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1、Chapter1Answers1.1ConvertingfrompolartoCartesiancoordinates:1.2convertingfromCartesiantopolarcoordinates:,,,,,1.3.(a)=,=0,because(b),.Therefore,===,=(c)=cos(t).Therefore,===,=(d),.Therefore,==0，because<.(e)=,=1.therefore,==,=.(f)=.Therefore,===,=1.4.(a)Thesignalx[n]isshiftedby3totheright.
2、Theshiftedsignalwillbezeroforn<1,Andn>7.(b)Thesignalx[n]isshiftedby4totheleft.Theshiftedsignalwillbezeroforn<-6.Andn>0.(c)Thesignalx[n]isflippedsignalwillbezeroforn<-1andn>2.(d)Thesignalx[n]isflippedandtheflippedsignalisshiftedby2totheright.ThenewSignalwillbezeroforn<-2andn>4.(e)Thesignal
3、x[n]isflippedandtheflippedandtheflippedsignalisshiftedby2totheleft.Thisnewsignalwillbezeroforn<-6andn>0.1.5.(a)x(1-t)isobtainedbyflippingx(t)andshiftingtheflippedsignalby1totheright.Therefore,x(1-t)willbezerofort>-2.(b)From(a),weknowthatx(1-t)iszerofort>-2.Similarly,x(2-t)iszerofort>-1,Th
4、erefore,x(1-t)+x(2-t)willbezerofort>-2.(c)x(3t)isobtainedbylinearlycompressionx(t)byafactorof3.Therefore,x(3t)willbezerofort<1.14(d)x(t/3)isobtainedbylinearlycompressionx(t)byafactorof3.Therefore,x(3t)willbezerofort<9.1.6(a)x1(t)isnotperiodicbecauseitiszerofort<0.(b)x2[n]=1foralln.Therefo
5、re,itisperiodicwithafundamentalperiodof1.(c)x3[n]isasshownintheFigureS1.6.-3-14……1……-10……-4……111-1n………5………x3[n]Therefore,itisperiodicwithafundamentalperiodof4.1.7.(a)=Therefore,iszerofor>3.(b)Sincex1(t)isanoddsignal,iszeroforallvaluesoft.(c)Therefore,iszerowhen<3andwhen.(d)Therefore,iszer
6、oonlywhen.1.8.(a)(b)(c)(d)1.9.(a)isaperiodiccomplexexponential.(b)isacomplexexponentialmultipliedbyadecayingexponential.Therefore,isnotperiodic.（c）isaperiodicsignal.==.isacomplexexponentialwithafundamentalperiodof.(d)isaperiodicsignal.ThefundamentalperiodisgivenbyN=m()=Bychoosingm=3.Weobt
7、ainthefundamentalperiodtobe10.(e)isnotperiodic.isacomplexexponentialwith=3/5.Wecannotfindanyintegermsuchthatm()isalsoaninteger.Therefore,isnotperiodic.1.10.x(t)=2cos(10t＋1)-sin(4t-1)PeriodoffirsttermintheRHS=.PeriodoffirsttermintheRHS=.Therefore,theoverallsignalispe
