電子科技信號(hào)試題2004年

(10points)Suppose

xtisaband-limitedsignal,where

ytx

Xj0f .

Impulse-trainsamplingisperformedon toobtain

ypt

n

SpecifytherangeofvaluesforthesamplingperiodTwhichensuresthat

ytisrecoverable

from

ypt.

(12points)ConsideranLTIsystemwithunitimpulseresponse

htsintsin2t

t2

,ifthe

inputis

xt1cos2

,determinetheoutput

yt.

(18points)ConsiderastableLTIsystemwithrationalsystemfunctionH

forwhich

thepole-zeroplotisshowninFigure3.Iftheinput

xt3,theoutput

yt1.

DeterminethesystemfunctionH ,thenindicatetheROCofH .

Determinetheunitimpulseresponse

ht

ofthissystem,isthissystemcausal?

Fortheinput

xttetut

,computetheoutput

yt.

Drawablockdiagramrepresentationofthissystem. jω

3 1 2

Figure3 pole-zeropattern

5.(15points)ConsideranLTIsystemwithunitstepresponse

sn11/2nun42nun1

3

3

(a)Findthesystemfunction

H

,sketchthepole-zeropatternof

H

,thenindicatethe

ROCof

H

.

(b)Determinetheunitimpulseresponsehn,isthissystemcausalandstable?

(c)Computetheoutputofthissystem,iftheinputsignalis

xncosn.

REFERENCEANSWERS

wtx2t2xt

(15points) （3points）

Wj

/2

8

5

4

3

2

1

0 23 4

/2

5 8

(8points)

Yj

5

4

1

0

(4points)

4 5

(10points)

theNyquistrate

Yj1Xj/3ej2/5

5

Yj0fo

s1

(3points)(2points)

(3points)

thelargestsamplingperiod

Tmax

2

s

1

500

(second) (2points)

(12points)

3

0

3

htsintsin2t

t t

(2points)

（4points）

Hj1FsintFsin2t

2 t

t

(3points)

ytcos2t

2

(3points)

4.(18points)

Hs

s3 s

3Res2

(a) (3points)

xt3yt3H01A2

Hs

s3 s

3Res2

(3points)

(b)

ht4e3tut6e2tut

5 5

Thesystemisnotcausal.

YsXsHs

(3points)

2

(c)

s1s2s3

1Res2

(3points)

yt1etut1e3tut2e2tut

3 5 15

(d) (3points)

(3points)

s-1

+2

-1

6

s-1

0

1/2

1

1/2

1/2

2

1/2

(15points)

Hz

+2

1z1

11z112z1

2

1z2

2

(a)

(5points)

11n 2

pole-zeropattern(3)

(b)points)

hn

un

32

2nun1

3 (3

(c)

xncosn