Linear System Theory and Design_chi-tsong chen--Solution Manual答案

《Linear System Theory and Design_chi-tsong chen--Solution Manual答案》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、LinearSystemTheoryandDesignSA01010048LINGQING2.1ConsiderthememorylesssystemwithcharacteristicsshowninFig2.19,inwhichudenotestheinputandytheoutput.Whichofthemisalinearsystem?IsitpossibletointroduceanewoutputsothatthesysteminFig2.19(b)islinear?Figure2.19

2、Translation:考虑具有图2.19中表示的特性的无记忆系统。其中u表示输入，y表示输出。下面哪一个是线性系统？可以找到一个新的输出，使得图2.19(b)中的系统是线性的吗？Answer:Theinput-outputrelationinFig2.1(a)canbedescribedas:y=auHereaisaconstant.Itisamemorylesssystem.Easytotestifythatitisalinearsystem.Theinput-outputrelationinF

3、ig2.1(b)canbedescribedas:y=au+bHereaandbareallconstants.Testifywhetherithasthepropertyofadditivity.Let:y=au+b11y=au+b22then:(y+y)=a(u+u)+2b1212Soitdoesnothasthepropertyofadditivity,therefore,isnotalinearsystem.Butwecanintroduceanewoutputsothatitislinea

4、r.Let:z=y−bz=auzisthenewoutputintroduced.Easytotestifythatitisalinearsystem.Theinput-outputrelationinFig2.1(c)canbedescribedas:y=a(u)ua(u)isafunctionofinputu.Choosetwodifferentinput,gettheoutputs:y=au1111LinearSystemTheoryandDesignSA01010048LINGQINGy=a

5、u222Assure:a≠a12then:(y+y)=au+au121122Soitdoesnothasthepropertyofadditivity,therefore,isnotalinearsystem.2.2Theimpulseresponseofanideallowpassfilterisgivenbysin2ω(t−t)0g(t)=2ω2ω(t−t)0forallt,wherewandtoareconstants.Istheideallowpassfiltercausal?Isispos

6、sibletobuiltthefilterintherealworld?Translation:理想低通滤波器的冲激响应如式所示。对于所有的t，w和to，都是常数。理想低通滤波器是因果的吗？现实世界中有可能构造这种滤波器吗？Answer:Considertwodifferenttime:tsandtr,ts

7、systemoutputattimetsisdependentonfutureinputattimetr.Inotherwords,thesystemisnotcausal.Weknowthatallphysicalsystemshouldbecausal,soitisimpossibletobuiltthefilterintherealworld.2.3Considerasystemwhoseinputuandoutputyarerelatedbyu(t)fort≤ay(t)=(Pau)(t):

8、=0fort>awhereaisafixedconstant.Thesystemiscalledatruncationoperator,whichchopsofftheinputaftertimea.Isthesystemlinear?Isittime-invariant?Isitcausal?Translation:考虑具有如式所示输入输出关系的系统，a是一个确定的常数。这个系统称作截断器。它截断时间a之后的输入。这个系统是线性的吗？它是定常的吗？是因果的吗？A