ju
n
e
201
6, p
p
. 1
213
~ 12
22
I
S
SN
: 208
8-8
7
0
8
,
D
O
I
:
10.115
91
/ij
ece.v6
i
3.9
879
1
213
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJECE
Freq
ue
ncy
Gen
e
rat
o
r
Dev
i
ce und
er test
(Sen
so
r,
sy
stem
,
…
)
Meas
urem
ent bloc
k
Am
plitude ?
Pha
s
e s
h
ift
?
,
,
,
Contr
o
l and
acquisition
Referenced Approximation Tec
hnique for a Rom-Less Sweep
Frequency Synthesizer
Atman Jbari
1
, Larbi
Bellarbi
1
,
Abdelhamid Errachid
2
1
Electr
i
cal
Engineering
Research Labor
ator
y
,
Higher School of
Tec
hnical Edu
cation,
Moham
m
e
d V Universit
y
in R
a
b
a
t,
Morocco
2
Claude
Bern
ard
-
L
y
on
1 Univ
ers
i
t
y
,
Labo
rator
y
o
f
Anal
yt
ica
l
S
c
ie
nces
, F
r
ance
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Dec 20, 2015
Rev
i
sed
Feb
17
, 20
16
Accepte
d
Mar 2, 2016
The m
a
in goa
l
of this paper
is to pr
esent
a no
vel ROM-less direct digital
frequency
s
y
n
t
h
e
sizer
for sweep
instrument
a
tion
s
y
stem
s. I
t
prov
ides a
m
a
in
s
w
eep chann
e
l
f
o
r frequen
c
y
an
al
y
s
is
and
a r
e
fe
rence
ch
annel
fo
r phas
e
and
amplitude meas
urement bloc
k o
p
erating at constant frequen
c
y
.
F
o
r phase to
amplitude conv
erter
,
we prop
os
e a n
e
w tr
igonometric
app
r
oximation
techn
i
que based
on a set of referenc
e angl
es. I
n
addition
,
we present th
e
design of the proposed s
y
nthes
i
zer and
its evaluation
in Matlab-Simulink
environm
ent.
T
h
e sim
u
lation
results illustr
a
t
e
the per
f
orm
a
nces and
demonstrate the effectiven
ess
of our
proposed cir
c
uit.
Keyword:
Di
rect
di
gi
t
a
l
s
y
nt
hesi
s
SFDR
Spectral a
n
alys
is
Swee
p fre
que
n
c
y
W
a
v
e
appr
ox
i
m
atio
n
Copyright ©
201
6 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Atm
a
n Jbari,
Electrical Engi
neeri
n
g Research La
boratory,
Hi
g
h
er
Sc
ho
ol
of
Tech
ni
cal
E
ducat
i
o
n,
Mohamm
ed V
Uni
v
ersity, Ra
bat, M
o
rocco.
Em
a
il: at
m
j
b
a
ri@g
m
a
il.co
m
1.
INTRODUCTION
Recent applica
tions of sens
ors ch
aracterization, syste
m
s id
entifi
cation and digital comm
unications
r
e
qu
ir
e con
t
ro
l
l
ed
f
r
e
q
u
e
n
c
y g
e
n
e
r
a
tor
s
w
i
t
h
h
i
gh
stab
ility an
d
low
f
r
e
quen
c
y r
e
so
l
u
tion
[
1
]-[6
]. I
n
the case
of s
w
eep
fre
q
u
e
ncy
anal
y
s
i
s
, i
t
i
s
al
so im
por
t
a
nt
t
o
im
pro
v
e
t
h
e
m
easure
m
ent
of re
qui
r
e
d pa
ram
e
t
e
rs
suc
h
as
am
pl
i
t
ude an
d
pha
se shi
f
t
bet
w
een i
n
p
u
t
a
n
d o
u
t
p
ut
wa
ve
s. The
schem
e
of i
n
st
r
u
m
e
nt
ati
on sy
st
em
i
s
sho
w
n
i
n
Fi
gu
re 1 w
h
ere t
h
e co
nt
rol
and ac
qui
si
t
i
o
n
bl
ock c
o
n
f
i
g
ur
es t
h
e anal
y
z
i
ng wa
ve fre
q
u
e
n
cy
and ac
qui
r
e
s t
h
e
out
put
s
o
f
t
h
e
m
easurem
ent
b
l
ock f
o
r p
r
oces
si
ng
an
d di
spl
a
y
i
ng resul
t
s
.
Fi
gu
re
1.
B
l
oc
k
di
ag
ram
of g
e
neral
i
n
st
r
u
m
e
nt
at
i
on
sy
st
em
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E
V
o
l
.
6,
No
. 3,
J
u
ne 2
0
1
6
:
12
1
3
– 12
22
1
214
,
,
Mul
t
i
pli
er-M1
LP-Fi
l
t
e
r F
1
,
Mul
t
i
pli
er-M2
,
,
L
P
-Fil
ter F
2
Fr
equency
gener
a
tor
Main channel
Ref
e
rence channel
F
r
e
quency
C
ontr
o
l
W
or
d
For stable
m
e
a
s
urem
ent pe
rform
a
n
ces, the
measurem
ent block
has
to
operate at consta
nt freque
ncy
du
ri
n
g
t
h
e e
n
t
i
r
e ra
nge
of i
n
put
f
r
e
que
ncy
anal
y
s
i
s
. In t
h
e fi
rst
st
age, a
Hi
g
h
fr
eq
ue
n
c
y
t
o
Low
fre
que
ncy
con
v
e
r
si
o
n
bl
o
c
k i
s
used
. Fi
g
u
re
2 sh
ows t
h
e st
ruct
u
r
e of t
h
i
s
co
nve
rsi
o
n
bl
oc
k w
h
ere t
h
e pr
ocessi
n
g
si
gnal
s
are:
-
I
npu
t sign
al:
co
s
2
;
-
Out
put
si
g
n
al
:
cos
2
;
-
Refere
nce sig
n
a
l:
cos
2
.
Fi
gu
re
2.
Di
ag
ram
of H
F
t
o
L
F
co
n
v
ersi
on
b
l
ock
After m
u
ltip
lic
atio
n
and low-p
a
ss filtering
u
n
d
e
r t
h
e
fo
ll
o
w
i
n
g co
nd
itio
n
s
:
≪
≪
;
≪
≪
,
w
e
get
out
o
f
t
h
e st
ruct
ure
,
t
w
o
si
g
n
al
s of
sam
e
freque
nc
y
F
and
p
h
a
se sh
ift
as
exp
r
esse
d i
n
E
quat
i
o
ns
(
1
-
2
)
.
2
(1
)
2
(2
)
In t
h
e sec
o
nd
stage, the
re
ference fre
que
nc
y
sh
ou
ld
fo
llow th
e ch
an
g
e
s o
f
i
n
pu
t freq
uen
c
y
in
or
der
t
o
keep
t
h
e o
p
erat
i
n
g fr
eque
ncy
con
s
t
a
n
t
.
For
t
h
is
pu
rpo
s
e, ou
r
w
o
r
k
aim
s
to
stud
y an
d
d
e
sign
a
no
vel
ci
rc
ui
t
whi
c
h i
n
t
e
grat
es b
o
t
h
f
r
eq
ue
ncy
ge
ne
rat
o
rs
o
f
a
n
al
y
s
i
s
a
n
d
re
fere
nce
s
i
gnal
s
.
T
h
e
pr
op
ose
d
swee
p f
r
eq
ue
n
c
y
sy
nt
hesi
zer
, as s
h
o
w
n i
n
Fi
g
u
re
3,
pr
ov
id
es t
w
o ch
an
n
e
ls
su
ch
as
the freque
nc
y shift
rem
a
in
s co
n
s
tan
t
. Th
e m
a
in
c
h
ann
e
l correspo
n
d
s
to
th
e m
a
in
o
u
t
p
u
t
wav
e
, wh
ereas th
e referen
ce ch
annel will
be use
d
by
t
h
e m
easurem
ent
b
l
ock.
Fig
u
r
e
3
.
input-
o
u
t
pu
ts of
t
h
e pr
opo
sed sweep
f
r
e
q
u
e
n
c
y syn
t
h
e
sizer
2.
THEORETICAL OF THE
DIRE
CT
DIGITAL FREQUE
NC
Y SY
NTHESIS
In sci
e
nt
i
f
i
c
a
nd i
n
d
u
st
ri
al
fre
que
ncy
ge
n
e
rat
o
r
s
, di
f
f
er
ent
t
echni
ques
are used t
o
pr
o
duce t
h
e
require
d
accurate waveform
s, such as anal
og
oscillato
rs,
mixing fre
que
n
cies sources
or phase
-
loc
k
e
d
loop
ci
rcui
t
s
.
Am
ong
t
h
ese t
e
c
h
ni
q
u
es,
Di
rect
Di
gi
t
a
l
F
r
eq
uency
Sy
nt
he
si
zers (
D
DFS
)
per
f
o
rm
im
port
a
nt
sp
ecification
s
: lo
w spu
r
s lev
e
l, fast switch
i
ng
sp
eed
, fast settlin
g
ti
me, sub
-
h
e
rtz freq
u
e
n
c
y reso
l
u
tion,
co
n
tinuo
us phase sw
itch
i
n
g
r
e
spon
se an
d lo
w
ph
ase
no
ise
[7],[8]. The pri
n
cipl
e of
DD
FS techn
i
qu
e w
a
s
in
trodu
ced
b
y
Tiern
e
y in
[9
], an
d
its
cor
r
es
po
n
d
i
n
g co
nve
nt
i
onal
d
e
si
g
n
architecture is shown in Figure 4,
w
h
er
e
th
e
co
mp
on
en
ts
a
r
e th
e fo
llo
w
i
n
g
,
-
Phase accum
u
lator:
provi
des the time re
fere
nce as counter ad
dres
s of the wave
form
me
m
o
ry. It is
u
p
d
a
ted at each
risin
g
or
fallin
g edg
e
of th
e
clo
c
k
sign
al.
-
Wav
e
fo
rm ROM:
c
ont
ai
n
s
sam
p
l
e
s of t
h
e
wave
f
o
rm
t
o
b
e
sy
nt
hesi
ze
d.
-
D/A C
o
n
v
erte
r
:
co
nv
erts each
n
u
m
eric v
a
lue in
to
its
p
r
op
ortio
n
a
l an
alog
v
o
ltag
e
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Ref
e
rence
d
A
p
pro
x
i
m
at
i
o
n
Te
chni
que
f
o
r
a
Ro
m Less
Sw
e
e
p
Fre
q
uency
Synt
hesi
zer (
A
t
m
a
n
J
b
ari
)
1
215
-
Low-p
a
ss filte
r
:
l
i
m
i
t
s
t
h
e spect
r
u
m
of t
h
e sy
nt
hesi
zed
wave at
t
h
e N
y
qui
st
ba
nd
wi
dt
h rel
a
t
e
d t
o
t
h
e
ope
rat
i
n
g cl
oc
k
fre
que
ncy
.
Fi
gu
re
4.
C
o
n
v
ent
i
o
nal
a
r
chi
t
ect
ure
of t
h
e
R
O
M
base
d
D
D
S
The out
put
fre
que
ncy
de
pen
d
s
on
t
h
e
refe
r
e
nce cl
oc
k
fre
que
ncy
, the
freque
ncy control
wo
rd
and the
s
i
ze of the
phas
e accum
u
lator
,
b
y
th
e fo
llow
i
n
g
expr
ession
[7
]:
(3)
The
wave
qua
lity depends
on t
h
e length of
t
h
e phase
accum
u
lator,
the ROM si
ze, the ADC
reso
l
u
tio
n
and
th
e o
r
d
e
r
o
f
low-p
a
ss filter.
Howev
e
r, th
e
m
o
st d
i
sad
v
a
n
t
ag
e of th
is arch
itectu
r
e is th
e u
s
e of
R
O
M
m
e
m
o
ry w
h
i
c
h t
h
e
hi
g
h
si
ze
re
qui
re
s
an
ex
pe
nsi
v
e
sem
i
cond
uct
o
r
area a
n
d c
o
n
s
um
es a l
o
t
o
f
po
we
r.
Hen
c
e, a set
o
f
in
teresting
app
r
ox
im
a
tio
n
meth
od
s
h
a
s
bee
n
d
e
vel
ope
d t
o
com
put
e di
rec
t
l
y
t
h
e am
pl
i
t
ude a
n
d
then
overc
o
me the ROM i
n
convenie
nt [9]-[11]. In
most rece
nt tec
hni
que
s, the
ROM is re
placed
by a
co
m
p
u
t
atio
n
un
it, called
W
a
v
e
Arith
m
e
t
i
c
Un
it, wh
ich
the co
m
p
lex
ity a
n
d
th
e co
nsu
m
p
tio
n
p
o
wer are v
e
ry
lo
w. Th
e ro
le
of th
is
WAU as
illu
strated
in Fi
g
u
re
5
is t
o
com
p
u
t
e th
e sin
e
v
a
lu
e
of each
i
n
pu
t
p
h
a
se.
Figure 5.
Archi
t
ecture of
t
h
e ROM
free DDS
The
p
r
i
n
ci
pal
m
e
t
hods
co
rre
spo
n
d
t
o
C
O
o
r
di
nat
e
R
o
t
a
t
i
o
n
DI
gi
t
a
l
C
o
m
put
e
r
(C
OR
D
I
C
)
al
g
o
ri
t
h
m
,
pol
y
n
o
m
i
al
appr
o
x
i
m
at
i
on as
Eul
e
r i
n
fi
ni
t
e
and
che
b
y
s
he
v seri
es
o
r
Ta
y
l
or f
o
rm
ul
at
ion
[
7
]
,
[
10]
,
[
1
1
]
. An
in
terestin
g
work
in
[8
], used a trig
o
n
o
m
etric ap
p
r
ox
im
a
t
i
o
n
for sm
al
l v
a
lu
es o
f
FC
W in
wh
ich
th
e d
e
sign
arch
itecture p
r
esen
ts two
adv
a
n
t
ag
es: lo
w
co
m
p
lex
ity
(t
wo
m
u
ltip
liers, two
ad
d
e
rs an
d
two
reg
i
sters) an
d
one
-cy
c
l
e
co
m
put
at
i
on (n
o
pi
pel
i
n
e st
ag
es). H
o
weve
r,
t
h
e com
put
at
i
on er
ro
r i
n
cr
eases st
ro
ngl
y
vers
us
fre
que
ncy
co
nt
rol
w
o
rd a
nd c
ons
eq
ue
nt
l
y
i
nduce
s
a p
o
o
r
s
p
u
r
i
o
us f
r
ee dy
nam
i
c range.
Hence
,
o
u
r
w
o
rk ai
m
s
to im
prove
this
techni
que
for t
h
e c
o
m
p
lete range
of
t
h
e
phas
e
accum
u
lator
with
high c
o
mputation
precis
i
on.
3.
THE PROPOSED
METHOD
For a si
ne cu
r
v
e ap
pr
oxi
m
a
t
i
on
, Sh
u-C
h
nu
g Yi
pr
o
pose
s
t
o
com
put
e t
w
o sim
u
l
t
a
neo
u
s
qua
drat
u
r
e
out
put
s
[
8
]
.
T
h
i
s
t
echni
que
u
s
ed a
di
f
f
ere
n
ce
∆
bet
w
ee
n t
w
o c
o
n
s
ecut
i
v
e
angl
es
(
;
)
and
Taylor
's
series of
sin
and
cos
at first
o
r
d
e
r, acco
rd
ing
t
o
th
e fo
llo
wi
n
g
expression
s,
sin
s
i
n
∆
cos
(4)
cos
cos
∆
s
i
n
(
5
)
Cl
ock
Output
P
h
as
e
Accum
u
lator (
PA
)
Wa
v
e
f
o
m
Map
in RO
M
WROM
D
ig
ita
l t
o
A
nalo
g
C
on
ver
t
er
(
DAC
)
L
ow
P
ass
F
il
ter
(
LPF
)
FCW
Phase
Wave A
r
ih
m
e
tic U
n
it
WAU
sin
Si
ne val
u
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E
V
o
l
.
6,
No
. 3,
J
u
ne 2
0
1
6
:
12
1
3
– 12
22
1
216
Th
us, t
h
e D
D
FS wa
ve can be com
put
ed f
o
r eac
h val
u
e
of p
h
ase
.
H
o
w
e
ver
,
t
h
e fre
q
u
e
ncy
cont
rol
w
o
r
d
sh
ou
ld
be sm
al
l en
ough
to r
e
du
ce t
h
e co
m
p
u
t
atio
n er
ror
[
8
]. In
t
h
e
p
r
op
o
s
ed desig
n
ar
ch
itectu
r
e, th
e
q
u
a
dratu
r
e DDFS co
m
p
rises two reg
i
sters,
two add
e
rs an
d
two
m
u
ltip
liers [8
].
O
u
r
pro
p
o
s
ed
tech
n
i
qu
e aim
s
to
k
e
ep
th
e ad
v
a
n
t
ag
es of
th
e Tr
i
g
ono
m
e
t
r
ic Ap
pr
ox
im
a
tio
n
Method
and al
s
o
t
o
re
duce t
h
e com
put
at
i
on
wave e
r
r
o
r
.
Fo
r t
h
i
s
ob
ject
i
v
e
,
we
pr
o
pose t
o
dec
o
m
pose t
h
e co
m
p
l
e
t
e
in
terv
al
0
i
n
t
o
su
bi
nt
er
val
s
:
whe
r
e t
h
e re
fe
rence
phases
0
,
,⋯
,
have
the
fol
l
o
wi
n
g
e
x
pr
essi
on
,
;
0
,⋯,
.
(6)
The
fi
rst
or
d
e
r
of
Tay
l
or'
s
seri
es
o
f
t
r
i
g
o
n
o
m
e
t
r
i
c
fu
nct
i
o
n
s
i
n
a
sm
al
l
l
e
ngt
h
subi
nt
er
val
, allo
w to
write:
sin
;
cos
1
. T
hus
,
we ca
n a
p
p
r
oxi
m
a
t
e
sin
as,
sin
cos
s
i
n
(7)
Furt
herm
ore, t
h
e localization of the
refe
re
nce su
b
i
n
t
er
v
a
l co
r
r
e
spon
d
i
ng
to
inpu
t phase allo
w
s
devel
opi
ng
t
w
o a
p
p
r
oxi
m
a
t
i
o
ns m
e
t
hods
,
R
e
ference
d
Tr
i
gon
omet
ri
c A
ppr
o
x
i
m
at
i
o
n
M
e
t
h
od
(R
TA
M
):
we co
m
p
ute th
e si
n
e
v
a
lue in
relatio
n to
θ
as fo
llo
ws,
∀
∈
;
s
in
cos
s
i
n
(
8
)
Symmet
r
i
c
al
R
e
ference
d
Tr
i
gon
omet
ri
c
A
ppr
o
x
i
m
at
i
o
n M
e
t
h
od (SR
T
A
M
):
w
e
co
mp
u
t
e
th
e s
i
n
e
va
lu
e
in
relation
to d
i
stan
ces
|
θ
|
and
|
θ
|
as fo
llo
ws,
∀
∈
;
sin
cos
s
i
n
θ
cos
s
i
n
θ
θ
(9)
Whe
r
e t
h
e c
o
efficients
cos
,s
i
n
sh
oul
d
be
k
n
o
w
n acc
or
di
n
g
t
o
t
h
e
s
e
t
refe
rence
an
gl
es.
To c
o
m
p
are t
h
e com
put
at
i
on
err
o
r
of t
h
ese
m
e
t
hods
, we
u
s
e t
h
e resi
dual
err
o
r
|
sin
s
i
n
∗
|
and
the m
ean of tot
a
l squa
re
residual error
between
sin
and its approxim
a
t
ed val
u
e
sin
∗
fo
r
poi
nt
s
as
fo
llows,
∑
sin
s
i
n
∗
(1
0)
Fi
gu
re 6 a
n
d
Fi
gu
re 7 s
h
ow
t
h
e resi
d
u
al
e
r
r
o
r
ove
r t
h
e
r
a
nge
0
according to t
h
e followi
ng
param
e
ters: phase accum
u
lator size
of
16
,
200
,
3
2
and
6
4
, re
spectivel
y. It is clear that
th
e Symmetri
cal RTAM has th
e least resid
u
a
l erro
r
than Refe
re
nc
ed T
A
M and Trigonom
etric AM.
Ad
di
t
i
onal
t
o
t
h
e di
st
ri
but
i
o
n
of
resi
d
u
al
er
r
o
r
,
we e
v
al
uat
e
the effect of
the num
b
er
of refe
rence phas
es
as
p
r
esen
ted in Fi
g
u
re
8
.
Th
e m
ean
o
f
to
tal
resid
u
a
l erro
r
de
creases acc
ordi
ng to the
number of
refe
re
nc
e
p
h
a
ses wh
ich
b
eco
m
e
s an
im
p
o
r
tan
t
p
a
rameter to
i
m
p
r
o
v
e
the qu
ality o
f
syn
t
h
e
sizers.
W
e
no
te th
at th
e
SRTAM m
e
t
h
od
has a low to
tal residual error th
an
th
e RTAM on
e. Hen
c
e, we retain
th
e SRTAM
app
r
oxi
m
a
t
i
on m
e
t
hod f
o
r t
h
e
desi
g
n
an
d t
h
e eval
uat
i
o
n o
f
perf
o
r
m
a
nces i
n
t
h
e ne
xt
sect
i
on. F
o
r t
h
e
d
e
si
gn
,
th
is arch
itectu
r
e req
u
i
res
on
e m
u
ltip
liers again
s
t tw
o
i
n
[8
],
o
n
e
ad
d
e
r
an
d a ROM
me
m
o
ry to
st
ore
2
1
w
o
r
d
s c
o
rres
p
o
n
d
in
g to
c
o
sine a
n
d
sin
u
s
refe
re
nce c
o
e
fficients. T
h
e
require
d
Matlab-Sim
u
link
b
l
o
c
k
s
will
b
e
p
r
esen
ted
and
d
e
tailed
in
th
e n
e
x
t
sectio
n.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Ref
e
rence
d
A
p
pro
x
i
m
at
i
o
n
Te
chni
que
f
o
r
a
Ro
m Less
Sw
e
e
p
Fre
q
uency
Synt
hesi
zer (
A
t
m
a
n
J
b
ari
)
1
217
0
0.
2
0.
4
0.
6
0.
8
1
1.
2
1.
4
1.
6
0
0.
2
0.
4
0.
6
0.
8
1
1.
2
1.
4
x 1
0
-3
P
h
a
s
e(r
a
d)
R
e
s
i
dual
E
r
r
o
r
T
r
i
g
o
nom
e
t
r
i
c
A
M
Ref
e
ren
c
ed
T
A
M
Sym
m
e
tr
i
c
a
l
R
T
AM
0
0.
2
0.
4
0.
6
0.
8
1
1.
2
1.
4
1.
6
0
0.
2
0.
4
0.
6
0.
8
1
1.
2
1.
4
x 1
0
-3
P
h
as
e
(
r
a
d)
R
e
s
i
d
ual
E
r
r
o
r
T
r
i
gon
om
et
r
i
c
A
M
Ref
e
re
nc
e
d
T
A
M
Sym
m
e
tr
i
c
a
l
R
T
AM
Figure 6. Residu
al
error v
e
rsus p
h
ase for
3
2
Figure 7. Residu
al
error v
e
rsus p
h
ase for
6
4
Fi
gu
re
8.
M
ean
o
f
T
o
t
a
l
R
e
sidual error
versus the
num
b
er of re
fere
nce
pha
s
es
4.
RESULTS
A
N
D
DI
SC
US
S
I
ON
4.
1.
Simulink impl
ementati
on
and Evaluation
of the
W
ave
Arithmetic
Unit
In t
h
i
s
sect
i
o
n,
we
pr
o
pose
t
h
e M
a
t
l
a
b-
S
i
m
u
l
i
nk i
m
pl
em
ent
a
t
i
on an
d
eval
uat
i
o
n
of
t
h
e
Wav
e
Arith
m
e
tic Unit th
at co
m
p
u
t
es th
e si
n
e
v
a
lu
e of the inpu
t ph
ase accord
i
n
g
t
o
SR
TA
M
ap
pr
o
x
i
m
at
i
on
m
e
t
hod.
Fi
g
u
r
e
9 gi
ves t
h
e r
e
qui
red i
n
p
u
t
and
o
u
t
p
ut
si
g
n
al
s w
h
i
l
e
Fi
g
u
re
10
pr
esent
s
t
h
e Si
m
u
l
i
nk-desi
g
n
architecture ac
cording t
o
th
e fo
llo
wi
n
g
p
a
rameters:
-
WAU: i
n
pu
t-14
b
its to
ou
tpu
t
-10
b
its.
-
Act
i
v
at
i
o
n
on
r
i
si
ng e
d
ge
of cl
ock
si
g
n
al
.
-
Num
b
er
of re
ference
phases:
3
2
.
-
Refere
nce a
ngl
es:
θ
(ra
d
)
=
[0
0
.
0
4
9
0
.
0
9
8
0
.
1
4
7
0.196
0
.
24
5
0
.
29
4
0
.
34
3
0
.
39
2
0
.
44
1 0.490
0.539
0
.
5
8
9
0.638
0
.
6
8
7
0
.
73
6
0
.
78
5
0
.
83
4
0
.
88
3
0
.
93
2 0.981
1.030
1.079
1
1.
12
9
1.
17
8
1.
22
7
1
.
2
7
6
1.
32
5
1.
37
4
1.
42
3 1.
4
7
2
1
.
5
2
1
1.
5
70]
-
Refere
nce qua
ntized
c
o
efficients on
10bits
form
at:
InCos
=[
102
3
1
022
10
19
101
2
1
004
993
979
964
946
925
903
878
851
822
791
758
724
687
649
609
568
526
482
437
391
344
297
2
4
8
1
9
9
1
5
0
100
5
0
0
]
.
0
20
40
60
80
10
0
12
0
14
0
16
0
18
0
20
0
10
-1
2
10
-1
0
10
-8
10
-6
10
-4
10
-2
Nu
m
b
e
r
o
f
Re
f
e
r
e
n
c
e
P
h
a
s
e
s
M
ean
T
R
E
RT
A
M
SR
T
A
M
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E
V
o
l
.
6,
No
. 3,
J
u
ne 2
0
1
6
:
12
1
3
– 12
22
1
218
InSin
=
[
0
50
100
150
199
248
297
344
391
437
482
526
568
609
649
687
724
758
791
822
851
878
903
9
2
5
9
4
6
96
4
9
7
9
993
1
004
1012
10
19
1022
102
3
]
.
Fi
gu
re
9.
I
n
p
u
t
s
an
d
o
u
t
p
ut
s o
f
SR
T
A
M
base
d
Wave
A
r
i
t
h
m
e
t
i
c
Uni
t
Fig
u
re
10
.
Simu
lin
k arch
itectu
r
e of
wav
e
ari
t
h
m
e
tic u
n
it 14b
its to
10
b
its
Fig
u
re
11
.
Simu
lin
k-m
o
d
e
l for DDS ev
al
u
a
tio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Ref
e
rence
d
A
p
pro
x
i
m
at
i
o
n
Te
chni
que
f
o
r
a
Ro
m Less
Sw
e
e
p
Fre
q
uency
Synt
hesi
zer (
A
t
m
a
n
J
b
ari
)
1
219
Figure 12. Simulink
arc
h
itect
ure
of the
phas
e accum
u
lator
For t
h
e evaluation, the m
o
st used
factor whic
h eval
uates the perform
ances of
direct digital
sy
nt
hesi
zer
i
s
t
h
e S
p
uri
ous
f
r
ee dy
nam
i
c range
(S
FDR
)
[8
]
,
[1
2]
. T
h
i
s
val
u
e
rep
r
ese
n
t
s
t
h
e
rat
i
o
of t
h
e
po
w
e
r
in
th
e fund
am
e
n
tal frequ
en
cy,
S
, to
p
o
wer
o
f
th
e larg
est spuriou
s
sig
n
al,
R
, reg
a
rd
less
o
f
wh
ere it falls i
n
th
e
fre
que
ncy
s
p
e
c
t
r
um
. To t
h
i
s
end
,
we
ha
ve
im
pl
em
ent
e
d t
h
e com
p
l
e
t
e
archi
t
ect
u
r
e o
f
DD
S ba
sed
o
n
t
h
e
p
r
op
o
s
ed
Wave Arith
m
e
t
i
c un
it on
Matlab-Si
m
u
lin
k
env
i
ronm
ent. T
h
e a
r
chitecture is s
h
own in Figure 11,
using the pha
s
e accum
u
lator of
16
bits presente
d in
Figure 12, che
bychev low pa
ss filter : pass band
f
r
e
q
u
e
n
c
y = 50
0KH
z
,
p
a
ss
ban
d
r
i
pp
le= 1dB, D
i
g
ital to
An
alog
Conv
er
t
e
r
:
10
b
its, Clock
:
1
M
H
z
. Fu
rth
e
r
,
a
co
m
p
u
t
er
p
r
o
g
ram
h
a
s b
e
en
written
i
n
MATLAB
t
o
sim
u
l
a
te th
e pro
p
o
s
ed
arch
itectures.
The SF
DR
i
s
eval
uat
e
d and
pl
ot
t
e
d i
n
Fi
g
u
r
e 13 a
nd Fi
gu
re 14
vers
us f
r
e
que
ncy
co
nt
r
o
l
wo
rd f
o
r
d
i
fferen
t
v
a
lu
es o
f
t
h
e ord
e
r
o
f
low-p
a
ss filter and
fo
r
16
and
32
refere
nces a
ngles
respectively. As a res
u
lt,
the SFDR cha
nge
s form
65
for sm
a
ll v
a
lu
es to
43
fo
r hi
gh
er
values
o
f
FC
W. F
u
rthe
rm
ore, there
is
sm
al
l
im
prove
m
e
nt
of
SFR
D
by
an
am
ount
of
1
f
o
r
3
2
re
fer
e
nce a
ngl
es
. R
e
gar
d
i
n
g t
o
t
h
e
im
pact
of l
o
w
-
p
a
ss
filter, t
h
e
SFDR
will b
e
u
n
c
h
a
n
g
e
d from
th
e 6
th
orde
r. T
h
e
obtained val
u
es
of SFDR are s
u
fficient
for
th
e pro
d
u
c
tion of si
n
u
s
o
i
d
a
l
wav
e
s
with
low
h
a
rm
o
n
i
c con
t
ribu
tion
.
In
ad
d
ition
t
o
p
r
ev
iou
s
sim
u
lati
o
n
,
we
com
p
are the s
p
uri
ous
content
of
our
m
e
thod
and the c
o
nve
ntional DDF
S
a
r
ch
itecture, as
illustrated in F
i
gure
1
5
. A
s
a con
s
eq
u
e
n
ce, t
h
e pr
opo
sed
m
e
th
od
pr
ov
id
es th
e sa
m
e
SFD
R in
th
e stud
ied
r
a
ng
e of
fr
eq
uen
c
y
cont
rol
w
o
r
d
a
n
d
can
d
be i
n
t
e
grat
e
d
i
n
t
h
e
sy
nt
hesi
zer
wi
t
h
hi
g
h
per
f
o
r
m
a
nce a
n
d
l
o
w c
o
m
p
l
e
xi
ty
.
Fi
gu
re 1
3
. Sp
u
r
i
o
us
F
r
ee Dy
n
a
m
i
c
R
a
nge ve
rsus
Fre
que
ncy
c
o
n
t
rol
wo
rd
f
o
r
1
6
Fi
gu
re 1
4
. Sp
u
r
i
o
us
F
r
ee Dy
n
a
m
i
c
R
a
nge ve
rsus
Fre
que
ncy
c
o
n
t
rol
wo
rd
f
o
r
3
2
0
0.
2
0.
4
0.
6
0.
8
1
1.
2
1.
4
1.
6
1.
8
2
x 1
0
4
0
10
20
30
40
50
60
70
80
FC
W
S
F
DR(
d
B
)
F
i
l
t
er
o
r
de
r
=
4
F
i
l
t
er
o
r
de
r
=
6
F
i
l
t
er
o
r
de
r
=
8
F
i
l
t
er
o
r
de
r
=
1
0
0
0.
2
0.
4
0.
6
0.
8
1
1.
2
1.
4
1.
6
1.
8
2
x 1
0
4
0
10
20
30
40
50
60
70
80
FC
W
S
F
DR(
d
B
)
F
i
l
t
er
or
der
=
4
F
i
l
t
er
or
der
=
6
F
i
l
t
er
or
der
=
8
F
i
l
t
er
or
der
=
1
0
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
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08
IJEC
E
V
o
l
.
6,
No
. 3,
J
u
ne 2
0
1
6
:
12
1
3
– 12
22
1
220
Figure 15. SF
DR
of DDSF
-ROM
and SRT
A
M
for
3
2
4.
2.
Design
and
Simulink Imple
mentati
on
of
a Sweep
Freq
uency S
y
nthes
i
z
e
r
To im
pro
v
e t
h
e perf
orm
a
nce
s
of t
h
e m
easurem
ent
bl
ocks of am
pl
i
t
ude or pha
se of st
u
d
i
ed sy
st
em
s
vers
us
i
n
p
u
t
fr
eque
ncy
,
we p
r
op
ose
t
o
desi
g
n
a
s
w
ee
p fre
q
u
ency
sy
nt
hesi
zer whi
c
h pr
ov
i
d
es
t
w
o
c
h
a
n
n
e
l
s
as
sho
w
n i
n
Fi
g
u
r
e 3:
m
a
i
n
channel
f
o
r exci
t
i
ng sy
st
em
,
and refere
nce channel for m
eas
urem
ent circuit. The
Sim
u
l
i
nk i
m
pl
em
ent
a
t
i
on i
s
gi
ve
n i
n
Fi
gu
r
e
1
6
.
The
m
a
in a
n
d
re
fere
nc
e cha
n
nel
s
are
n
o
t
e
d
and
resp
ectiv
ely. Th
e HF to
LF ci
rcu
it is also
i
m
p
l
em
en
te
d
u
s
ing
th
e produ
ct blo
c
k
and
low pass-filter. In
Fi
g
u
re
17
, we
pl
ot
t
h
e fol
l
o
wi
n
g
si
gnal
s
:
pha
se a
ccum
u
l
a
t
o
r, m
a
i
n
cha
n
nel
,
r
e
fere
nce c
h
an
nel
an
d m
easurem
ent
signal fo
r
2000
,
_
500
and
1
. The s
p
ectrum
s
of diff
e
r
e
n
t signals are
shown
i
n
Fi
g
u
r
e 18
. We not
e
t
h
at
t
h
e
sy
nt
hesi
ze
d fre
q
u
e
n
c
ies
co
rresp
ond
to th
eoretical valu
es:
30,517
;
3
8
,
146
; and the
freque
ncy of t
h
e m
easurem
e
n
t signal
7
,
62
.
In t
h
e s
w
ee
p
m
ode, we
ha
ve to c
h
ange t
h
e fre
quency c
ont
rol
word
for t
h
e sam
e
value of
_
to
kee
p
t
h
e measurem
ent fre
que
ncy
co
nst
a
nt
.
Fo
r t
h
i
s
pr
op
ose
d
ci
rcui
t
,
we
gi
ve i
n
Fi
gu
re
1
9
,
si
m
u
latio
n
s
ou
tpu
t
s fo
r the co
n
t
ro
l range:
5121536
and
_
50
cor
r
esp
o
ndi
ng t
o
synthesized int
e
rval
7,8125
23,4375
and m
easurem
ent fre
quency
of
762
. It i
s
clear that
the m
easurement signal
has
consta
nt fre
quency duri
ng the
swe
e
p cy
cle whose
val
u
e is c
ont
roll
ed
by
refe
rence
w
o
r
d
_
. Th
is co
nsequen
ce
v
a
lid
ates
th
e m
a
in
o
b
j
e
ctiv
e of
o
u
r
work
.
Fi
gu
re 1
6
. Si
m
u
l
i
n
k
-
arc
h
i
t
ect
ure
an
d
e
v
al
uat
i
on o
f
S
w
ee
p DD
S
200
0
4
000
60
00
800
0
100
00
120
00
1
400
0
16
000
35
40
45
50
55
60
FC
W
SF
D
R
(
d
B)
DDF
S
-RO
M
Sy
m
m
e
tr
i
c
a
l
R
T
AM
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Ref
e
rence
d
A
p
pro
x
i
m
at
i
o
n
Te
chni
que
f
o
r
a
Ro
m Less
Sw
e
e
p
Fre
q
uency
Synt
hesi
zer (
A
t
m
a
n
J
b
ari
)
1
221
Fi
gu
re
1
7
.
P
h
a
s
e
an
d o
u
t
p
ut
c
h
an
nel
s
of
t
h
e pr
o
pose
d
Swee
p DD
S
Fi
gu
re
1
8
.
Spe
c
t
r
um
of t
h
e
m
a
i
n
cha
n
nel
,
re
fere
nce c
h
a
nne
l
and
m
easurem
ent
wave
Fi
gu
re 1
9
. O
u
t
put
s
o
f
S
w
ee
p DD
S
f
o
r:
512
,
1536
and
_
50
.
0
0.
5
1
1.
5
2
2.
5
3
3.
5
4
4.
5
x 1
0
5
-
100
-8
0
-6
0
-4
0
-2
0
0
20
40
F
r
eque
nc
y
(
k
H
z
)
dB
m
RB
W:
4
8
8
.
2
8
Hz
, NF
FT
: 30
73
, Sp
an
: 50
0 kH
z,
C
F
:
2
5
0
k
H
z
M
e
as
u
r
em
en
t
c
h
ann
el
M
ain c
h
a
nnel
R
e
f
e
r
e
nc
e
c
h
anne
l
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E
V
o
l
.
6,
No
. 3,
J
u
ne 2
0
1
6
:
12
1
3
– 12
22
1
222
5.
CO
NCL
USI
O
N
This
work ha
s
prese
n
ted the a
r
chitecture
of a
direct
di
gi
t
a
l
f
r
eq
ue
ncy
sy
nt
h
e
si
zer f
o
r
i
n
st
r
u
m
e
nt
at
i
o
n
sy
st
em
s. Al
l
o
f
t
h
e
re
qui
red
bl
oc
ks
ha
ve b
een
det
a
i
l
e
d, s
i
m
u
l
a
t
e
d and
di
scuss
e
d
.
I
n
t
h
i
s
co
nt
e
x
t
,
w
e
ha
ve
pr
o
pose
d
a
n
ovel
a
p
pr
oxi
m
a
t
i
on m
e
t
h
o
d
w
h
i
c
h ex
pl
oi
t
s
t
h
e re
fe
r
e
nce
phase
s a
n
d
desi
gne
d
a
W
a
ve
Arith
m
e
tic Un
it. Th
is
WAU
h
a
s low
h
a
rd
ware co
m
p
lex
ity u
s
ing
o
n
e
m
u
ltip
lier, o
n
e
add
e
r and
a low size
me
m
o
ry of reference c
o
efficients. The m
a
in adva
ntage of
th
e p
r
o
p
o
s
ed
circu
it is to
p
r
ov
id
e two
in
tegrated
channels: a m
a
in cha
nnel for excitation and
a refere
nce
c
h
a
nnel
f
o
r m
easurem
ent
bl
ock.
Hence
,
t
h
e am
pl
i
t
ude
and
pha
se an
d ot
he
r param
e
t
e
rs can be m
easure
d
at
t
h
e sam
e
operat
i
n
g f
r
eq
ue
ncy
whi
c
h cor
r
es
p
o
n
d
s
t
o
t
h
e
di
ffe
re
nce
bet
w
een
re
fere
nc
e an
d m
a
i
n
fre
que
nci
e
s.
Si
m
u
l
a
t
i
ons
res
u
l
t
s
dem
onst
r
at
ed
t
h
e ef
fect
i
v
e
n
e
ss an
d
the pe
rform
a
nces of the
design arc
h
i
t
ect
ure
s
t
h
at
ca
n
be i
m
prove
d acc
or
di
n
g
t
o
re
fere
n
ce p
h
ases a
n
d
l
o
w
-
p
a
ss filters. Con
s
eq
u
e
n
tly, it i
s
v
e
ry u
s
efu
l
to
in
tegrat
e th
e p
r
o
p
o
s
ed
circu
it in
ASIC or FPGA for indu
strial
ap
p
lication
s
.
REFERE
NC
ES
[1]
K. N. Huang and Y. P. Hua
ng, “Multiple-f
reque
nc
y
u
ltrasoni
c di
stance m
easure
m
ent using direc
t
digit
a
l frequ
e
n
c
y
s
y
nthes
i
zers
,
”
S
e
nsors and Actuators A,
vol. 149
,
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, 2009
.
[2]
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y
and R. K
e
mpte
r, “
M
ulti
carri
er com
m
unica
tion t
echniques for spectrum sensing and
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i
o
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EEE
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. 80-85
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[3]
A.
Jbari,
et al.
,
“
M
ultiplexed Frequenc
y Spec
tru
m
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rum
e
ntation for the Chara
c
ter
i
z
a
tion of Multiple
QCM-Ba
se
d Biose
n
sors,
”
Inter
national
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e
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tions
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Valencia, Espag
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2007.
[4]
J. M. R. Salis, “Spurious Perf
or
mance of Direct Digital S
y
n
t
hesi
zers Generating Modulated
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c
tr
ote
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hnica
l confer
en
ce
, vol.1, pp
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L. Wang
, “Testing of Rad
i
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is
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., “A Blind C
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Omran,
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“A ROM-Le
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y
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y
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Yi
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i
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O
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[9]
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[10]
A.
Ashrafi,
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y
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y
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hev poly
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[11]
R.
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a
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p
a
d
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ay
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ory
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