关于MATLAB实现FIR滤波器优化设计方法-英文论文

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1、FIRFilterDesignTechniquesAbstractThisreportdealswithsomeofthetechniquesusedtodesignFIRfilters.Inthebeginning,thewindowingmethodandthefrequencysamplingmethodsarediscussedindetailwiththeirmeritsanddemerits.DifferentoptimizationtechniquesinvolvedinFIRfilterdesignarealsocovered,includingRabiner’sme

2、thodforFIRfilterdesign.Theseoptimizationtechniquesreducetheerrorcausedbyfrequencysamplingtechniqueatthenon-sampledfrequencypoints.AbriefdiscussionofsometechniquesusedbyfilterdesignpackageslikeMatlabarealsoincluded.IntroductionFIRfiltersarefiltershavingatransferfunctionofapolynomialinzandisanall

3、-zerofilterinthesensethatthezeroesinthez-planedeterminethefrequencyresponsemagnitudecharacteristic.TheztransformofaN-pointFIRfilterisgivenby(1)FIRfiltersareparticularlyusefulforapplicationswhereexactlinearphaseresponseisrequired.TheFIRfilterisgenerallyimplementedinanon-recursivewaywhichguarante

4、esastablefilter.FIRfilterdesignessentiallyconsistsoftwoparts(i)approximationproblem(ii)realizationproblemTheapproximationstagetakesthespecificationandgivesatransferfunctionthroughfoursteps.Theyareasfollows:(i)Adesiredoridealresponseischosen,usuallyinthefrequencydomain.(ii)Anallowedclassoffilter

5、sischosen(e.g.thelengthNforaFIRfilters).(iii)Ameasureofthequalityofapproximationischosen.(iv)Amethodoralgorithmisselectedtofindthebestfiltertransferfunction.Therealizationpartdealswithchoosingthestructuretoimplementthetransferfunctionwhichmaybeintheformofcircuitdiagramorintheformofaprogram.Ther

6、eareessentiallythreewell-knownmethodsforFIRfilterdesignnamely:(1)Thewindowmethod(2)Thefrequencysamplingtechnique(3)OptimalfilterdesignmethodsTheWindowMethodInthismethod,[Park87],[Rab75],[Proakis00]fromthedesiredfrequencyresponsespecificationHd(w),correspondingunitsampleresponsehd(n)isdetermined

7、usingthefollowingrelation(2)(3)Ingeneral,unitsampleresponsehd(n)obtainedfromtheaboverelationisinfiniteinduration,soitmustbetruncatedatsomepointsayn=M-1toyieldanFIRfilteroflengthM(i.e.0toM-1).Thistruncationofhd(n)tolengthM-1issamea