UNIVERSITY OF CALIFORNIA AT...
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