数字信号处理chapter4 Structure of Digital Fil

Applicationofdigitalfilterinengineering——PreprocessoftestdataSimple?Complex?ExperimentsorTheories?ApplicationandTextbook?2023/4/211.Originalwaveform2023/4/212.OriginalSpectrum2023/4/213.Frequencyresponseoftheselectedfilter2023/4/214.Waveformafterfiltering2023/4/215.Spectrumafterfiltering2023/4/216.Digitalfilter1.Filterisaparticularlyimportantclassoflineartime-invariantsysteminDSP.2.Purpose:Filter,detectionandpredictionofsignal.3.Content:

characteristicsstructuresdesignapproach.2023/4/217.CHAPTER4BASICSTRUCTUREOFDIGITALFILTERh(k),k=0,1,…(ImpulseResponse)x(n)(InputSequence)y(n)(OutputSequence)2023/4/218.CONTENTS4.1RepresentationofDigitalFilter4.2StructureofIIRFilter4.3StructureofFIRFilter4.4Review2023/4/219.4.1Representationofdigitalfilter1Expressionofdigitalfilter（1）Differenceequation

Suchas:one-ordersystem（2）Impulseresponse

Suchas:

h(n)（3）Systemfunction

Suchas:2023/4/2110.2Diagram（1）Block-diagram

Suchas:Diagramofone-orderdigitalfilterBlockdiagramz-1z-1a0a1b1Delayz-1aFirst-orderNth-orderUnitDelayConstantmultiplicationAddition2023/4/2111.（2）Flow-graph

Suchas:z-1z-1Flowgraphofone-orderdigitalfilterz-1FlowgraphDifferentstructurewilldeterminesystem’saccuracy,error,stability,costefficiencyandspeed,etcal.2023/4/2112.3ImplementationoftheDigitalFilter（1）Hardware(Special-purpose)

Digitalsignalprocessor（2）SoftwareDigitalFilterAlgorithm4ClassificationoftheDigitalFilter(1)FiniteImpulseResponse(FIR)

FIRfilter(2)InfiniteImpulseResponse(IIR)

IIRfilter2023/4/2113.FiniteImpulseResponse

InfiniteImpulseResponseh(n):Finitelengthh(n):infinitelengthNonrecursivelyRecursively

2023/4/2114.4.2StructureofIIRfilter1.CharacteristicsofIIRfilterSystemfunction:Atleastonecoefficientbiisnotzero,

itsdifferenceequationis:TherearefeedbackloopsinIIRstructure,calledrecursively.Therearepolesinsideunitcircleonz-plane,otherwiseunstable.IIRfilter’sstructureisnotunique.2023/4/2115.DirectForm

CascadeFormParallelFormThesame

H(z)mayhavedifferentimplementationstructurecostefficiency

computationerrorstabilityfiniteword-lengthsensitivity

2023/4/2116.2.StructureofIIRfilter（1）DirectFormSystemfunction:Differenceequation:2Ndelayunitsarerequired.DirectForm2023/4/2117.（2）DirectFormII2023/4/2118.x(n)y(n)b1b2bNa1a2aNz-1z-1z-1z-1z-1z-1a0x(n)y(n)b1b2bNa1a2aNz-1z-1z-1a0（2）DirectFormIINDelayUnit.DirectFormII2023/4/2119.Wecanfindthat:DirectFormIIrequiresNdelayunits.Commondisadvantageofthetwoform:Coefficientai

,bicannotbeadjustedconveniently.WhenNislarge,toosensitivetofiniteword-lengthInstabilityErrors.2023/4/2120.（3）CascadeFormN-ordertransferfunctioncanbeexpressedbyitspolesandzeros:BecauseH(z)’sparameterai,biisrealvalue,zerociandpolediarerealrootsorconjugatecomplexroots,thatis:arerealroots,

arecomplexroots，andN1+N2=N2023/4/2121.Two-orderCascadeFormWecansee:Cascadeform’sstructureisflexible,poleandzerocanbeadjustedconvenientlyanddonotinfluenceeachother.Twoorder’spositioncanbeselectedarbitrarily,differentschemehasdifferenterrorandcanbeoptimized.x(n)y(n)11211121z-1z-11M2M1M2Mz-1z-1表示取整][1121122112211·--++=Õúûùêëé+=----NiiiiizzzzA)z(Hbbaa2023/4/2122.（4）ParallelFormTransferfunctioncanbeexpressedintopartialfraction,andcanbecomposedintoparallelform:expandingintorealbootsandconjugatecomplexrootsform:where:N=L+2M，L,one-ordernetwork,M,two–ordernetwork.2023/4/2123.（4）ParallelFormWecansee:Polecanbeadjustedindependently,zerocannot;Iftherearemulti-orderpole,partialfractionexpansionisdifficult.Highspeedcomputation,lowererrorthancascadeform.2023/4/2124.4.3StructureofFIRfilter1.CharacteristicofFIRfilterh(n)isafinite-lengthsequence,itssystemfunctionis:FIRdoesn’thavefeedbackloop,

itisnotarecursiveformfilter,sothereisnoproblemofstability.2.StructureofFIRfilterx(n)y(n)h(0)z-1z-1h(1)h(2)z-1h(N-1)（1）

Direct-formConvolutionsum2023/4/2125.Generally,h(n)isrealvalue,H(z)’szeroarerealorconjugatecomplexvalue.Everypairofconjugatezerocomposedintoasecond-ordercoefficient,so:x(n)y(n)1121z-1z-11M2Mz-1z-1010MCharacteristics:

Everyorderzerocanbecontrolled,socanbeappliedwhentransferzeroarerequiredtobecontrolled.

Morecoefficients.

Morecomputationtime.（2）CascadeformProductofsecond-orderfactors2023/4/2126.4.4Review1.StructureofIIR

filter

Recursivelyform,problemofstability.Poleinsidetheunitcircle.（1）Directform:Adjustinconvenient,sensitivetoword-lengtheffect;（2）Cascadeform:Poleandzerocanbe