5
TSDT14 Signal Theory Lecture 4 LTI Filtering, White Noise, Colored Noise Mikael Olofsson Department of EE (ISY) Div. of Communication Systems 2012-09-04 TSDT14 Signal Theory - Lecture 3 Ergodicity 1(2) 2 A WSS process: 2012-09-04 TSDT14 Signal Theory - Lecture 3 Ergodicity 2(2) 3 2012-09-04 TSDT14 Signal Theory - Lecture 3 Filtering Stochastic Processes 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

  • Upload
    others

  • View
    4

  • Download
    0

Embed Size (px)

Citation preview

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

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

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

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

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

ww

w.liu

.se