UNIVERSITY OF CALIFORNIA AT...
10
UNIVERSITY OF CALIFORNIA AT BERKELEY Decimation and Interpolation Decimation • Anti-aliasing (decimation) filtering before downsampling • Filter has cutoff frequency of π/M Interpolation • Anti-imaging (interpolation) filtering after upsampling • Filter has cutoff frequency of π/L M h[n] L g[n]
Transcript of UNIVERSITY OF CALIFORNIA AT...
UN
IVE
RS
ITY
OF
CA
LIF
OR
NIA
AT
BE
RK
EL
EY
Dec
imat
ion
and
Inte
rpol
atio
n
Dec
imat
ion
• A
nti-a
liasi
ng (
deci
mat
ion)
filte
ring
befo
re d
owns
ampl
ing
• F
ilter
has
cut
off f
requ
ency
ofπ
/M
Inte
rpol
atio
n
• A
nti-i
mag
ing
(inte
rpol
atio
n) fi
lterin
g af
ter
upsa
mpl
ing
• F
ilter
has
cut
off f
requ
ency
ofπ
/L
Mh[
n] Lg[
n]
UN
IVE
RS
ITY
OF
CA
LIF
OR
NIA
AT
BE
RK
EL
EY
Rat
iona
l Rat
e C
hang
ers
Cha
nge
the
Sam
plin
g R
ate
by a
Fac
tor
of L
/M
• R
atio
nal d
ecim
atio
n sy
stem
• G
ener
al s
truc
ture
• f[
n] is
a lo
wpa
ss fi
lter
with
cut
off f
requ
ency
• F
ilm to
NT
SC
form
at r
equi
res
a 30
/24
= 5
/4 r
ate
chan
ge
• S
peec
h co
mpr
essi
on fr
om 4
8 K
Hz
to 8
KH
z re
quire
s a
rate
chan
ge o
f 1/6
, so
ther
e is
no
upsa
mpl
er
• W
hat a
bout
CD
to D
AT c
onve
rsio
n? 4
80/4
41?
LM
f[n]
f sL
f sL
f sL
f s /
MS
ampl
ing
Rat
e
min
π L---π M-----
,
UN
IVE
RS
ITY
OF
CA
LIF
OR
NIA
AT
BE
RK
EL
EY
Ups
ampl
ing
cont
inuo
us ti
me
disc
rete
tim
e
upsa
mpl
ing
by 3
writ
ten
as3
or 1
:3
Ups
ampl
ing
by L
• T
akes
one
sam
ple
and
inse
rts
L-1
zero
es a
fter
it
• In
crea
se s
ampl
ing
rate
by
L
• T
ime
dom
ain
• F
requ
ency
dom
ain
• F
requ
ency
axi
s ex
pand
edby
a fa
ctor
of L
yn[
]x
n L---if
n L---I
∈
0o
the
rwis
e
= Yω(
)X
Lω
()
=
UN
IVE
RS
ITY
OF
CA
LIF
OR
NIA
AT
BE
RK
EL
EY
Dow
nsam
plin
g
cont
inuo
us ti
me
disc
rete
tim
e
dow
nsam
plin
g by
3w
ritte
n as
3 or
3:1
Dow
nsam
plin
g by
M
• T
akes
inM
sam
ples
and
outp
uts
the
first
sam
ple
• R
educ
es s
ampl
ing
rate
byM
• T
ime
dom
ain
• F
requ
ency
dom
ain
• F
requ
ency
axi
s co
mpr
esse
dby
a fa
ctor
ofM
•M
-1 a
liasi
ng v
ecto
rs
yn[
]x
Mn
[]
=
Yω(
)X
ω2
πk– M
--------
--------
---
k0
=
M1
– ∑=
UN
IVE
RS
ITY
OF
CA
LIF
OR
NIA
AT
BE
RK
EL
EY
Res
ampl
ing
Cha
ngin
g th
e S
ampl
ing
Rat
e
• C
onve
rsio
n be
twee
n au
dio
form
ats
• S
peec
h co
mpr
essi
on
• V
ideo
form
at c
onve
rsio
n
Dig
ital
Aud
io T
ape
Com
pact
Dis
c44
.1 K
Hz
48 K
Hz
48.0
44.1
--------
--
1 6---S
peec
hon
DAT 48
KH
z
Spe
ech
for
Tele
phon
e8
KH
z
Film
Tele
visi
on
24 fr
ames
/sec
30 fr
ames
/sec
30 24------
UN
IVE
RS
ITY
OF
CA
LIF
OR
NIA
AT
BE
RK
EL
EY
Ana
log-
to-D
igita
l Con
vers
ion
1 T---
yn
T(
)x
t()
yt()
h(t)
Q[. ]
yn
T(
)
Ant
i-Alia
sing
Filt
erS
ampl
erQ
uant
izer
n
y(t)
y(n
T)
xt()
ttn
y(n
T)
^
UN
IVE
RS
ITY
OF
CA
LIF
OR
NIA
AT
BE
RK
EL
EY
Dis
adva
ntag
es o
f Dig
ital S
yste
ms
Pro
gram
mab
ility
•Sp
eed
is to
o sl
ow f
or s
ome
app
lica
tion
s
•H
igh
aver
age
pow
er a
nd
peak
pow
er c
onsu
mp
tion
RIS
C (2
Wat
ts) v
s.D
SP
(50
mW
)
•A
lias
ing
from
un
der
sam
pli
ng
•C
lipp
ing
from
qu
anti
zati
on
DAT
A
ME
MO
RY
PR
OG
ME
MO
RY
HA
RVA
RD
AR
CH
ITE
CT
UR
E vQ[v
]
v
UN
IVE
RS
ITY
OF
CA
LIF
OR
NIA
AT
BE
RK
EL
EY
Adv
anta
ges
of D
igita
l Sys
tem
s
Pro
gram
mab
ility
•M
odifi
able
in th
e fi
eld
•Im
ple
men
t mu
ltip
le s
tan
dar
ds
•B
ette
r u
ser
inte
rfac
es
•To
lera
nce
for
ch
ange
s in
sp
ecifi
cati
ons
•G
et b
ette
r u
se o
f h
ard
war
e fo
r lo
w-s
pee
d o
per
atio
ns
•D
ebu
ggin
g
•U
ser
pro
gram
mab
ilit
y
UN
IVE
RS
ITY
OF
CA
LIF
OR
NIA
AT
BE
RK
EL
EY
Adv
anta
ges
of D
igita
l Sys
tem
s
Per
fect
rec
onst
ruct
ion
of a
sign
al is
pos
sibl
e ev
en a
fter
seve
re d
isto
rtio
n
Bet
ter
trad
e-of
f bet
wee
nba
ndw
idth
and
noi
seim
mun
ity
band
wid
th
perf
orm
ance
anal
og
digi
tal
Incr
ease
sig
nal-t
o-no
ise
ratio
sim
ply
by a
ddin
gm
ore
bits
SN
R =
-7.
2 +
6 d
B/b
it
UN
IVE
RS
ITY
OF
CA
LIF
OR
NIA
AT
BE
RK
EL
EY
Alia
sing
f s-f
s
•A
lias
ing
dis
tort
ion
•Q
uan
tiza
tion
noi
se
•B
and
wid
th li
mit
atio
ns
•C
ost o
f A
/D &
D/A
con
vers
ion
• A
1 H
z Si
ne w
ave
sam
pled
at 1
.8 H
z•
A 0
.8 H
z si
ne w
ave
sam
pled
at 1
.8 H
z
