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1、一、英文原文一、英文原文:FIRFilterDesignTechniquesArojitRoychowdhury(RollNo:02307424)Supervis:ProfP.C.PeyAbstractThisreptdealswithsomeofthetechniquesusedtodesignFIRfilters.Inthebeginningthewindowingmethodthefrequencysamplingmethodsa

2、rediscussedindetailwiththeirmeritsdemerits.DifferentoptimizationtechniquesinvolvedinFIRfilterdesignarealsocoveredincludingRabiner’smethodfFIRfilterdesign.Theseoptimizationtechniquesreducetheerrcausebyrequencysamplingtech

3、niqueatthenonsampledfrequencypoints.AbriefdiscussionofsometechniquesusedbyfilterdesignpackageslikeMatlabarealsoincluded.IntroductionFIRfiltersarefiltershavingatransferfunctionofapolynomialinzisanallzerofilterinthesenseth

4、atthezeroesinthezplanedeterminethefrequencyresponsemagnitudeacteristic.TheztransfmofaNpointFIRfilterisgivenby(1)()=10()NnnhnZ????FIRfiltersareparticularlyusefulfapplicationswhereexactlinearphaseresponseisrequired.TheFIRf

5、ilterisgenerallyimplementedinanonrecursivewaywhichguaranteesastablefilter.FIRfilterdesignessentiallyconsistsoftwoparts(i)approximationproblem(ii)(ii)realizationproblemTheapproximationstagetakesthespecificationgivesatrans

6、ferfunctionthroughfoursteps.Theyareasfollows:(i)Adesiredidealresponseischosenusuallyinthefrequencydomain.(ii)Anallowedclassoffiltersischosen(e.g.thelengthNfaFIRfilters).(iii)Ameasureofthequalityofapproximationischosen.(i

7、v)Amethodalgithmisedtofindthebestfiltertransferfunction.Therealizationpartdealswithchoosingthestructuretoimplementthetransferfunctionwhichmaybeinthefmofcircuitdiagraminthefmofaprogram.Thereareessentiallythreewellknownmet

8、hodsfFIRfilterdesignnamely:W(w)inthefrequencydomainithastheeffectofsmoothingHd(w).TheseveraleffectsofwindowingtheFouriercoefficientsofthefilterontheresultofthefrequencyresponseofthefilterareasfollows:(i)Amajeffectisthatd

9、iscontinuitiesinH(w)becometransitionbsbetweenvaluesoneithersideofthediscontinuity.(ii)Thewidthofthetransitionbsdependsonthewidthofthemainlobeofthefrequencyresponseofthewindowfunctionw(n)i.e.W(w).(iii)Sincethefilterfreque

10、ncyresponseisobtainedviaaconvolutionrelationitisclearthattheresultingfiltersareneveroptimalinanysense.(iv)AsM(thelengthofthewindowfunction)increasesthemainlobewidthofW(w)isreducedwhichreducesthewidthofthetransitionbbutth

11、isalsointroducesmerippleinthefrequencyresponse.(v)Thewindowfunctioneliminatestheringingeffectsatthebedgedoesresultinlowersidelobesattheexpenseofanincreaseinthewidthofthetransitionbofthefilter.Someofthewindows[Park87]comm

12、onlyusedareasfollows:1.Bartletttrianglewindow(9)()2(1)1012(1)222(1)1(1)21wnnNnNnNnNN??????????????2.Generalizedcosinewindows(includesRectangularHanningHammingBlackman)????????????21141()01011abcospnNccospnwnotheNnNrwise?

13、??????????????(10)3.Kaiserwindowwithparameterβn=012…N12(1(2(1)(1)))()()oOInNIWn??????=0Otherwise(11)Thegeneralcosinewindowhasfourspecialfmsthatarecommonlyused.ThesearedeterminedbytheparametersabcTABLEIValueofcoefficients

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