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ID:39786331
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时间:2019-07-11
《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.2.3Considerasystemwhoseinputuandoutputyarerelatedbyu(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
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