电子科大数字信号处理课件.ppt

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1、Chapter10FIRDigitalFilterDesignPreliminaryConsiderationFIRDigitalFilterDesignMethodsMATLABFunctionsinFIRFilterDesign10.1PreliminaryConsiderationDigitalFilterSpecificationsSelectionoftheFilterTypeBasicApproachtoFIRDigitalFilterDesignFIRDigitalFilterOrderEst

2、imationScalingtheDigitalTransferFunction10.1.1BasicApproachestodesignFIRfiltersUnlikeIIRdigitalfilterdesign,FIRfilterdesigndoesnothaveanyconnectionwiththedesignofanalogfilters.ThedesignofFIRfiltersisbasedonadirectapproximationofthespecifiedmagnituderespons

3、e,withoftenaddedrequirementthatthephaseresponsebelinear.10.1.2EstimationoftheFilterOrderTheorder(length)ofG(z)isdirectlyestimatedfromthedigitalfilterspecification.Severalauthorshaveadvancedformulas:Kaiser’sFormula:EstimationoftheFilterOrderBellanger’sFormu

4、la:Hermann’sFormula:ReferenceP46310.6(a-e).EstimationoftheFilterOrderAComparisonofFIRFilterOrderFormulas:(1)TheestimatedfilterorderNoftheFIRfilterisinverselyproportionaltothetransitionbandwidth(ωp-ωs).(2)TheorderofKaiser’sandBellanger’sformulasdependsonthe

5、productδpandδs.ThecomparisonresultisshowninP465.10.2FIRFilterDesignBasedonWindowedFourierSeriesBecauseFIRfiltersaredescribedbyatransferfunctionthatisapolynomialinz-1,wewilluseanotherwaytodesignthem.Methods:(1)TruncatingtheFourierseriesrepresentationofthepr

6、escribedfrequencyresponse.(directandstraightforward)(2)SamplingthefrequencyresponsetogettheDFTofh[n],anduseIDFTtogeth[n].10.2.1LeastIntegral-SquaredErrorDesignofFIRFiltersLetHd(ejω)denotesthedesiredfrequencyresponsefunction,hd[n]denotestheimpulseresponsesa

7、mples,so:Inmostapplication,formeetingtheFRHd(ejω)requirements,hd[n]isinfinite.LeastIntegral-SquaredErrorDesignofFIRFiltersSowewantfind:aLength-N,causalSo:Theprocedureofusinght[n]toreplacehd[n]iscalledtruncatingorwindowing.Usingwhatapproximatingcriterion:Mi

8、nimumIntegral-SquaredError.LeastIntegral-SquaredErrorDesignofFIRFiltersDefineintegral-squarederror:UsingParseval’srelation,weget:Whenht[n]=hd[n]for-M≤n≤M,theΦRisminimum.10.2.2ImpulseResponsesofIdealFiltersIde