MELECON
'85/
Volume
11:
Digi al Signal P ocessing
A. Luque, A.
R.
Figuei as Vidal, V. Cappellini
(eds
.)
Else ie Science Publishe s B. V. (No h·Holland)
I©
IEEE 1985 295
DESIGN
~ND
IMPLEMENTATION OF A
2048
-FFT
CAPTURE SPECTRUM
ANALYZER
M.
~m
e
ngual,
J.
Casamajo ,
G.
Vazquez,
J.
Laba a
Dep o.
P ocesado
de
Se~al
en
Comunicaciones
E.T.S.I.
Telecomunicaci6n.
Apdo.
30002,
08071
Ba celona,
Spain
This
pape
desc ibes
he
ha dwa e
implemen .a ion
o
a
digi al
:Spec um
analyze
which,
by
using
a
cap u e
p ocess
o
he
signal
unde
p ocessing,
pe o ms
some
non
pa ame ic
signal
p ocessing
echniques.
All
he
possibili ies
o
implemen
a
spec um
analyze
will
a ise
o
a
bank
il e
analysis
app oach.
When
he
ins umen
wo ks
as
an
o -line
p ocesso ,
he
bank
il e
can
be
a
linea
ans o m,
which
esul s
in
a FFT
as
conce ns
wi h
he
analysis
o
he
powe
densi y
con en
o
he
da a
sample.
Thus
he
FFT
p ocesso
can
be
iewed
as
a
se
o
equispaced
il e s
wi h
non-ideal
cu -o
and
seconda y
lobes
bu
op imum
o
analyze
pu e
ones
in
a
whi e
noise
en i onmen .
1.
INTRODUCTION
Gi en
a
andom
p ocess
x (
)
, a
way
o
cha ac e ize
i
is
by
means
he
powe
spec al
densi y.
This
is
an
ideal
unc ion
which
ela es
how
he
signal
powe
is
dis ibu ed
in
he
ecuency
domain.
~11
he
me hods
o
es ima ing
he
powe
spec um
a ise
om
a
bank
o
band-pass
il e s
(al hough
hey
mus n'
be
implemen ed
necessa ily
so).
I
hese
il e s
a e
signal
dependen ,
pa ame ic
me hods
a ise
and
he
non-pa ame ic
a
any
o he
case.
Among
he
las
ones,
he
mos
popula
a e
hose
which
make
use
o
he
FFT
algo i hm.
One
o
hese
me hods
is
he
W.O.S.A.
(weigh ing
o e lapped
spec um
a e aging).
~nalyze
a chi ec u e
has
been
designed
o
acomplish
wi h
his
me hod.
The
echnique
o
es ima e
he
spec um
by
means
he
W.O.S.A.
is
he
ollowing:
gi en
a
signal
sample
eco d
x(n),
O.,:n.,:M-1,
i
is
di ided
in o
L
segmen s
(wi h
possible
o e lapping
be ween
hem)
o
N
poin s
each
one.
Whe e
N
is
he
FFT
size
ha
p ocesses
he
analyze .
Each
segmen
is
windowed
( h ee
pos-
sible
windows
a e
a ailable:
ec angula ,
Ba le
and
Hanning)
and
FFT
p ocessed.
Finally,
he
modi ied
pe iodog ams
a e
a e aged,
by
means
o
an
uni o m
o
exponen ial
a e age ,
o
achie e
he
spec al
es ima e.
2.
IMPLEMENTATION
Fo
implemen ing
he
W.O.S.A.
me hod,
se e al
a chi ec u e
models
a e
employed,
which
a e
complexi y-p ice
dependen s.
I
he
FFT
p ocesso
is
high
speed
enough,
i
could
be
hough
o
disposse
wo
memo y
bu -
e s;
while
one
o
hem
is
adqui ing
signal,
CH
2185-7/85/0000-0295(8)/$01.00
©19851EEE
he
F T
o
he
o he
is
he
way
in
which
anal
yze s.
To
achie e
audio
equencies,
i
echniques
and,
in
any
pu pose
a chi ec u es.
one
is
e alua ed.
This
wo k
eal
ime
spec um
eal
ime
analysis
upon
is
necessa y
bi -slice
case,
he
use
o
special
This
is
a
adeo
when
one
is
no
in e es ed
in
an
expensi e
ins umen .
The
o he
possibili y
is
ha
o
adqui ing
he
signal
unde
es
("cap u e"),
s o ing
i
in
a
memo y
bu e
and
es ima ing
he
powe
spec um
densi y
o -line.
An
a chi ec u e
o
achie e
his
idea
is
much
mo e
simple
and
allows
he
use
o
con en ional
16
bi
mic op ocesso s.
Al hough
a
]JP
design
can'
achie e
eal
ime
p ocessing
upon
a
bandwid h
o
20
KHz,
howe e
i
is
possible
eal
ime
p o·cessing
un il
2
KHz
(depending
upon
he
speed
p ocessing
and
he
FFT
size).
Ou
design
is
acco dingly
wi h
his
philosophy.
Fo
cap u ing
he
signal
i
is
p o ided
20
K
wo d
o
s a ic
RAM.
All
he
associa ed
unc ions
he
analyze
achie es
a e
suppo ed
in
a
2048
sample
FFT.
I
is
well
known
ha
spec al
esolu ion
is
closely
ela ed
o
he
in e se
o
he
ime
domain
wid h
o
he
window.
So
ha
spec al
esolu ion
in
he
W.O.S.~.
me hod
1s
dependen
upon
he
ime
du a ion
o
he
2048
poin s.
Howe e ,
because
o
he
20
K
wo ds
o
signal
s o ed,
i
is
possible
h oughou
he
buil
in
"zoom
FFT"
o
achie e
a
spec al
esolu ion
en
imes
g ea e
he
W.O.S.~.
Besides,
ano he
12 K
wo d
s a ic
[lM·I
a e
sup-
po ed
in
he
basic
model
o
allow
in ennedia e
esul s.
~
u he
enla gemen
o
32
K ·1.
is
o eseen.
So
i
will
be
possible
o
slo e
ideal
measu emen s
and
compa e
wi h
ac ual
one's.
296
M.
Amengual
e
al.
RAM
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·~u-~ u
::=:::;>
kT
~l loiAL
C:o cTil•UJUI.
l j
C.P.V.
I
"'
.I
;"P.
iC
6IDaO
!
IIWU+--
l &I!&O~O
~
-(-
c:.>~.,A.OLJ.QI.
4~
~
~
A niA&.INOiNc;
-
Sg_
-
"'lo
T
-1
1011 1
j::j 8
8 1 .
._
_...,,
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+---
<.-.
,...__~
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--
Figu e
1.
Gene al
Block
diag am.
The
ROM
memo y
uni
is
also
32
KW
size.
I
isn'
oo
la ge
because
da um
ables
mus
be
s o ed
besides
e e ences
and
p og am
i sel .
The
adquisi ion
uni
consis
in
an
an ialiasing
analog
il e
bank
(C.C.D);
a
sample
and
hold
and
a
12
bi
A/D
con e e ,
om
which
an
inpu
dynamic
ange
o
abou
72
dB
is
a ained.
The
analyze
has
also
been
i ed
wi h
he
IEEE-
bus,
by
means
o
a
bus
con olle
chip.
So
ha ,
i
can
wo k
as
a
pe iphe ic
om
a
hos
compu e
To
pe o m
he
di e en
p ocessing
pos-
sibili ies,
he
use
manages
he
analyze
h oughou
a
key
boa d;
so
ha ,
he
ha dwa e
design
also
inco po a es
a
p og ammable
keyboa d
con olle .
Among
he
ea u es
o
his
keyboa d
con olle
chip
a e:
o
es ablish
se ial
com-
munica ions
(RS-232)
wi h
pe iphe ical
de ices,
as
p in e s
o
plo e s,
and
also
p og amable
one
gene a o
which
sample
and
hold
uni .
p o ides
a
go e ns
he
G a!=hic
esul s,
and
di e en
menus
a e
displayed
in
an
in elligen
g aphic
e minal
which
is
~P
con olled
(by
a
Z-80
~P).
Com-
munica ions
be ween
he
CPU
and
he
g a ic
e minal
a e
also
p o ided
h oughou
he
IEEE-
bus.
The
global
a chi ec u e
o
he
analyze
can
be
iewed
in
igu e
(1).
In
his
design,
he
con ol
uni ,
so
as
he
compu a ional
uni
is
he
~p
MC68000.
THis
CPU
disposses
o
16
in e n
egis e s
o
32
bi
( 8
da a
egis e s
and
8
add ess
egis e s).
In e ac ion
be ween
he
adquisi ion
uni
o
he
keyboa d
and
he
CPU
is
achie ed
by
in e -
up ions.
While
he
g aphic
e minal
com-
munica ions
and
he
RS-232
ones
(p o ided
by
he
keyboa d
con olle )
a e
polling
pe o med.
Th ee
in e nal
in e up
le els
a e
allowed.
A
he
highe
one,
uni
adquisi
ion
and
key-
boa d
a e
disabled;
his
co esponds
o
he
CPU
p ocessing
ime.
A
he
nex
le el,
uni
adquis
i
ion
is
enabled
and
keyboa d
disabled
and
a
he
hi d
le el,
keyboa d
and
uni
adquisi ion
a e
enabled,
bu
only
keyboa d
is
unc ionally
enabled
because
he
keyboa d
clock
is
ese ,
so
he
adquisi ion
uni
is
in
idle
s a e.
Communica ions
wi h
a
hos
compu e ,
al hough,
i
isn'
s ill
so wa e
de elopped,
also
will
Implemen a ion
o
a
2048-FFT
Cap u e
Spec um
Analyze
297
be
in e up
pe o med
in
he
IEEE-bus.
The
p esen a ion
uni ,
i.e.
he
!Jl-,lphic
e :minal
has
been
designed
in elligen
(i
is
suppo ed
by
a
Z-80)
o
discha ge
he
MC6BOOO
om
askes
being
no
ypically
compu a ionals.
This
disposses
o
a
g aphic
sc een
con olle
pe o ms
a
512
poin
esolu ion
in
he
ho izon al
axis
and
256
poin
esolu ion
in
he
uni
ha
e ical
one.
I
can
be
seen
a
igu e
1,
ha
no
loa ing-
poin
cop ocesso
is
included.
Because
o
his,
all
he
ma hema ics
ope a ions
(ei he
linea
o
non-linea )
mus
be
pe o med
by
he
68000
CPU
in
ixed-poin
o ma .
Special
ou ines
ha e
been
de elopped
o
e alua e
non-linea
ma hema ics
unc ions:
loga i hms,
exponen ials
and
phases.
E alua ion
o
lhal
unc ions
is
w ·(o ·mcd
wi h
aid
[o
some
signi ica i c
alues
which
a c
s o ed
in
he
110~1
memo y
.
Fo
he
loga :i hm
e alua ion,
i
has
been
implemen ed
he
algo i hm
li)
log
x =
log
2 +
log
x/2
(
1)
This
ecu sion
is
ollowed
un il
x
is
less
o
equal
han
a
ce ain
alue
(
1024),
in
which
case,
he
loga i hm
alue
is
ound
a
he
able.
Exponen ial
ecu sion
is
jus
he
in e se
han
he
loga i hm
one.
I
xis
less
han
log
(1024),
hen
ex
may
be
ob ained
di ec ly
om
he
loga i hms
able;
i
x
is
g ea he
han
log
1024
i
will
be
x=n
log
2 +
log
u,
whe e
log
u <
log
1024,
so
he
p oblem
now
is
o
ind
e1n u
a
he
able
and
inally
ex=2n
e1n u
Fo
calcula ing
phases,
he
algo i hm
ollowed
has
been
(2)
a c
g
x=TT/2 -
a c
g
1/x;
i
x>l
(
2)
I
x<l
hen
a c
g
x
is
ob ained
om
abula ed
alues.
Ob iously,
since
he
CPU
wo ks
o e
in ege
numbe s,
all
numbe s
ha
a e
less
han
one
mus
be
le
shi ed
decimal
poin
s o ed.
Also
i
is
s o ed
in
ROM
he
cosinus
and
sinus
necessa y
alues
o
compu ing
a
2048
poin
F.F.T.
Fo
compu ing
a
2048
poin
F.F.T.
i
is
necessa y
(3).
sen
21!
i
20411
cos
211
i
20~0
. i
="
0,
...
1023
102
3
I
could
be
su icien
s o e
(4),
i.e.
a
quad an
(
3)
sen
2TT
i
2048
(
4)
Ou
!'o
op imicing
execu ion
ime
i
has
been
abula ed
(5)
scn
21! i
2048
i
0,
...
1535
(
5)
Indexing
om
i=O
sinus
a e
ob ained
and
om
i=0+512,
cosinus
do
.
Also
i
has
been
abula ed
he
bi - e e sed
_
unc ion.
The
unc ions
included
in
so wa e
op ions
a e:
W.O.S.A.,
signal
enhacemen ,
spec um
a e aging,
zoom-FFT,
au oco ela ion,
Hilbe
ans o m,
en elope,
ins an aneous
equency,
minimum
phase
and
complex
and
eal
ceps um.
O he
g aphic
ea u es
a e
included
which
allow
on-
line
signal
edi ion
bo h
in
ime
and
equency
do111ain.
I
is
expec ed
o
ex end
he
sys em
o
pe o ming
wo
channel
signal
p ocessing.