FiniteImpuseResponseFilters有限脉冲响应滤波器

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1、FiniteImpuseResponseFiltersFiltersAfilterisasystemthatprocessesasignalinsomedesiredfashion.Acontinuous-timesignalorcontinuoussignalofx(t)isafunctionofthecontinuousvariablet.Acontinuous-timesignalisoftencalledananalogsignal.Adiscrete-timesignalordiscretesignalx(kT)isdefinedonly

2、atdiscreteinstancest=kT,wherekisanintegerandTistheuniformspacingorperiodbetweensamplesTypesofFiltersTherearetwobroadcategoriesoffilters:Ananalogfilterprocessescontinuous-timesignalsAdigitalfilterprocessesdiscrete-timesignals.Theanalogordigitalfilterscanbesubdividedintofourcate

3、gories:LowpassFiltersHighpassFiltersBandstopFiltersBandpassFiltersIdealFiltersPassbandStopbandStopbandPassbandPassbandPassbandStopbandLowpassFilterHighpassFilterBandstopFilterPassbandStopbandStopbandBandpassFilterM(w)M(w)wwwwwcwcwc1wc1wc2wc2Discrete-TimeSignalsDiscrete-TimeSys

4、temT{}x[n]y[n]=T{x[n]}inputoutputThediagramsuggeststhattheoutputsequenceisrelatedtotheinputsequencebyaprocessthatcanbedescribedmathematicallybyanoperatorT.MovingAverageFilterAsimple,butusefulfilteristhemovingaveragefilter.Assumewehavethefollowinginputs,x[n]:246A3-pointaveragef

5、orafinite-lengthsignalofthevalues{x[0],x[1],x[2]}={2,4,6}givestheanswer⅓(2+4+6)=4.Thisvaluedefinesoneoftheoutputvalues.Thenextoutputvalueisobtainedbyaveraging{x[1],x[2],x[3]}={4,6,4}thatyieldsavalueof14/3.y[0]=⅓(x[0]+x[1]+x[2])y[1]=⅓(x[1]+x[2]+x[3])whichgeneralizestothefollowi

6、nginput-outputequationy[n]=⅓(x[n]+x[n+1]+x[n+2])Thisequationiscalledadifferenceequation.Forthetriangularinput,theresultisthesignaly[n]astabulatedbelow:Notethatthevaluesboldtypeinthex[n]rowarethenumbersinvolvedinthecomputationofy[2].Theoutputsequenceisplottedbelow:246Notethatth

7、eoutputsequenceislongerthantheinputsequenceandsomewhatrounded.Ingeneral,valuesfromeitherthepresentorfutureorbothcanbeusedFIRfiltercalculations.Afilterthatusesonlythepresentandpastvaluesoftheinputiscalledacausalfilter.Afilterthatusesfuturevaluesoftheinputiscalledanon-causalfilt

8、er.Analternativeoutputindexingschemecanproduceafilterthatisca