滤波器 外文翻译 外文文献 英文文献 用改进的窗函数设计FIR数字滤波器.docx
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滤波器 外文翻译 外文文献 英文文献 用改进的窗函数设计FIR数字滤波器.docx
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滤波器外文翻译外文文献英文文献用改进的窗函数设计FIR数字滤波器
ResearchonFIRDigitalFilterDesignUsinganImprovedWindowFunction
TANJiajie,LUOChangyou,HUANGSanwei,DENGXiaohui
(DepartmentofPhysicsandElectronicInformationScience,HengyangNormalUniversity,HengyangHunan421008,China)
Abstract:
Windowfunctionhasbeenusedtodesignalinearphasedigitalfilerforlongtimes,buttheuseofoptimizationtechniquesfordesigningdigitalfilterhasbecomewidespreadinrecentyearAnewmethodhasbeenproposedtoimproveFIRwindowfunctioninthispaper,ThewindowfunctionthatcombineswithcosinesequencesinlinearisdifferentfrompreviousHann,HammingandBlackmanwindowfunctionThepaperalsoproposeslinearprogrammingtooptimizecharacterizationofFIRdigitalfilteraccordingtoitsmagnitudecondition,andgivesoutthealgorithmtodesigndigitalfilterusingtheimprovedwindowfunction,Finally,wehavedesignedFIRfilterusingnewwindowforsimulationandcomparedwiththefilterdesignedbyHammingwindow,BlackmanwindowfunctionThesimulationresultsshowthatfiltersdesignedusingthismethodtomeetthedesignspecifications
Keywords:
improvedwindowfunction;FIRdigitalfilter;windowfunction;linearprogramming
0leadspeech
ThedesignmethodofFIRdigitalfiltersaremainly:
windowfunctionmethod,frequencysamplingmethodandthechebyshevetccorrugatedapproximationmethod[1-4].WindowfunctionmethodisthemostcommonlyuseddesigningFIRdigitalfilters,thesimplestmethodof[4-5].Theessenceofwindowfunctionmethodisthetruncatedidealimpulseresponsetoapproximatethemethodpetitionsfilterindex.Frequencysamplingmethodisadesignoptimizationmethodforitsshortcomingiswhenthedesignthatusethevariableislimitedtoafewsamplesvaluesoftransitional,cut-offfrequencynoteasycontrol[3].Chebyshevetccorrugatedapproximationmethodisakindofoptimizationdesign,butexistingcomputationalcomplexity,bigdisadvantagecomputation[1-2].
Windowfunctionmethodissimpleindesign,haveclosedformofformula,thusverypractical.Defectisthestopbandbandpass,cut-offfrequencynoteasycontrol[2-3].Digitalfilter,windowfunctionofauto-heatingwindowfunctionmethodofselecting,thekeyis:
designtochoosetheappropriatewindowfunction,choosetherightordernumberofdigitalfilter,improveamplitudefrequencycharacteristics,reduceGibbsphenomenon,solveconvergenceproblem[1-2].[3]choosewindowfunction,throughtoGuassGuasswindowfunctionimproved,designalow-passfilterhasbettersuperiority;[4]theerrorinformation,usingtheknownintheiterationprocessthroughthewindowfunctionmethodcontinuouslyreviseddesignresultinfilterordernumber,undertheconditionofinvariablefrequencyresponseapproximation,filteridealfrequencyresponse.[5]useintegersequence,suchaswhereFibonaccisequence,Golombsequence,ConwayHofstadterRecursivesequence,Triangularseriesproducewindowfunctiontodesignthefilter,itseffectisbetterthanthatofclassicaldesignmethod.[6]choosedualwindowwindowfunctionsequenceofstructurewassystemcharacteristicsapproximationerroristheminimum;[7]willbewellSaramakiDolph-andChebyshevewindowwiththewelldesigned,itseffectFIRdigitalfiltersthanKaiserwell;[8]putgoodeffectinHammingReImannwellwellwellandKaiserwindow.[9]putforwardakindofexponentialwindowfunction,thiswindowfunctionhasthewidthcanbeadjustedwiththewindowdesigncharacteristics,thedigitalfiltershavemorecentralized,Lorddiscenergyside-lobelessfeatures.[10]usinglinearprogrammingdesignlinearphasefirfilterascendingcosineto100%superbandwidth.[11]linearprogrammingmethodisadoptedtodesigndigitalfilter.ThispaperUSEStheexistingwindowfunction,andcarryontheweightedcombination,reference[10or11],andlinearprogrammingwithlongHamming,Blackmanwindowarecompared.Theadvantagesofthismethodisstronglogicality,goalclear,easytoachieve,andtoexplorethebestsolutions.
1commonwindowfunction
Windowfunctionselectprinciple:
windowfunctionasfocusonenergy,Lorddisctransitionalsteep;Reducethewindowfunctionspectrumside-lobelevel,increasestopbandattenuation,andreducethestopbandbandpassandrippleeffect.Commonwindowfunctionhave[1-4]:
Rectanglewindow,Hanningwindow,Hammingwindow,Blackmanwindow,Kaiserwindow.WindowfunctionmethoddesignideaofFIRfiltersis[1-2]:
makesurethefrequencyresponseofidealfilter
.Thefrequencyresponseofpracticaldesignfilter
Toapproximate
.Foragain
ReversetransformgetFinallyusewindowfunction
Totruncate
meanh(n)=
.Totruncate
Willproducegibbsphenomenon,allthewindowfunctionchoicestoreducethisphenomenonforthepurpose.Judgeidealwindowfunctionmainlyaccordingtothefollowingthreecriteria!
TheLordishighdoubleamplitudeanditswidthshouldtrytonarrowTheamplitudeside-lobefastspeed,thebiggestdropside-loberelativetothemainvalveshouldbeaslowaspossible.#transitionalrequirementswilltrytonarrow.Factsprovethetwostandardcannotsimultaneouslysatisfywindowfunctionshouldbe,sothetwocompromise[1-3].InordertoreducecausedduetoaddwindowtruncationrippleandtransitionalgrowswiderimpactinengineeringdesigncommonHammingwindowandKaiserwindow.
2improvedwindowfunction[1-2]enumeratedwindowfunction,Hanningwindow,Hammingwindow,Blackmanwindowiscosinesequenceandrectangularsequenceoflinearcombination.Inordertorestraintheamplitude,side-lobeHanningwindow,Hammingwindowonthebasisofthesecond,addcosine,whentheharmoniccomponentdesignandidealwindowfunctionandrelatedtothefrequencyresponseofdifferentfromBlackmanwindow,windowfunctionimprovedformbelow
(1)
Formula
(1)ofa,b,cundetermined,theirsizeandgivenfiltertechnologyindexesrelated.Forconvenience,thiswindowfunctionlengthchoiceforodd.Thenextseveralspecialcasediscussionthistype.Case1,takea=1,b=c=0,forrectangularwindow.Condition2,takea=0.5,b=-0.5,c=0,forHannwindow.Case3,takea=0.53,b=-0.46,c=0,forHammingwindow.Situation,a=4,b=00.42jc=0.08,5,Blackmanwindowfor.Byaboveknowable,theimprovedwindowfunctionwiththesefourwindowfunctionthenature,belongtothegeneralformofthewindowfunction.
3improvedwindowfunctionalgorithm
Accordingtothegivenfiltertechnologyindex
Determinethebacklogfilterunit,butbysamplingresponseformulabelowaskout:
(2)
Calculatingtheactualfilterunitsamplingresponse:
h(n)=
(3)
Filterthefrequencyresponseis:
(4)
Willformula
(1)generationintotheformula(4):
(5)
Reference[1-2][10or11],considerFIRfilterssatisfythefirstkindoflinearphaseconditions,For
Accidentallysymmetry,AndNanoddnumber,orderingh(n)=
。
Thenthe
magnitudeofthenexttype:
written
WillcontinuetohavethetypeofJane[1-2]
Inform
(6)
Thentype(6)canbeencoded
(7)
Inform
(8)
(9)
(10)
Iffilterconditionsfortheamplitude,thepass-bandwithsatisfaction
Stopbandinsidemeet
Thepass-bandwithcanlistbelowequation:
(11)
(12)
Stopbandinsidecanlistequation:
(13)
(14)
Forbandpasscorrugated,
Forstopbandcorrugated.Fortheconvenienceofdiscussion,heretakecoefficienta,b,cgreaterthanzeroasconstraints.Thisproblemcanbeconvertedintolinearprogrammingproblem[10-12],formula(11),(12)(13)(14)canbeasconstraints.Throughthisafterconverting,problemsolving,becomeconvenient.Formula(11)(13)andformula(12)(14)addrelaxationvariablesrespectively,punishvariabletransformationintostandardlinearprogrammingequations[12]:
(15)
(16)
(17)
(18)
Includingd,e,f,g,thegreaterthan0.Thewayofsolvingthisproblemcanbesolvedbyleastsquareoriterationmethod.Calculatea,b,c,candeterminethewindowfunction.Accordingtotheaboveprocess,thiskindofthedesignoffilteralgorithmaccordingtothefollowingsteps:
Ⅰetc.Infrequencydomain,andtheintervaltakeNpointsfortheoddnumberoffrequencydomain,thesequencedodiscreteFourierinversetransform,digitalfiltersouttheidealsamplingresponseunits
Ⅱ.Byformula(8)(9)(10)askoutrespectively
、
、
。
Ⅲ.Fromtheformula(11),(12)(13)(14)listoptimizationconstraints.Ⅳ.Solvinglinearequations,findouta,b,c,soastodeterminetheoptimalsolutiondigitalfilterh(n)。
Ⅴ.Checkingtechnologyindexwhethermeettherequirements.
4applicationexamples
Designonelowtongdigitalfilters,itstechnicalindexisasfollows:
Bandpasscut-offfrequency
Stopbandcut-offfrequency
passbandripple
Stopbandcorrugated
.
Cut-offfrequencyfor
BlackmanwindowFIRdigitalfiltersforwindowlength
ThelengthofHammingwindowfor41.HammingwindowandBlackmanwindowwiththeFIRfiltersdesignedtherangecharacteristicsasshowninfigure1.WiththemodifiedwindowmethoddesignFIRfiltersasshowninfigure2.
Figure1HammingwindowandBlackmanwindowdesignrangecharacteristics
Figure2improvementwindowrangecharacteristicsgraph
Infigure1andfigure2fromtheperspectiveofthefilter,improvethefrequencycharacteristicsofthefunctionofthewindowisflatbandpass,stopbandhaveripple;Improvethewindowdesigncut-offfrequencybandpassstrictlycomplywiththedesignrequirements,andtraditionalwindowmethodcutofffrequencyishigher.Differentliesinthetransitionalzone,improvingwindowfunctionsfortransitionalzone0.2
-0.4
Strictanddesignrequirementsconsiste
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