filtering stochastic processes - linköping university · 2012-09-06 · tsdt14 signal theory...
TRANSCRIPT
![Page 1: Filtering Stochastic Processes - Linköping University · 2012-09-06 · TSDT14 Signal Theory Lecture 4 LTI Filtering, White Noise, Colored Noise Mikael Olofsson Department of EE](https://reader034.vdocuments.us/reader034/viewer/2022043017/5f397fdbf8444d16050b914f/html5/thumbnails/1.jpg)
TS
DT
14 S
ignal T
heory
Lectu
re 4
LT
I F
ilte
ring
, W
hite N
ois
e,
Colo
red N
ois
e
Mik
ael O
lofs
son
Depart
me
nt
of
EE
(IS
Y)
Div
. of
Com
mu
nic
atio
n S
yste
ms
20
12
-09
-04
T
SD
T1
4 S
ign
al T
he
ory
- L
ectu
re 3
Erg
odic
ity 1
(2)
2
A W
SS
pro
cess:
20
12
-09
-04
T
SD
T1
4 S
ign
al T
he
ory
- L
ectu
re 3
Erg
odic
ity 2
(2)
3
20
12
-09
-04
T
SD
T1
4 S
ign
al T
he
ory
- L
ectu
re 3
Filt
ering S
tochastic P
rocesses
4
![Page 2: Filtering Stochastic Processes - Linköping University · 2012-09-06 · TSDT14 Signal Theory Lecture 4 LTI Filtering, White Noise, Colored Noise Mikael Olofsson Department of EE](https://reader034.vdocuments.us/reader034/viewer/2022043017/5f397fdbf8444d16050b914f/html5/thumbnails/2.jpg)
20
12
-09
-04
T
SD
T1
4 S
ign
al T
he
ory
- L
ectu
re 3
Expecta
tion o
f th
e O
utp
ut
5
20
12
-09
-04
T
SD
T1
4 S
ign
al T
he
ory
- L
ectu
re 3
AC
F o
f th
e O
utp
ut
6
20
12
-09
-04
T
SD
T1
4 S
ign
al T
he
ory
- L
ectu
re 3
Exam
ple
Filt
ering
7
20
12
-09
-04
T
SD
T1
4 S
ign
al T
he
ory
- L
ectu
re 3
Arg
um
ent fo
r RX( f ) ! 0
8
![Page 3: Filtering Stochastic Processes - Linköping University · 2012-09-06 · TSDT14 Signal Theory Lecture 4 LTI Filtering, White Noise, Colored Noise Mikael Olofsson Department of EE](https://reader034.vdocuments.us/reader034/viewer/2022043017/5f397fdbf8444d16050b914f/html5/thumbnails/3.jpg)
20
12
-09
-04
T
SD
T1
4 S
ign
al T
he
ory
- L
ectu
re 3
Norm
aliz
ed F
ilters
9
20
12
-09
-04
T
SD
T1
4 S
ign
al T
he
ory
- L
ectu
re 3
Cro
ss-C
orr
ela
tion
10
20
12
-09
-04
T
SD
T1
4 S
ign
al T
he
ory
- L
ectu
re 3
Uncorr
ela
ted a
nd Independent P
rocesses
11
20
12
-09
-04
T
SD
T1
4 S
ign
al T
he
ory
- L
ectu
re 3
Join
tly G
aussia
n P
rocesses
12
![Page 4: Filtering Stochastic Processes - Linköping University · 2012-09-06 · TSDT14 Signal Theory Lecture 4 LTI Filtering, White Noise, Colored Noise Mikael Olofsson Department of EE](https://reader034.vdocuments.us/reader034/viewer/2022043017/5f397fdbf8444d16050b914f/html5/thumbnails/4.jpg)
20
12
-09
-04
T
SD
T1
4 S
ign
al T
he
ory
- L
ectu
re 3
Join
t S
tationarity
13
20
12
-09
-04
T
SD
T1
4 S
ign
al T
he
ory
- L
ectu
re 3
LT
I F
iltering
14
20
12
-09
-04
T
SD
T1
4 S
ign
al T
he
ory
- L
ectu
re 3
Filt
ering w
ith O
rthogonal F
ilters
1(2
)
15
20
12
-09
-04
T
SD
T1
4 S
ign
al T
he
ory
- L
ectu
re 3
Filt
ering w
ith O
rthogonal F
ilters
2(2
)
16
![Page 5: Filtering Stochastic Processes - Linköping University · 2012-09-06 · TSDT14 Signal Theory Lecture 4 LTI Filtering, White Noise, Colored Noise Mikael Olofsson Department of EE](https://reader034.vdocuments.us/reader034/viewer/2022043017/5f397fdbf8444d16050b914f/html5/thumbnails/5.jpg)
ww
w.liu
.se