4. Design of Discrete-Time Filters .pdf

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1、4.DesignofDiscrete-TimeFilters4.1.Introduction(7.0)4.2.FrameofDesignofIIRFilters(7.1)4.3.DesignofIIRFiltersbyImpulseInvariance(7.1)4.4.DesignofIIRFiltersbyBilinearTransformation(7.1)4.5.DesignofFIRFiltersbyWindowing(7.2)4.1.Introduction4.1.1.OverviewAdiscrete-timefi

2、lterisadiscrete-timesystemwhichpassessomefrequencycomponentsandstopsothers.Anidealdiscrete-timefilterisbestinfrequencyselectivity.Itpassesthefrequencycomponentsinthepassbanddistortionlesslyandstopsthefrequencycomponentsinthestopbandcompletely.Unfortunately,itisnonca

3、usalandcannotbeimplementedinrealtime.Thisisundesiredinmanyapplications.Insuchacase,weneedtodesignacausaldiscrete-timefilterwhichapproximatestheidealdiscrete-timefilterfunctionally.Thegoalofthedesignisanimpulseresponse,afrequencyresponse,asystemfunction,alinearconsta

4、nt-coefficientdifferenceequationoranother.AnidealfiltercanbeapproximatedbyanIIRorFIRfilter.AnIIRfilterusuallyneedslesscost,i.e.,lesscomputationandmemory,andanFIRfilterusuallyhasabetterperformance,especiallyinthephaseresponse.Ifageneralizedlinearphaseisneeded,weusual

5、lyuseanFIRfilter.4.1.2.AnalysisofIdealFiltersConsideranideallowpassfilter.Theanalysiscanbeextendedtoothertypesofidealfilters.Overperiod[,),thefrequencyresponseofanideallowpassfilterisdefinedasexp(j),

6、

7、cH().(4.1)0,otherwiseLetx(n)=Aexp(jn)beafrequencyc

8、omponentoftheinputsignal.iiiThen,thecorrespondingoutputsignalofthisfilterisyi(n)=Aiexp(jin)H(i).(4.2)If

9、

10、,thenicy(n)=Aexp[j(n)],(4.3)iiii.e.,x(n)ispassedwithaconstantdelay.If

11、

12、>,theniicy(n)=0,(4.4)ii.e.,xi(n)isstoppedcompletely.Thus,theideallowpassfilterh

13、asthebestfrequencyselectivity.Theimpulseresponseoftheideallowpassfilterissin(n)ch(n).(4.5)(n)Sinceh(n)0forn<0,theideallowpassfilterisnoncausalandcannotbeimplementedinrealtime.However,inpracticalapplications,acausallowpassfilterisoftenrequired.Insuchcases,w

14、eneedtofindacausallowpassfilterwhichapproximatestheideallowpassfilterfunctionally.Dependingonaspecificapplication,thiscausallowpassfilterc