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ActiveNoiseControl:ATutorialReview

SENM.KUOANDDENNISR.MORGAN,SENIORMEMBER,IEEE

Activenoisecontrol(ANC)isachievedbyintroducingacancel-ing“antinoise”wavethroughanappropriatearrayofsecondarysources.Thesesecondarysourcesareinterconnectedthroughanelectronicsystemusingaspeciﬁcsignalprocessingalgorithmfortheparticularcancellationscheme.ANChasapplicationtoawidevarietyofproblemsinmanufacturing,industrialoperations,andconsumerproducts.TheemphasisofthispaperisonthepracticalaspectsofANCsystemsintermsofadaptivesignalprocessinganddigitalsignalprocessing(DSP)implementationforreal-worldapplications.

Inthispaper,thebasicadaptivealgorithmforANCisdevelopedandanalyzedbasedonsingle-channelbroad-bandfeedforwardcontrol.Thisalgorithmisthenmodiﬁedfornarrow-bandfeedfor-wardandadaptivefeedbackcontrol.Inturn,thesesingle-channelANCalgorithmsareexpandedtomultiple-channelcases.Variousonlinesecondary-pathmodelingtechniquesandspecialadap-tivealgorithms,suchaslattice,frequency-domain,subband,andrecursive-least-squares,arealsointroduced.Applicationsofthesetechniquestoactualproblemsarehighlightedbyseveralexamples.Keywords—Activenoisecontrol,activevibrationcontrol,adap-tivenoisecancellation,adaptivesystems,digitalsignalprocessing(DSP)applications.

I.INTRODUCTION

A.Overview

Acousticnoiseproblemsbecomemoreandmoreevidentasincreasednumbersofindustrialequipmentsuchasengines,blowers,fans,transformers,andcompressorsareinuse.Thetraditionalapproachtoacousticnoisecontrolusespassivetechniquessuchasenclosures,barriers,andsilencerstoattenuatetheundesirednoise[1],[2].Thesepassivesilencersarevaluedfortheirhighattenuationoverabroadfrequencyrange;however,theyarerelativelylarge,costly,andineffectiveatlowfrequencies.Mechanicalvibrationisanotherrelatedtypeofnoisethatcommonlycreatesproblemsinallareasoftransportationandmanu-facturing,aswellaswithmanyhouseholdappliances.Activenoisecontrol(ANC)[3]–[6]involvesanelec-troacousticorelectromechanicalsystemthatcancelstheprimary(unwanted)noisebasedontheprincipleofsuper-position;speciﬁcally,anantinoiseofequalamplitudeand

ManuscriptreceivedJune1,1997;revisedDecember18,1998.

S.M.KuoiswiththeDepartmentofElectricalEngineering,NorthernIllinoisUniversity,DeKalb,IL60115USA.

D.R.MorganiswithBellLaboratories,LucentTechnologies,MurrayHill,NJ07974-0636USA.

PublisherItemIdentiﬁerS0018-9219(99)04043-8.

oppositephaseisgeneratedandcombinedwiththeprimarynoise,thusresultinginthecancellationofbothnoises.TheANCsystemefﬁcientlyattenuateslow-frequencynoisewherepassivemethodsareeitherineffectiveortendtobeveryexpensiveorbulky.ANCisdevelopingrapidlybecauseitpermitsimprovementsinnoisecontrol,oftenwithpotentialbeneﬁtsinsize,weight,volume,andcost.ThedesignofacousticANCutilizingamicrophoneandanelectronicallydrivenloudspeakertogenerateacancelingsoundwasﬁrstproposedina1936patentbyLueg[7].Sincethecharacteristicsoftheacousticnoisesourceandtheenvironmentaretimevarying,thefrequencycontent,amplitude,phase,andsoundvelocityoftheundesirednoisearenonstationary.AnANCsystemmustthereforebeadaptiveinordertocopewiththesevariations.Adaptiveﬁlters[8]–[16]adjusttheircoefﬁcientstominimizeanerrorsignalandcanberealizedas(transversal)ﬁniteimpulseresponse(FIR),(recursive)inﬁniteimpulseresponse(IIR),lattice,andtransform-domainﬁlters.Themostcommonformofadaptiveﬁlteristhetransversalﬁlterusingtheleast-mean-square(LMS)algorithm.Anearlyductcancellationsystembasedonadaptiveﬁltertheorywasdevelopedin[17]and[18].

Itisdesirableforthenoisecancelertobedigital[19],[20],wheresignalsfromelectroacousticorelectromechani-caltransducersaresampledandprocessedinrealtimeusingdigitalsignalprocessing(DSP)systems.Inthe1980’s,de-velopmentofDSPchipsenabledlow-costimplementationofpowerfuladaptivealgorithms[21]andencouragedwide-spreaddevelopmentandapplicationofANCsystems[22].ThecontinuousprogressofANCinvolvesthedevelopmentofimprovedadaptivesignalprocessingalgorithms,trans-ducers,andDSPhardware.Moresophisticatedalgorithmsallowfasterconvergenceandgreaternoiseattenuationandaremorerobusttointerference.ThedevelopmentofimprovedDSPhardwareallowsthesemoresophisticatedalgorithmstobeimplementedinrealtimetoimprovesystemperformance.

Inthispaper,noiseisdeﬁnedasanykindofundesirabledisturbance,whetheritisbornebyelectrical,acoustic,vibration,oranyotherkindofmedia.Therefore,ANCalgorithmsintroducedinthispapercanbeappliedtodifferenttypesofnoiseusingappropriatesensorsandsecondarysources.Forelectricalengineersinvolvedinthe

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developmentofANCsystems,[3],[5],and[6]provideexcellentintroductiontoacousticsandvibration.B.CurrentApplications

ANCisanattractivemeanstoachievelargeamountsofnoisereductioninasmallpackage,particularlyatlowfrequencies.ManyapplicationsofANCinvolvingrealandsimulatedexperimentsareintroducedin[4].CurrentapplicationsforANCincludeattenuationofunavoidablenoiseinthefollowingendequipment.

1)Automotive:Includingelectronicmufﬂersforexhaustandinductionsystems,noiseattenuationinsidevehiclepassengercompartments,activeenginemounts,andsoon.2)Appliances:Includingair-conditioningducts,airconditioners,refrigerators,kitchenexhaustfans,washingmachines,furnaces,dehumidiﬁers,lawnmowers,vacuumcleaners,headboards,roomisolation,andsoon.

3)Industrial:Fans,airducts,chimneys,transformers,powergenerators,blowers,compressors,pumps,chainsaws,windtunnels,noisyplants(atnoisesourcesormanylocalquietzones),publicphonebooths,ofﬁcecubiclepartitions,earprotectors,headphones,andsoon.

4)Transportation:Airplanes,ships,boats,pleasuremo-torboats,helicopters,snowmobiles,motorcycles,diesello-comotives,andsoon.

C.PerformanceEvaluationandPracticalConsiderationsWhenANCisdeployedinrealapplications,manyprac-ticalproblemsariseandneedtobeaddressed[23].Anap-proachtoadaptiveANCperformanceanalysisthatinvolvesahierarchyoftechniques,startingwithanidealsimpliﬁedproblemandprogressivelyaddingpracticalconstraintsandothercomplexities,isessential[24].Performanceanalysisresolvesthefollowingissues:1)thefundamentalperfor-mancelimitations;2)thepracticalconstraintsthatlimitperformance;3)performancebalancedagainstcomplexity;and4)howtodetermineapracticaldesignarchitecture.Ateachstep,adegreeofconﬁdenceisgainedandabenchmarkisestablishedforcomparisonandcrosscheckingwiththenextlevelofcomplexity.

Inordertobesuitableforindustrialuse,theANCsystemmusthavecertainproperties[25]:1)maximumefﬁciencyoverthelargestfrequencybandpossibletocancelawiderangeofnoise;2)autonomywithregardtotheinstallation,sothatthesystemcouldbebuiltandpresetinthemanufacturingareaandtheninsertedonsite;3)selfadaptabilityofthesysteminordertodealwithanyvariationsinthephysicalparameters(temperature,airﬂowspeed,etc.);and4)robustnessandreliabilityofthedifferentelementsofthesystemandsimpliﬁcationofthecontrolelectronics.

D.PaperOutline

ANCisbasedoneitherfeedforwardcontrol,whereacoherentreferencenoiseinputissensedbeforeitpropagatespastthesecondarysource,orfeedbackcontrol[26],[27],wheretheactivenoisecontrollerattemptstocancelthe

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Fig.1.Single-channelbroad-bandfeedforwardANCsysteminaduct.

noisewithoutthebeneﬁtofan“upstream”referenceinput.StructuresforfeedforwardANCareclassiﬁedinto1)broad-bandadaptivefeedforwardcontrolwithareferencesensor,whichwillbediscussedinSectionII,and2)narrow-bandadaptivefeedforwardcontrolwithareferencesensorthatisnotinﬂuencedbythecontrolﬁeld(e.g.,tachometer),whichwillbepresentedinSectionIII.InSectionIV,theconceptofadaptivefeedbackANCwillbedevelopedfromthestandpointofreferencesignalsynthesis,therebyprovidingalinktothefeedforwardsystemsinprevioussections.InSectionV,thesesingle-channelANCsystemswillbeexpandedtomultiple-channelcases.SectionVIwillintro-ducevariousonlinesecondary-pathmodelingtechniques.SectionVIIwillintroducevariousspecialANCalgorithmssuchaslatticeANC,frequency-domainANC,subbandANC,andrecursive-least-squares(RLS).Finally,severalexamplesapplyingANCtoreal-worldproblemswillbehighlightedinSectionVIII.

II.BROAD-BANDFEEDFORWARDANC

Thissectionconsidersbroad-bandfeedforwardANCsystemsthathaveasinglereferencesensor,singlesec-ondarysource,andsingleerrorsensor.Thisgenrewillbeexempliﬁedbythesingle-channelduct-acousticANCsystemshowninFig.1,wherethereferenceinputispickedupbyamicrophone.ThereferencesignalisprocessedbytheANCsystemtogeneratethecontrolsignaltodrivealoudspeaker.TheerrormicrophoneisusedtomonitortheperformanceoftheANCsystem.Theobjectiveofthecontrolleristominimizethemeasuredacousticnoise.Notethatthissetupisonlyusedasanexampleofbroad-bandANC;thegeneraltechniquesarewidelyapplicabletoavarietyofacousticandvibrationproblems.

A.BasicPrinciples

Thebasicbroad-bandANCsystemshowninFig.1isdescribedinanadaptivesystemidentiﬁcationframework

isillustratedinFig.2,inwhichanadaptiveﬁlter

usedtoestimateanunknownplant

consistsoftheacousticresponsefromthereferencesensortotheerrorsensorwherethenoiseattenuationistoberealized.Iftheplantisdynamic,theadaptivealgorithmthenhasthetaskofcontinuouslytrackingtimevariationsoftheplantdynamics.ThemostimportantdifferencebetweenFig.2andthetraditionalsystemidentiﬁcationschemeistheuseofanacousticsummingjunctioninsteadofthesubtractionofelectricalsignals.However,forconsistency

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Fig.2.SystemidentiﬁcationviewpointofANC.

wewillcontinuetorepresentthesummingjunctionbyasubtraction;itisreallyarbitraryanywaybecauseitcanbeimplementedwithasignchangeofthesecondarysignal[4].

istominimizeTheobjectiveoftheadaptiveﬁlter

theresidualerrorsignalaftertheadaptiveﬁlterconverges.Wethenhave

for

isidenticalandtotheprimarydisturbance

areacousticallycombined,theresidualerroris

from

-transformoftheerrorsignalis

isgivenby[4]

(1)

isthemagnitude-squaredcoherencefunctionwhere

[28]betweentwowide-sensestationaryrandomprocesses

andistheautopowerspectrumof

Thisrequires

torealizetheoptimaltransferfunction

and

hastosimulta-neouslymodel

indecibelsisgivenby

shown

in(3).Itisimpossibletocompensatefortheinherentdelay

doesnotcontainadueto

delayofatleastequallength.

C.Filtered-XLMSAlgorithm

Theintroductionofthesecondary-pathtransferfunctionintoacontrollerusingthestandardLMSalgorithmshowninFig.3willgenerallycauseinstability[30].Thisisbecausetheerrorsignalisnotcorrectly“aligned”intimewith

KUOANDMORGAN:ACTIVENOISECONTROL

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thereferencesignal,duetothepresenceof

toremoveitseffect.ThesecondsolutionistoplaceanidenticalﬁlterinthereferencesignalpathtotheweightupdateoftheLMSalgorithm,whichrealizestheso-calledﬁltered-XLMS(FXLMS)algorithm[9].Sinceaninversedoesnotnecessarilyexistfor

Fig.4.BlockdiagramofANCsystemusingtheFXLMSalgo-rithm.

controlledbytheLMSalgorithmisshownin

Fig.3.Theresidualsignalisexpressedas

isthetimeindex,istheimpulseresponseof

denoteslinearconvolution,secondarypath

and

arethecoefﬁcientandsignalvectors

istheﬁlterorder.Theﬁlterof

mustbeofsufﬁcientordertoaccuratelymodeltheresponseofthephysicalsystem.

Assumingameansquarecostfunction

theadaptiveﬁlterminimizestheinstantaneoussquarederror

(5)

usingthesteepestdescentalgorithm,whichupdatesthecoefﬁcientvectorinthenegativegradientdirectionwithstepsize

(6)

isaninstantaneousestimateofthemean-where

square-error(MSE)gradientattime

,whereand

Fig.5.EquivalentdiagramofFig.4forslowadaptationand^(z)=S(z):S

whereistheestimatedimpulseresponseofthesecondary-pathﬁlter

bytheﬁlter

ofphase

errorbetween

and

duringaninitialtraining

stageformostANCapplications.Thedetailedexperimentalsetupandprocedureforofﬂinesecondary-pathmodelingissummarizedin[4].Thetopicofadaptiveonlinesecondary-pathmodelingwillbediscussedlaterinSectionVI.

2)AnalysisoftheFXLMSAlgorithm:Considerthecase

ischangingslowly,soinwhichthecontrolﬁlter

andthattheorderof

through

issmall.

ThemaximumstepsizethatcanbeusedintheFXLMSalgorithmisapproximately[33]

isunknownand

mustbeestimatedbyanadditionalﬁlter

(9)

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isthenumberofsamplescorresponding

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totheoveralldelayinthesecondarypath.Therefore,thedelayinthesecondarypathinﬂuencesthedynamicresponseoftheANCsystembyreducingthemaximumstepsizeintheFXLMSalgorithm.

Boucherandcoworkers[34],[35]discusstheeffectsofsecondarypathmodelingphaseerrorsontheoptimumstepsizeandconvergencetime.Theanalysisappliestothespecialcasewhenthereferencesignalisnarrow-bandbutthedisturbanceisstillbroadband.Numericresultssuggestthatphaseerrorsof40

[39]

(12)

where

(13)

where

becausethepolescomeclosertotheunitcircle.Fornarrow-bandsignals,errorsintheestimationofthesecondarypathtransferfunctioncanbeconsideredintwoparts:amplitudeerrorsandphaseerrors[36].Anymagnitudeestimationerrorwillproportionallychangethe

andhencewillsimplyscaletheidealpowerof

stabilityboundaccordingly.However,thereisnosimplerelationshipbetweenphasemodelingerrorandstabilityintherangeof

Anothercomplicationthatoftenarisesinthebroad-band

andarepresentcaseisthatmeasurementnoises

inthereferenceanderrorsignals,respectively.Theoptimalunconstrainedtransferfunction

thusrepresentsacompromise

betweenbiasingtheconvergenceweightvectorawayfromtheoptimumsolutionandmoderatingthecontroleffort.D.FeedbackEffectsandSolutions

TheacousticANCsystemshowninFig.1usesaref-erencemicrophonetopickupthereferencenoiseandprocessesthisinputwithanadaptiveﬁltertogeneratean

tocancelprimarynoiseacousticallyintheantisound

duct.Unfortunately,theantisoundoutputtotheloudspeakeralsoradiatesupstreamtothereferencemicrophone,result-inginacorruptedreferencesignal

isindependentofthe

associatedwiththeerrorsensor.measurementnoise

associatedwiththeHowever,themeasurementnoise

referencesensordoesaffecttheoptimumweightandhencereducesthecancellationperformance.Thebestfrequencyresponseofthecontrollerisacompromisebetweencan-andampliﬁcationofcellationoftheprimarynoise

themeasurementnoisethroughthecontroller[25].Somepracticalconsiderationstoreduceundesiredmeasurementnoisearegivenin[4].

InFig.4,ifthesecondary-pathtransferfunction

noise,and

istheprimary

isthesignalpickedupbythereferencesensor,

and

isincloseagreementwithElliott’sapproximationgivenin(10).Therefore,effortsshouldbemadetokeepthedelaysmall,suchasdecreasingthedistancebetweentheerrorsensorandthesecondarysourceandreducingthedelayinelectricalcomponents.

3)LeakyFXLMSAlgorithm:InanANCsystem,thedi-rectapplicationoftheFXLMSalgorithmsometimesleadstoanotherproblem:highnoiselevelsassociatedwithlow-frequencyresonances,whichmaycausenonlineardistortionbyoverloadingthesecondarysource.Anobvioussolutiontothisproblemistheintroductionofoutputpowercon-straints.Similarresultscanbeobtainedbyconstrainingtheadaptiveﬁlterweightsbymodifyingthecostfunctionas

KUOANDMORGAN:ACTIVENOISECONTROL

tothereferencesensor.The

steady-statetransferfunctionoftheadaptiveﬁlteris[4]

hasconvergedtothenoiseless

optimalsolution(14),then

whiletheopen-loopgain

isgreaterthanunity.

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Fig.6.BlockdiagramofANCsystemwithfeedback.

Fig.7.ANCwithacousticfeedbackneutralization.

1)FeedbackNeutralization:Thesimplestapproachtosolvingthefeedbackproblemistouseaseparatefeedbackcancellation,or“neutralization,”ﬁlterwithinthecontroller,whichisexactlythesametechniqueasusedinacousticechocancellation[43].Thiselectricalmodelofthefeedbackpathisdrivenbythesecondarysignal,anditsoutputissubtractedfromthereferencesensorsignal[44].Aduct-acousticANCsystemusingtheFXLMSalgorithmwithfeedbackneutralizationisillustratedinFig.7.Thefeedbackcomponentofthereferencemicrophonesignaliscanceledelectronicallyusingafeedbackneutralizationﬁlter

iscomputedas

vectorof

istheweight

isthereferencesignalvector,

istheweightvectorof

(17)(18)

where

canbeestimatedsimultaneouslybyusingthe

ofﬂinemodelingtechnique[4].

2)AdaptiveIIRFilter:Equation(14)showsthatwhenfeedbackispresent,theoptimalsolutionoftheadaptiveﬁlterisgenerallyanIIRfunctionwithpolesandzeros.ThisrationalfunctioncanbeapproximatedbyanFIRfunctionofsufﬁcientorder,butasmallerstepsize

and

thanfor

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Fig.9.Basicconﬁgurationofnarrow-bandANCsystem.

algorithmhaveneverbeenprovenformally.Amodiﬁedleakyversionofthesimpliﬁedhyperstableadaptivere-cursiveﬁlter(SHARF)algorithm[52]hasbeendevelopedforANCapplicationstoimprovethestabilityoftheIIRadaptiveﬁlter[53].Inthatalgorithm,alowpassﬁlterisusedtosmooththeerrorsignalfortheﬁltered-UrecursiveLMSalgorithm,therebyprovidingahigherstabilitymargin.III.NARROWBANDFEEDFORWARDANC

Manynoisesareperiodic,suchasthosegeneratedbyengines,compressors,motors,fans,andpropellers.Directobservationofthemechanicalmotionofsuchsourcesgenerallyispossiblebyusinganappropriatesensor,whichprovidesanelectricalreferencesignalthatcontainsthefundamentalfrequencyandalltheharmonicsoftheprimarynoise.However,thistechniqueisonlyeffectiveforperiodicnoisebecausethefundamentaldrivingfrequencyistheonlyreferenceinformationavailable.

A.Introduction

Abasicblockdiagramofnarrow-bandANCforreducingperiodicacousticnoiseinaductisillustratedinFig.9.Thissystemcontrolsharmonicsourcesbyadaptivelyﬁlteringa

internallygeneratedbysynthesizedreferencesignal

theANCsystem.Thistechniquehasthefollowingadvan-tages:1)undesiredacousticfeedbackfromthecancelingloudspeakerbacktothereferencemicrophoneisavoided;2)nonlinearitiesandagingproblemsassociatedwiththereferencemicrophoneareavoided;3)theperiodicityofthenoiseremovesthecausalityconstraint;4)theuseofaninternallygeneratedreferencesignalresultsintheabilitytocontroleachharmonicindependently;and5)itisonlynecessarytomodeltheacousticplanttransferfunctionoverfrequenciesinthevicinityoftheharmonictones;thus,anFIRﬁlterwithsubstantiallylowerordermaybeused.Thereferencesignalgeneratoristriggeredbyasyn-chronizationpulsefromanonacousticsensor,suchasatachometersignalfromanautomotiveengine.Ingeneral,twotypesofreferencesignalsarecommonlyusedinnarrow-bandANCsystems:1)animpulsetrainwithaperiodequaltotheinverseofthefundamentalfrequencyoftheperiodicnoise[54]and2)sinewavesthathavethesamefrequenciesasthecorrespondingharmonictonesto

KUOANDMORGAN:ACTIVENOISECONTROL

becanceled.Theﬁrsttechniqueiscalledthewaveformsynthesismethod,whichwasproposedbyChaplin[55].Thesecondtechniqueembodiestheadaptivenotchﬁlter,whichwasoriginallydevelopedforthecancellationoftonalinterference[56]andappliedtoperiodicANC[57].

ThewaveformsynthesismethoddiscussednextinSectionIII-Bemployssynchronoussampling.However,forsomeapplications,theactualperiodwillvaryfromthenominalvalueasafunctionofloadingconditions.Therefore,itissometimesdesirabletooperateasynchro-nouslywithaﬁxedsamplingratesothatthesecondary-pathestimateﬁltercoefﬁcientsdonothavetobechangedasafunctionofactualmachinerotationrate.Also,somedigitalsignalprocessorscannotbeefﬁcientlyutilizedonasynchronoussignal-drivenbasis.AsynchronousANCsystemsusingtheFXLMSalgorithmeliminatetheproblemofhavingtochangeasthesamplingratevariesandareimplicitinthelaterformulationsofSectionsIII-CandIII-D.

B.WaveformSynthesisMethod

1)StructuresandAlgorithms:Thewaveformsynthesizer[55]storescancelingnoisewaveformsamples

isthenumberofsamplesoveronecycleofthe

waveformand

(19)

representsthe

andcanbeimplementedasapointer

incrementedinacircularfashionbetweenzeroand

foreachsamplingperiod,controlledbyinterruptsgeneratedfromthesynchronizationsignal.

Theresidualnoisepickedupbytheerrormicrophoneissynchronouslysampledwiththereferencesignaltimingpulses.Inapracticalsystem,thereisadelaybetweenthetimethesignal

isthetimedelay,whichis

constantforagivenloudspeaker-microphonearrangement,mustbeupdated

asthesamplingratevaries,sinceitissynchronizedwiththenoisesource.

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thcoefﬁcientoftheﬁlter

mod

Fig.10.Equivalentdiagramofwaveformsynthesismethodusingimpulsetraininputandneglectingsecondarypatheffects.

(24)

2)PrincipleandAnalysis:ThewaveformsynthesismethodisequivalenttoanadaptiveFIRﬁlteroforder

excitedbyaKroneckerimpulsetrainofperiod

where

]isspeciﬁed

by(22).Thepresenceof

isthediscreteKroneckerdeltafunctionand

input

betweentheprimaryisderivedas[54]

isthenumberofsamplesofdelayfrom

toissmallcomparedtotheﬁlterlength

from

forthedelayedLMSalgorithmis[59]

planetocreate

nullsinthefrequencyresponseatharmonicfrequencies

andaccord-inglyincreasestheout-of-bandovershootofthefrequencyresponse[59],[60].Asthestepsize

fromstabilityconsiderations;thatis,

(Hz)[54].Thisshowsthatthebandwidthofthenotchﬁlterisproportionaltothestepsize

mustbecompensated

forbyusingtheFXLMSalgorithm.Assumingasecondary-oforderpathestimate

and

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Fig.11.Single-frequencyadaptivenotchﬁlter.

and

referencesignal.A90

fromtheprimaryis[56]

.Thus(31)

where

arelocatedinthe

input

thorderadaptiveﬁlter,(27)becomes[61]

(32)

whereand

and

aretheﬁlteredversionsof

atfre-andisthephasedifferencequency

atForsmallhasbetween

complexconjugatepolesatradius

arepositive,theradiusof

thepolecanbegreaterthanoneonlyif

(34)

andtheconvergencetimeconstantissloweddownbyafactorof

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theout-of-bandgainproblemistoequalizethesecondary-pathtransferfunction

3)Direct/ParallelForm:Aconﬁgurationofmultipleref-erencesignalgeneratorsandcorrespondingadaptiveﬁltershasbeendeveloped[66]toimprovetheperformanceofANCsystemsforautomotiveapplications.Theideaistoseparateacollectionofmanyharmonicallyrelatedsinu-soidsintomutuallyexclusivesetsthatindividuallyhavefrequenciesspacedoutasfaraspossible.Ingeneral,ifthereare

containsstaggeredsinusoidalfrequenciesof

everyother

and

cosinetableanda90

orusesonlyone

iseffectivelyincreased,ascompared

tothedirectimplementationtechnique.

4)CascadeForm:Ideally,multiple-sinusoidreferencesaremoreeffectivelyemployedinacascadeof

(37)

where

thsectionadaptiveﬁlter.Each

sinusoids

(35)

where

thsinusoid.Whenthefrequencies

ofthereferencesinusoidsareclosetogether,alongﬁlter

producesanotchatIfanestimateofthe

secondary-pathtransferfunctionisavailable,itispossi-bletoconﬁgurea“pseudocascade”arrangement[60]thatideallyperformsasatruecascadebutrequiresonlyonesecondarypathestimate

potentiallycontainsthefundamentalandall

harmoniccomponentsoftheperiodicnoise.Theshape

isdependentontheduty-cycleofthespectrumof

whereratio

sinusoids,

adaptiveﬁlteroutputs

isderivedasinthesingle-frequencycase.Sinceonlyoneerrorsensorisused,there

isonlyoneerrorsignal

adaptiveﬁltersbasedontheFXLMSalgorithm.

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Fig.15.WidebandadaptivefeedbackANCsystemusingtheFXLMSalgorithm.

Fig.13.izer.

Blockdiagramofsingle-frequencyactivenoiseequal-

Fig.14,theprimarynoiseisexpressedinthe

isthesignal

obtainedfromtheerrorsensorand

andusethisasa

synthesizedreferencesignal

Fig.14.Single-channelfeedbackANCsystem.

andthebalancingbranch.Thegains

],thepseudo-errorcanbeexpressedas

,whichistheresidualnoiseofthe

conventionalANCsystem.TheadaptiveﬁlterminimizesthepseudoerrorsignalusingtheFXLMSalgorithm.Aftertheﬁlterhasconverged,

containsaresidualcomponentofthenarrow-bandnoisewhoseamplitudeiscontinuously,linearly,andtotallycontrolledbyadjustingthegainvalue

isﬁlteredbythe

andthencombinedwithsecondary-pathestimate

toregeneratetheprimarynoise.

Thecompletesingle-channeladaptivefeedbackANCsystemusingtheFXLMSalgorithmisillustratedinFig.15,

isalsorequiredtocompensateforthesecondarywhere

issynthesizedaspath.Thereferencesignal

arethecoefﬁcientsoftheusedtoestimatethesecondary

path.

2)AlgorithmAnalysis:FromFig.15,wehaveifoftheLMSalgorithmissmall(slowconvergence),theadaptiveﬁlter

canbecommutedwith

canbemodeledby

apuredelay,thatis,

predictionerrorﬁlter

anadaptivepredictoroftheprimarynoise

iscalledthe

actsas

feedbackANCfrom

is[4]

fortheANCﬁlter.In

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Fig.17.HybridANCsystemwithcombinationoffeedbackANCandfeedforwardANC.

Fig.16.Blockdiagramofadaptivepredictor.

ANCsystemdiscussedinSectionII.Thestabilityrobust-nessoftheadaptivefeedbackcontrollertochangesintheplantresponsecanbeseparatelyassessedusingageneral-izationofthecomplementarysensitivityfunction[75].Thestabilityrobustnessisimprovedbyincorporatingvariousformsofeffortweightingintothecostfunction,resultingintheleakyFXLMSalgorithmusedinfeedforwardANCsystems.

3)OtherFeedbackANCAlgorithms:Theoutput-whiteningfeedbackANCmethod[76]assumesthattheprimarynoise

oftheprimarynoiseattheerrorsensorthantheoutputofthereferencesensor,whichislocatedawayfromthecontrolpoint.Thisisparticularlytruewheneverthenoiseﬁeldisisotropicandthereferencesensorisnolongerfullycoherentwiththenoiseattheerrorsensorlocation.B.HybridANCSystems

ThefeedforwardANCsystemsdiscussedinSectionIIusetwosensors:areferencesensorandanerrorsensor.ThereferencesensormeasurestheprimarynoisetobecanceledwhiletheerrorsensormonitorstheperformanceoftheANCsystem.TheadaptivefeedbackANCsystemusesonlyanerrorsensorandcancelsonlythepredictablenoisecomponentsoftheprimarynoise.AcombinationofthefeedforwardandfeedbackcontrolstructuresiscalledahybridANCsystem,asillustratedinFig.17[80].ThereferencesensoriskeptclosetothenoisesourceandprovidesacoherentreferencesignalforthefeedforwardANCsystem.Theerrorsensorisplaceddownstreamandsensestheresidualnoise,whichisusedtosynthesizethereferencesignalfortheadaptivefeedbackANCﬁlter,aswellastoadaptthecoefﬁcientsofboththefeedforwardandfeedbackANCﬁlters.ThefeedforwardANCattenuatesprimarynoisethatiscorrelatedwiththereferencesignal,whilethefeedbackANCcancelsthepredictablecompo-nentsoftheprimarynoisethatarenotobservedbythereferencesensor.

ThehybridANCsystemusingtheFIRfeedforwardANCandtheadaptivefeedbackANCisillustratedinFig.18,

isgeneratedusingthewherethesecondarysignal

outputsofboththefeedforwardANCﬁlterhastworeferenceinputs:and

thecoefﬁcientsoftheﬁlters

fromthereferencesensorand

areusedtoadapt

isminimumphase.

Then,fromlinearestimationtheory,theoptimalcontrollerisexpressedas

thatisspectrallywhite;inotherwords,allthe

energythatispredictablefromtheMAmodel

andpredictthenextvalueof

anddevelopaprocedureforestimatingits

parameters.ThepredictionpartisthenformulatedusingthestandardKalmanﬁltersetup.

TheperformanceoftheKalmanalgorithmwascom-paredwiththefeedforwardANCalgorithmdiscussedinSectionIIbyZangi[79].Theoutputoftheerrorsensorcontainsmuchmoreinformationaboutthefuturevalues

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Fig.18.HybridANCsystemusingtheFIRfeedforwardANCwiththeFXLMSalgorithm.

V.MULTIPLE-CHANNELANC

Sincethenoiseﬁeldinanenclosureoralarge-dimensionductismorecomplicatedthaninanarrowduct,itisgenerallynecessarytouseamultiple-channelANCsystemwithseveralsecondarysources,errorsensors,andperhapsevenseveralreferencesensors.Someofthebest-knownapplicationsarethecontrolofexhaust“boom”noiseinautomobiles[81]–[84],earth-movingmachines[85],andthecontrolofpropeller-inducednoiseinﬂightcabininteri-ors[86]–[88].OtherANCapplications,suchasvibrationcontrolincomplexmechanicalstructures,alsorequiremultiplechannels.

A.Principles

Theoreticalpredictions,computersimulations,andlab-oratoryexperimentsonharmonicANCinashallowen-closurewerepresentedinatrilogyofpapersbyNelsonetal.[]–[91].Thetotalpotentialacousticenergy

isthedensityoftheacousticmedium,

therrorsensorpositionintheenclosurewithatotalof

referencesensorstoformthereferencesignal

vector.ForadaptivefeedbackANC,thereferencesignalsareinternallysynthesizedbasedonthesecondaryanderrorsignals.Themultiple-channelANCsystemgenerateserrorsensorsaredistributedoverdesired

locationstomeasuretheresidualnoisecomponents.

Ablockdiagramofamultiple-channelANCsystemthatincludesfeedbackpathsfromthesecondarysourcestothereferencesensorsisillustratedinFig.20.Thewidearrowsrepresentanarrayofsignals(acousticorelectrical)

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955

forandaretheﬁlteredreferencesignalvectors,whichareformedbyﬁltering

bythesecondary-pathestimatesfromthe

therrorsensor.In(46),

representstheimpulseresponseofanFIRﬁlterthatisusedtoestimate

Fig.20.Blockdiagramofanadaptivemultiple-channelfeedfor-wardANCsystemwithfeedbackpaths.

isusedtoreplace

thataresymbolicallyexpressedasvectors.Thematrixrepresents

secondary-pathtransfersecondarysourcesto

from

possiblefeedforwardchan-nels,eachdemandingaseparateadaptiveﬁlter,andthese

adaptiveﬁltersarerepresentedbythematrix

with

tocontroltheinﬂuenceofthe

onlyif

functions,

thsecondarysignalisobtainedbyﬁlteringthe

throughthecorrespondingadaptivereferencesignal

FIRﬁlter

(43)

where

theweightvectorofthe

(47)

wherethesuperscript

playsthesamerole

asthereferencesignalautocorrelationmatrixinthesingle-channelcase.Theeigenvaluesof

isthecommonreference

signalvectorforalladaptiveﬁlters.

Thecostfunctionoftheadaptiveﬁltersisapproximatedbythesumoftheinstantaneoussquarederrorsas

equa-tions[4]

(45)

where

(46)

956

Thus,theconvergenceofthe

generalbroad-bandmultiple-channelFXLMSalgorithmislimitedbyboththespatialandtemporalcharacteristicsofthesystem.

Aswiththesingle-channelleakyFXLMSalgorithm,thecostfunctioncanbemodiﬁedtoincludethecontroleffort,writtenas

(48)

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where

andmoderatingthe

controleffort

forand

(52)

(49)

where

theigenvalueof

Theeffectof

aretheﬁlteredreferencesignalvectors.

Apracticalapplicationofmultiple-reference/multiple-outputactivecontrolforpropellerblade-passagenoiseinsidea50-seataircrafthasbeenreported[33].Thatsystemusesthreereferencesignals(internallygeneratedsinusoids)forthefundamentalfrequencyanditsﬁrsttwoharmonics,16secondarysources,and32errorsensors,resultingina3

32multiple-reference/multiple-outputANCsystem.C.Multiple-ChannelIIRAlgorithm

Thepurposeofthebroad-bandfeedforwardmultiple-reference/multiple-outputadaptiveIIRcontroller[41],[73],[96]istoprovidemultiple-channelANCcapabilitywithlongerimpulseresponsesandfeedbackcompensationusingalow-orderrecursivesection.AsillustratedinFig.21,thecontrollercontainstwoﬁltersections.Theﬁrstsectionisablockofall-zeroFIRﬁltersfromeachreferencesensortoeachsecondarysource,whilethesecondsectionimplementsamatrix-IIRstructureofall-poleﬁlters.Thefeedforwardsectionofthecontrollerisrepresentedbythetransferfunctionmatrix

frominputtothe

thcomponentoftheoutputvector

repre-sentstherecursivesectionofthecontrollerwithelement

from

,whichdrivesthe

willnotonlyspeedup

convergencebutcanalsopreventphysicallyunreasonablevaluesofcontroleffort.Thevalueof

secondarysourcesto

the

secondaryactuatorstothereferencesensorinthebroad-bandmultiple-channelANCsystemistousefeedbackneutralization.

(53)

D.Multiple-Reference/Multiple-OutputFXLMSAlgorithmThegeneralmultiple-reference/multiple-outputANCsys-temusingtheFXLMSalgorithmisshowninFig.20,where

hasthattheANCﬁlter

areelementsofthesignalvector

isthe

referenceinputindexand

thsecondarysourceis

(50)

where

arethereferencesignalvectors.Therearedifferentsecondarypathsbetweenthe

secondarysourcesanderrorsensors,whicharemodeled

togenerateanarrayofﬁlteredreferencesignalsby

forthemultiple-channelFXLMSalgorithm

(51)

wherewhere

and

arethefeed-forwardandfeedbackﬁltercoefﬁcients,respectively,and

are,respectively,thereferenceinputsignal

vectorsandoutputsignalvectors.

Amultiple-reference/multiple-outputﬁltered-UrecursiveLMSalgorithm[41],[96]fortheIIRﬁlterstructuremini-mizesthesumofthe

(54)(55)

and

are,respectively,theﬁlteredreferenceandoutputsignalvectors.

Multiple-channeladaptiveIIRﬁlteringhasbeensuccess-fullyappliedtotheactivecontrolofrandomnoiseinasmallreverberantroom[41].Inthatwork,theperformanceofadaptivemultiple-channelFIRandIIRﬁlterswascompared

957

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Fig.21.Blockdiagramofmultiple-channelANCsystemusinganIIRadaptiveﬁlter.

experimentallyforanANCsystemwithfoursecondarysourcesandeighterrorsensors.Thematrix-IIRstructureresultsinamorestableconﬁgurationinthepresenceoffeedback,especiallyifasmallleakagefactorisincluded.Theexperimentalresultsalsoshowthatfarbetterperfor-manceisachievedbyusingIIRﬁltersratherthanFIRﬁlterswhentheprimarynoisesourcehasalightlydampeddynamicbehavior.

D.Multiple-ChannelAdaptiveFeedbackANCSystemsThesingle-channelfeedbackANCsystemshownin

systemthathasFig.15iseasilyextendedtoa

ofthefeedbackANCsystemissynthesizedas

anestimateoftheprimarynoise

(56)

istheimpulseresponsesofﬁlter,whichwhere

fromthemodelsthesecondarypath

arethesecondary

signalsobtainedfromtheadaptiveﬁlters

byadjustingtheweightvectorforeachadaptive

ﬁlter

(57)

where

(58)

isthereferencesignalvectorﬁlteredbythesecondary-pathestimate

adaptivefeedbackANCsystem

isillustratedinFig.22.Inthissystem,therearesecondarypathsfromthe

therrorsensor,whichareestimatedbythecorre-spondingﬁlters

secondarysignalserrorsignalssecondary-pathestimatestogenerate

(59)

istheimpulseresponseofthesecondary-where

pathestimate

Fig.22.

BlockdiagramofK2MfeedbackANCsystem.

forthecorresponding

adaptiveﬁlters,

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Fig.23.Blockdiagramofonlinesecondary-pathmodelingtech-niqueproposedin[9].

Fig.24.BlockdiagramofANCsystemwithonlinesec-ondary-pathmodelingusingadditiverandomnoise.

A.FundamentalProblem

AnANCsystemusingtheFXLMSalgorithmwithadap-tiveonlinesecondary-pathmodeling[9]isillustratedin

generatesasecondaryFig.23.Theadaptiveﬁlter

thatpassesthroughthesecondarypathnoise

forthetobeunobtrusive,itshouldobserveonly

thesignalsalreadyinthesystem.Consequently,inapracticalANCsystem,atradeoffbetweenindependenceandintrusionhastoberesolved.

B.AdditiveRandomNoiseTechnique

1)BasicTechniqueandConvergenceAnalysis:Anonlinesecondarypathmodelingtechniqueusingadditiverandomnoise[99]isillustratedinFig.24.Azero-meanwhitenoise

isinternallygeneratedandisaddedtothesecondary

todrivethesecondarysource.Theadaptivesignal

isconnectedinparallelwiththesecondarypathﬁlter

only.

Itisusefultodeﬁnethecomponentoftheerrorduetotheoriginalnoiseas

(61)

where

aretheimpulseresponsesofattimeisuncorrelatedisalsouncorrelatedwith

alsoservesasanexcitationsignalfor

secondary-pathmodeling.Thecoefﬁcientsoftheadaptive

areadjustedonlinetomodelcontinuouslytheﬁlter

secondarypath

isapersistentexcitationsignal,andthat

time-invariantsystems,thesteady-statesolutionof[4]

areis

onlyif[orequivalently,].

isaffectedbytheEquation(60)alsoshowsthat

adaptiveﬁlter

and

isvery

with

complicated.Forexample,bysubstituting

,whichisanundesiredsolutionand

shouldbeavoided.

Therearetwoimportantrequirementsofsecondary-pathmodeling.Theﬁrstisthatanaccurateestimateof

willhaveaneffecton

theconvergenceoftheadaptivealgorithm.

AsillustratedinFig.24,thecoefﬁcientsoftheadaptive

areupdatedbytheLMSalgorithm,whichisﬁlter

expressedas[4]

(62)

isthecoefﬁcientvectorofandiswhere

inthereferencesignalvector.Theexpectedvalueof

(62)convergestoitsoptimalsolutionandareuncorrelated.However,thisdoesnotmean

willbeequaltothatinstantaneousvaluesof

in(62)is

adisturbancethatisfrustratingconvergenceoftheLMSalgorithmandwillthereforedegradetheperformanceoftheadaptiveﬁlter

directly.However,

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Foronlinemodeling,actslikeanuncorrelatedplant

Afterconvergence,thisresidualnoisenoiseofpower

willperturbtheadaptiveweightsofdueto

and

impulseresponsesoftheﬁltersforsufﬁcientlysmallstepsize

arethe

and

and(62)willconverge

isthe

andorderoftheadaptiveﬁlter

[4].Asanexample,supposethat

(anonlinenormalizedmodelingerror

[4].Therefore,itwouldtake100times

toconvergeonlineasitwouldtoconvergeaslongfor

ofﬂine.InmostANCapplications,theinterferenceismuchlargerthantheexcitationsignalandthe

isthereforeveryslow,oritconvergencerateofﬁlter

mayfailtoconvergebecauseofﬁnite-wordlengtheffects.2)MethodsforImprovement:Toimprovetheconver-inthepresenceoftheinterferencegenceof

thatiscorrelatedwiththe

[100],[101].Anadditionaladaptiveprimarysource

asthereferencesignalisusedtocanceltheﬁlterwith

inerrorsignalpickedupbyundesiredcomponent

theerrorsensor.Theconvergencerateofthemodelingﬁlter

hasbeenshowntoimprovebyafactorof

and

isusedduringtheinitializationstageor

aredetected,atifsigniﬁcantchangesin

andareupdated.Otherwisethewhichtimesonly

systemupdates

astheexcitationsignal.Thecostsonlyonedelayunitbecauseimplementationof

delayunitsarealreadyincludedin

haveconverged,wehave[4]

inerrorsignal

[102].Theoptimumdelayfortheadaptivepredictorisequaltothelengthoftheimpulseresponseofthesecondarypathbeingmodeled.

C.OverallModelingAlgorithm

Anoverallonlinesecondary-pathmodelingalgorithm[49],[103]–[105]triestoeliminatethebiasingterm

in(60)byintroducinganotheradaptiveﬁltertomodel

thatistheoutputsignalof

providessufﬁcientexcitationatall

frequencies.Therefore,thecorrespondingand

andthe

lengthoftheimpulseresponseof

arelarge.Adaptiveﬁlters

and

areabletotrack

inboth

areabletotrack“slow”changesonlinewhenisused[107].

D.Multiple-ChannelModelingAlgorithms

1)InterchannelCouplingEffect:Onlinemodelingof

secondarypathsismoredifﬁcultthanfora

fromsingle-channelcase,sincetheerrorsignal

the

andsecondarypathsfor

todecorrelatetheprimaryand

andwillconvergesecondarysignalssothat

960

andare

generatedbyadaptiveﬁltersandarecombinedwithadditive

todrivethesecondarysources.Theerrorrandomnoise

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Fig.26.Secondary-pathmodelingfora12222ANCsystemusingonerandomnoisegenerator.

signalismeasuredbytheﬁrsterrorsensor,whichis

canceledbytheresidualerroroftheprimarynoise

thenoisesfrombothsecondarysources.Adaptiveﬁlters

andareusedtomodelthesecondarypathsand

iszeromeanand

isuncorrelatedwith

willconvergeto[4]

andinthiscase],the

isbiasedbythecross-coupledsecondaryestimate

andispaths

adaptedatthesametimeas

secondary

pathsfromoneofthesecondarysourcestothesecondarysourcescouplestoeacherrorsensor.Thisprocessisrepeated

secondarypathtransfer

functions.Ashortcomingofthissolutionisthetotaltimerequiredtomodelallthesecondarypaths(bothofﬂineandonline),whichmaybetoolongforsomeANCapplications.Analternativesolutionistouse,forexample,tworandom

2system.Therandomnoisegenerators[4]fora1

andaremutuallyuncorrelatedandalsonoises

uncorrelatedwithothersignals.Thistechniquecanbegeneralizedtosolvetheinterchannelcouplingproblemof

ANCsystemusinga

secondarypathsusingasinglerandomnoisegenerator.

TheoverallmodelingalgorithmdiscussedinSectionVI-Ccanalsobeextendedtomultiple-channelANCsystemswith

isthenumberofsecondarysources.

Foreacherrorsignal,

areusedtomodelthecorrespondingsecondaryandcombinedwithanadaptiveﬁlterpaths

tocancelthehighlycorrelateddisturbancefromtheprimarynoisesource.Thismultiple-channelANCal-gorithmwasappliedtocontrolstructuralvibration[109].3)AudioInterferenceCancellation:AnintegratedANC-audiosystemenhancesadesiredaudiosignalbyutilizingANCtoreduceunwantedacousticnoise.Thisintegratedsystemusessharedanalogcomponentssuchasmixers,ampliﬁers,andloudspeakerssothatmultiple-channelANCmaybeappliedinavarietyofapplications,suchasau-tomobiles,withouttheexpenseofsystemredundancies.Inthisintegratedsystem,theaudiosignalpickedupbytheerrorsensorsinanenclosurebecomesaninterferencetotheANCsystem.TheaudiointerferencetotheANCﬁltercanbereducedusinganadaptivenoisecancelerwiththedesiredaudiosignalasthereferencesignal[110].As-sumingthattheaudiosignalisofpersistentexcitationanduncorrelatedwiththeprimarynoise,theadaptiveﬁlterusedfortheaudiointerferencecancellationwillconvergetothesecondarypath,andthusalsoperformsonlinesecondary-pathmodeling.Inaddition,musicwouldbemoreenjoyablethanrandomnoise,bothintheinitialtrainingstageandforonlineoperation.Thisintegratedsystemisexpandedtoincorporatehands-freecellularphoneoperation[111].Interferencecancellationandonlinemodelingareinher-entlymoredifﬁcultforthemultiple-channelcase.First,theleftandrightaudiosignalsmaybepartiallycorrelatedandthatwouldcauseproblemsinuniquelyidentifyingthecross-coupledsecondarypaths.Furthermore,theinterchanneldecouplingdelaytechniquecannotbeusedherebecausethatwoulddestroythestereoeffectofthedesiredsignals.Consequently,ofﬂinetechniquesorsomecombinationofonlineandofﬂinetechniqueswouldhavetobeemployedformultiple-channelsystems.

VII.OTHERANCSTRUCTURESANDALGORITHMS

TheadaptivetransversalﬁlterusingtheFXLMSalgo-rithmisthemostwidelyusedtechniqueforANCsys-tems,owingtoitssimplicityandrobustness.However,theLMSalgorithmhasthedisadvantageofrelativelyslowandsignal-dependentconvergence.ThismaybeonlyaminorproblemforANCsystemswithstationarynoisesourcessuchastransformers,electricpowergenerators,diesel-poweredboats,locomotives,andcompressors.Fornonstationarynoisesourcessuchasautomobiles,slowconvergenceisacriticalproblemwhenattemptingtocanceltransientnoise,whichoccursatvehiclestartups,stops,orgearshifts,orwithsuddenchangesofenginespeedsorroadnoisefromtires.

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Fig.27.Overallstructureoflatticepredictorandmultipleregressionﬁlter.

Anadaptivesysteminvolvestwobasicparts:aﬁlteringoperationthatproducesanoutputsignalandanadaptationalgorithmthatadjuststhecoefﬁcientsoftheﬁlter.Ifatransversalﬁlterisused,theconvergenceratecanbeimprovedbyusingmoreadvancedalgorithmssuchasadjustable-step-sizeLMSalgorithmsandrecursive-least-squares(RLS)algorithm.Theotherapproachistoconditionthereferencesignalbyemployingdifferentﬁlterstructuressuchasthelatticeﬁlter,subbandﬁlter,ororthogonaltransform.

ThesimplestapproachforimprovingtheconvergenceoftheLMSalgorithmistouseadaptivestepsizes[112]–[115].Theselectionofstepsizecanbebasedonthemagnitudeoftheerrorsignal,polarityofsuccessivesamplesoftheerrorsignal,measurementofthecorrelationoftheerrorsignalwiththereferencesignal,andotherfeatures.Theperformanceofthesetechniquesishighlydependentontheselectionofcertainparametersinthealgorithms,andtheoptimalchoiceishighlysignaldependent.Avariable-step-sizeLMSalgorithmwasusedtoimproveconvergenceforanair-conditioningductANCapplication[116],[117].A.LatticeANC

1)LatticeStructuresandAlgorithms:Theadaptivelat-ticepredictorisamodularstructurethatconsistsofanumberofcascadedstageswithtwoinputandtwooutputchannels.Thelatticestructureenjoystheadvantagesofasimpletestforﬁlterstability,goodperformanceinﬁnite-wordlengthhardwareimplementations,andgreatlyreducedsensitivitytotheeigenvaluespreadofthereferencesignal[15].Therecursiveequationsthatdescribethelatticestructureareexpressedas[4]

ofadaptiveﬁlterare

updatedbythegradientlatticealgorithmtominimizethemeansquareofthesumofforwardandbackwardpredictionerrorsateachstage[118],[119]

(68)

thstage.Thesteady-statewhere

reﬂectioncoefﬁcientsofthelatticepredictorhaveamag-nitudelessthanone[15].Thispropertyisveryimportantandconvenientforaﬁxed-pointhardwareimplementation.Anotherimportantpropertyofthelatticestructureisthatthe

aremutuallyuncorrelatedbackwardpredictionerrors

[15].Thus,thelatticepredictortransformsthecorrelatedreferencesignals

(69)

where

(66)(67)

istheforwardpredictionerror,isthewhere

isthereﬂectioncoefﬁ-backwardpredictionerror,

isthestage(order)index,andcient,

isthetotalnumberofcascadedstages.Thereference

isusedastheinputsignalforstageone,assignal

showninFig.27andexpressedby

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followingtheadaptiveregres-sionﬁlterresultsintheFXLMSalgorithm,expressedas[4]

(72)

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Fig.28.ANCsystemusingalatticeﬁlterandtheFXLMSalgorithm.

whereistheﬁlteredbackwardpredictionerrorvectorwithelements

isalsoﬁlteredby

toyield-pointdatabuffer.Thisﬁlteredreferencesignalvectoristhentransformedinto

usingtheFFT.Theresidualthefrequencydomain

measuredbytheerrorsensorisalsostoredinanerror

forex-pressedin(73)requiresintensivecomputationandstorage

isﬁlteredbythesinceeach

secondary-pathestimate

hasbeensplitinto

for

eachfrequencybinthatisinverselyproportionaltothesignalpoweratthatbin.Thisresultsinthenormalizedfrequency-domainFXLMSalgorithmexpressedas

(74)

andthereﬂectioncoefﬁcients

arecopiedfromtheadaptivelatticepredictorshowninFig.28.Thisslavedlatticeﬁlterthengenerates

where

isthecomplexconjugateof

(75)

isthenormalizedstepsizeatfrequencybin

(76)

isalowpass-ﬁlteredestimateofthepowerof

samples.

Insteadofﬁlteringthesignalsamplebysample,thefrequency-domainFXLMSalgorithmprocessesthesignalblockbyblock.Thus,thereare

isﬁrstﬁlteredby

-pointdatabufferandthentransformedtothefrequency-domainsignals

toproducethefrequency-domain

outputsignals

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Fig.30.DelaylesssubbandANCsystem.

hasbeenrecentlyadvancedforthatapplicationinvolvestheuseofsubbands[129],[130].Processingthesignalsinsubbandshasatwofoldadvantage:1)thecomputationalburdenisreducedbyapproximatelythenumberofsub-bands,sinceboththenumberoftapsandweightupdateratecanbedecimatedineachsubbandand2)fasterconvergenceispossiblebecausethespectraldynamicrangeisgreatlyreducedineachsubband.Unfortunately,thebandpassﬁltersusedinsubbandprocessingwillintroduceasubstantialdelayinthesecondarypath.

Amodiﬁcationofthesubbandtechniqueeliminatesdelayinthesecondarypath[131],[132].Thebasicideaisthattheadaptiveweightsarecomputedinsubbandsbutarethencollectivelytransformedintoanequivalentsetofwidebandﬁltercoefﬁcients.Fig.30showsthebasicconﬁgurationofthedelaylesssubbandANCtechnique.Thedisturbanceandreferenceareassumedtobederivedfromacommonnoisesourcethroughthelineartransferfunctions

developedasatransformationofﬁltered-Xderivedsubbandweights,therebyeliminatinganydelayassociatedwiththecancellationsignal.

Theﬁlteredreferencesignalanderrorsignal

aredecomposedintosetsofsubbandsignalsusingthebandpassﬁlters

(possiblyafterap-propriatebandshifting)andthesubbandadaptiveweightsarecomputedbythecomplexLMSalgorithm.Theadap-tiveweightsineachsubbandarethentransformedintothefrequencydomain,appropriatelystacked,andinverse-transformedtoobtainthewidebandﬁltercoefﬁcients.OnewaytoimplementthedelaylesssubbandadaptiveﬁlteristoemploythepolyphaseFFTtechnique[123].Ageneralformulationofthecomputationalrequirementsintermsoftheadaptiveﬁlterlength,numberofsubbands,andpolyphaseﬁlterlengthcanbefoundelsewhere[132].D.RLSAlgorithmforANC

TheRLSalgorithmcanbeusedwithanadaptivetransversalﬁltertoprovidefasterconvergenceandsmallersteady-stateerrorthantheLMSalgorithm.The“fasttransversalﬁlter”[133]isanefﬁcientversionoftheRLSalgorithm,whichreducestherequiredoperationstoapproximately

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RLSalgorithmsandthefasttransversalﬁlter[15].WenowshowhowtheRLSalgorithmcanbemodiﬁedforANCapplications,whichincorporatesasecondarypathfollowingthetransversalﬁlter.ThismethodcanalsobeappliedtomodifythefasttransversalﬁlterforANCapplications.Theleast-squaresmethodassumesacostfunctionattime

fromthepreviousinsteadofesti-andtheninvertingittoobtainmating

(77)

(79)(80)

where

theﬁlteredreferencesignalvectorwithelements

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Fig.32.SchematicdiagramofacousticANCexperimentinareverberantroom(adaptedfrom[132]).

Fig.33.[141]).

Blockdiagramofelectronicmufﬂer(adaptedfrom

obtainstheerrorsignalwhichistobeminimized.The

isderivedfromanothermicrophonereferencesignal

ontheright,whichisincloseproximitytotheprimarydisturbance.

TheapplicationofANCtothecancellationofbroad-bandacousticnoiseinareverberantroomrequiresalargenumberoftaps.Inordertominimizethecomputationalrateandtoenabletherealizationofthistechniqueusingasinglelow-costDSPchip,thesubbandtechniqueshowninFig.30canbeused.Applicationofthistechniqueusinga512-tapwidebandﬁlterhasachievedmorethan15dBofcancellationoverabandof100–500Hz[132].

B.Single-ChannelNarrow-BandFeedforwardSystems1)EngineExhaustNoise:Thecharacteristicsofengine-generatednoisecanvaryrapidlywithabruptchangesinengineloading,suchaswhentheengineisquicklyacceleratedordecelerated.Inaddition,engine-generatednoiseisdominatedbyharmonicallyrelatedcomponentshavingfrequenciesthatvaryasafunctionoftheenginerotationalspeed.Thedominantharmoniccomponentswilldependonthenumberofcylinders,duetothedifferingﬁringpatterns.

Anexampleofelectronicmufﬂerperformance[140]wasobtainedfora450-horsepower,six-cylinder,two-cycledieselengineusedtopoweranauxiliaryelectricalpowergenerator.Themultiple-frequencyparallelFXLMSalgo-rithmofSectionIII-D2wasusedforthisapplication.Theelectronicmufﬂereliminatesthebackpressureassociatedwithaconventionalpassivemufﬂer,evenwhilereducingthenoiselevel.TheANCsystemisnormallylimitedtolow-frequencyoperation;however,itcanbecombinedwithalow-pressure-droppassivesilencertoattenuatetheresidualnoiseathigherfrequencies.Thus,thecombinationisabletoachievebothaimsoflowpressuredropandlownoise,simultaneously.

Theblockdiagramoftheelectronicmufﬂerdevelopedin[141]isshowninFig.33.Two4.5-inlow-frequency,high-temperatureloudspeakersareused.Thecancelingnoiseisportedaroundthepipeinacoaxialarrangement,andcancellationtakesplaceintheopenairattheendofthepipe.Theerrormicrophonewasmountedontherearofthe

966

Fig.34.Activeheadsetforcancelingnarrow-bandperiodicnoise(adaptedfrom[142]).

vehicle,10infromtheendpipe.ThesystemconsistsofthreemajorsubsystemsdiscussedinSectionIII-C.Theﬁrstisthewaveformgenerator,whichconvertsthepulsetrainfromtheenginetachometerintoasetofsinewaveshavingfrequenciesthataremultiplesoftheenginerotationrate.Inthenextsubsystem,thesesinewavesareadaptivelyﬁltered(toadjustamplitudeandphase)andthenmixedtodrivethecancelingloudspeaker.Thethirdsubsystemmonitorstheresidualnoiseatthecontrollocationandadaptstheﬁltercoefﬁcients.

2)ANCHeadsets:Thepurposeofhearingprotectorsistoprotecttheearfromharmfulnoise.TheapplicationoffeedforwardANCusingthewaveformsynthesismethodhasbeendeveloped[142]tocancelrepetitivebackgroundnoiseattheearsofapersonwhileretainingtheabilitytohearotherambientsounds,asillustratedinFig.34.Thesynchronizationsignalscanbeobtainedbyeitheroptical,ultrasonic,orelectricalmeans(e.g.,wireorradio).ThesynchronizationsystemcanbecommontoanumberofANCheadsets,suchasinthecaseofavehiclecarryingmultiplepassengers.Becausethecancellationonlyaffectsnoisesynchronizedtothesourceoftherepetitiveback-groundnoise,mostofthelow-frequencysoundthatisnotsynchronizedremainsunaffected.

3)FanNoise:Asingle-channelnarrow-bandANCsys-temcanbeusedtocancelnoiseradiatedfromsmallaxialﬂowfans.Onesuchapplicationappearsin[143],whichusesaninfrareddetectorplacedoverthefantoderivebladepassagerate.Experimentsshowedthattheradiationofbladepassagetonescouldbeattenuatedby12dBusingthismethod.ThedevelopmentofanANCsystemforductedfansusingthewaveformsynthesismethodhasalsobeenreported[144],[145].

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C.Multiple-ChannelFeedforwardSystems

Multiple-channelfeedforwardANCapplicationshavebeendemonstratedforvibrationANConmechanicalstruc-tures,acousticANCinenclosuressuchasautomobileandaircraftcabins,free-ﬁeldtransformernoise,andacousticANCinlarge-dimensionalductswithhigh-ordermodes.1)VehicleEnclosures:Mostmidsizefour-cylindervehi-clessufferfromenginenoise,particularlythelowfrequency“boom”attheengineﬁringfrequency,whichisthedomi-nantsourceofinternalnoiseathigherenginespeeds[82].Withrespecttotheinteriorspaceofautomobiles,threeaspectscanbeconsideredbeneﬁcialforthesuccessofANC:1)theperiodicityofengine-relatednoise;2)therelativelysmallvolumeofthecabin,whichleadstoasmalloverlapoftheresonantmodesinthelowerfrequencyrange;and3)thefactthatANCisonlyrequiredinthespacewheretheheadsofthedriverandpassengeraretypicallylocated.Therefore,alow-costsolutionistoprovideaquietzoneinsidethecabinaroundthedriver’sandpassengers’headposition.

Engine-relatednarrow-bandnoisecomponentscanbecanceledeitherbythewaveformsynthesismethodorbytheadaptivenotchﬁltertechnique.Theenginespeedismeasuredbyanelectricalsensor,providingapulsesequencefromwhichareferencesignalissynthesized.Thecancelingsignalisgeneratedbyanadaptiveﬁlterthatfeedssecondaryloudspeakersservingascontrolsources.Afastalgorithmtoadapttheadaptiveﬁltercoefﬁcientsisessentialtoprovideacancelingsignalthattracksunderrapidlychangingrideconditions.Therefore,anANCsysteminacabinwillcontinuetofunctionevenwhenwindowsorhatchesareopened,andthereforeenablesexternalwarningsoundstobeheard.

ElliottandcoworkersdevelopedanANCsystemforthereductionofenginenoiseinacar[33],[81].Inthissystem,areferencesignalwasobtainedfromtheignitioncircuitandsixloudspeakersinthecarwereused.Theseloudspeakersandtheirassociatedpowerampliﬁerscanbesharedwiththein-carentertainmentsystem.UptoeighterrormicrophoneswereusedtomonitortheperformanceoftheANCsystem.Areductionof10–15dBattheengineﬁringfrequencywasachievedbythisANCsystem.

Activecontroloflow-frequencyroadnoisepresentsagreaterchallengethancontrollingenginenoise.Inthatapplication,multiplebroad-bandprimarynoisesrequirehigher-orderadaptiveﬁlters,thusconsiderablyincreasingtheconvergencetimeandcomputationalburden.Inoneapplication[146],sixaccelerometerswereplacedclosetothefrontwheels.Twosecondaryloudspeakerswereplacedinthedoorsadjacenttothedriverandfrontpassenger,andtwoerrormicrophonewereplacedonthefrontheadrestsattheouterearpositions.Themultiple-channelFXLMSalgorithmdiscussedinSectionV-Bwasusedforthisapplication.Abroad-bandreductionofabout7dB(A-weighted)inthesoundpressurelevelwasmeasuredwhendrivingonatypicalroadsurface.Inthisapplication,theimportantdesignissuesaretheplacementofreference

KUOANDMORGAN:ACTIVENOISECONTROL

sensorsformaximumcoherencewithrespecttotheinteriornoisetobecanceledandthetimedelayofthereferencesignals.

VibrationalANCinautomobilesisasimpleextensionofacousticANC[82].Accelerometersandactuatorsarelocatedonthechassissideofactiveenginemounts.Thepotentialbeneﬁtsofactiveenginemountsareverydramatic,notonlyreducingacousticnoiseandmechanicalvibrationwithinthecabinbutalsoimprovingthecontrolandridequalitiesofthevehicle.

2)AircraftCabins:Theinteriornoiseofpropeller-drivenaircraftwasfoundtobedominatedbytonesatthefunda-mentalandharmonicfrequenciesofthepropeller.Feed-forwardANCsystemswith16loudspeakersand32mi-crophoneshavebeendevelopedfornoisecontrolinthepassengercabinofapropelleraircraft[88].The32mi-crophonesarelocatedatseatedheadheightthroughoutthepassengercabin.Analternativetechniqueforcontrollingaircraftinteriornoiseistouselightweightvibrationalsecondarysourcesonthefuselage[147],[148].

3)Free-FieldRadiation:Inmanysituations,undesirednoiseisradiatedintothefarﬁeld.Ifthenoisesourceisﬁxedandwelldeﬁned,itispossibletosuppresstheradiationscatteredbytheprimarynoisesourcebysurroundingthenoisesourcewithalayerofsecondarysources.Thisconceptisknownasanactivenoisebarrier.TheANCtechniquecanbecombinedwithapassivebarrierinordertoimprovethenoiseattenuationatlowfrequencies.Thelocationandseparationoftheerrorsensorsandsecondarysourcescanbeoptimizedtogetlargenoiseattenuationoverawide

4area.Aconﬁgurationoftwoindependent1

systemswastestedin[149]usingthenarrow-bandmultiple-channelFXLMSalgorithm.Acancellationof6–30dBwasdemonstratedoverawidearea.Toobtaingreaterspatialcoverage,itisnecessarytodeployasystemwithmorechannels.Potentialapplicationsofthistechniquearereduc-ingenvironmentalnoiseinlocalareas,suchasquietingthepositionofamachineoperatorinanoisyfactory,providinganoisescreenforabedatanairporthotel,creatinganoisebarrieratairports,highways,andsoon.

4)TransformerNoise:ANCalsooffersanalternativetolargepassivebarriersforattenuatingtransformernoise[150].Thisnoiseiscomposedofeven-numberedharmonicsofthe60-Hzpowerfrequency.Experimentsusingfoursecondaryloudspeakersandsixerrormicrophoneswiththe

6narrow-bandFXLMSalgorithmhaveshown1

thatsparsearraysofcancelersareeffectiveinprovidingattenuationoversigniﬁcantanglesofazimuth.Cancellationvaluesof15–20dBwereobtainedover35–40

ofazimuthat240Hz

[150].Asimilarsystemcomposedofthreecontrollers,threemicrophones,andthreeloudspeakershasbeendeveloped[151],andmorethan10-dBsoundpressurelevelreductionwasachieved.

5)IntegrationwithAudioandCommunicationSystems:AsANCcontinuestoprogress,theneedforsuccessfulin-tegrationwithexistingsystemsbecomesapparent.Thisexpectationofauniﬁeddigitalsolutionisexempliﬁed

967

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Fig.35.Experimentalstructurefortwo-channelvibrationANCexperiment(from[152]).

inmodernautomotiveelectronics.AuniﬁedapproachtocombineANC,in-carentertainment,andcommunication(cellularphone)systemshasbeenproposed[111]usinganadaptivenoisecancelertoattenuatenoisepickedupbythemicrophonebeforetransmission,anacousticechocancelertoreduceacousticechofromtheloudspeakertothemicrophoneforhands-freefull-duplexcellularphones,andamultiple-channelANCsystemtoreducetheacousticnoiseinsideanautomobilepassengercompartment.

Ithasbeenfoundthatthestandardin-carentertainmentloudspeakerpositionsareoftenquiteacceptableforANCapplications,whiletheerrormicrophonescanbedistributedatpositionsdeterminedbyacousticmodeanalysisofthevehicle[82].Productionvehicleswillutilizethesameloudspeakersasusedbythein-carentertainmentsystem,sharingthesamepowerampliﬁer.Thein-carentertainmentsystemismovingtoacompletelydigitalsystem,inwhichcaseANCmayultimatelybecomeasoftwareadditiontothedigitalaudiosystem.

6)ModalANCforaVibratingBeam:ThemodalANCconceptintroducedinSectionVII-Bisexempliﬁedbythecontrolofavibratingcantileverbeam[138].Themodeswerecalculated,anddrivingfrequencies

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Fig.36.Experimentalsetupfor12222multiple-channelbroad-bandfeedforwardANCsystem(adaptedfrom[154]).

wasimplementedonaTexasInstrumentsTMS320C30-basedsystem.Themicrophonethatsensestheresidualerrorsignalwasplacedontheaxisofthepipeatvariouslocationsfromthepipeexit.Theconvergenceofthesystemdependsonadjustmentofthemicrophonepreampliﬁergainbecausethemicrophonesignalisusedtosynthesizethereferencesignal.TheadaptivefeedbackANCsystemwastestedusingrealnoiserecordedfromarunningtractorengineandabout30dBofreductionoftheharmoniccomponentsisachieved[156].

2)Multiple-ChannelSystems:Themultiple-channelfeed-backANCalgorithmwastestedforasystemwithtwosecondaryloudspeakersandoneerrormicrophone,the2

theaverage,about20dBattenuationwasobtainedformostofthesigniﬁcantharmonicspresentintheprimarynoise.Theexperimentalsetupforthe2

1caseexceptthattwoerrormicrophones

areused.Thesecondaryloudspeakerswereagainmountedontheroofofthecabinandthetwoerrormicrophoneswereplacedbelowandfacingthetwoloudspeakers.Theperformanceofthe2

1system.IX.CONCLUSIONS

ANCcancelstheunwantednoisebygeneratingantinoiseofequalamplitudeandoppositephasethroughthesec-ondarysources.ThispaperhasemphasizedthepracticalaspectsofANCsystemsintermsofadaptivealgorithmsandDSPimplementationsforreal-worldapplications.ThemostwidelyusedANCsystemwiththeadaptivetransversalﬁlterandtheFXLMSalgorithmwasﬁrstdevelopedandanalyzedbasedonsingle-channelcasesforbroad-bandfeedforward,narrow-bandfeedforward,andadaptivefeedbackcontrol.Thesesingle-channelANCalgorithmswerethenexpandedtomultiple-channelcasesforcontrollingthenoiseﬁeldinanenclosureoralarge-dimensionduct.Variousadaptivealgorithmssuchasthelattice,frequency-domain,subband,andRLSalgorithmswerealsomodiﬁedforANCappli-cations.Thefundamentalproblemsandseveralsolutions

969

1adaptivefeedbackANC

systemwastestedusingrecordedtractorenginenoise.On

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toonlinesecondary-pathmodelingwerediscussedforpro-vidingsomedirectionsonnewalgorithmdevelopments.Applicationexamplesdemonstratedtheconnectiontoreal-worldproblems.REFERENCES

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[156]D.Vijayan,Feedbackactivenoisecontrolsystems,M.S.thesis,

NorthernIllinoisUniv.,DeKalb,IL,May1994.

SenM.KuoreceivedtheB.S.degreefromNationalTaiwanNormalUniversity,Teipei,Taiwan,in1976andtheM.S.andPh.D.degreesfromUniversityofNewMexico,Albuquerque,in1983and1985,respectively.

In1993,hewaswithTexasInstruments,Houston,TX.HeiscurrentlyanAssociateProfessorattheDepartmentofElectricalEngineering,NorthernIllinoisUniversity,DeKalb,IL.Hehasservedasaconsultantintheareasofdigitalsignalprocessingapplications

toGeneralMotors,TexasInstruments,Motorola,Tellabs,andothers.HeistheauthorofActiveNoiseControlSystems:AlgorithmsandDSPImplementations(NewYork:Wiley,1996)andofnumeroustechnicalpapers.Hehasbeenawardedtwopatents.Hisresearchfocusesonactivenoisecontrol,adaptiveechocancellation,digitalaudioapplications,anddigitalcommunications.

In1993,Dr.KuoreceivedtheIEEEConsumerElectronicsSocietyChesterSallAwardfortheFirstPlaceTransactionsPaperAward.HeisamemberofEtaKappaNu.

DennisR.Morgan(SeniorMember,IEEE)wasborninCincinnati,OH,onFebruary19,1942.HereceivedtheB.S.degreein1965fromtheUniversityofCincinnati,OH,andtheM.S.andPh.D.degreesfromSyracuseUniversity,Syracuse,NY,in1968and1970,respectively,allinelectricalengineering.

From1965to1984,hewaswiththeGen-eralElectricCompany,ElectronicsLaboratory,Syracuse,NY,specializingintheanalysisanddesignofsignalprocessingsystemsusedin

radar,sonar,andcommunications.HeisnowaDistinguishedMemberofTechnicalStaffatBellLaboratories,LucentTechnologies(formerlyAT&T),MurrayHill,NJ,wherehehasbeenemployedsince1984.From1984to1990,hewaswiththeSpecialSystemsAnalysisDepartment,Whippany,NJ,wherehewasinvolvedintheanalysisanddevelopmentofadvancedsignalprocessingtechniquesassociatedwithcommunications,arrayprocessing,detectionandestimation,andadaptivesystems.Since1990,hehasbeenwiththeAcousticsResearchDepartment,whereheisengagedinresearchonadaptivesignalprocessingtechniquesappliedtoelectroacousticsystems.Hehasauthorednumerousjournalpublicationsandisco-athorofActiveNoiseControlSystems:AlgorithmsandDSPImplementations(NewYork:Wiley,1996).

Dr.MorganhasservedasAssociateEditorforIEEETRANSACTIONSONSPEECHANDAUDIOPROCESSINGsince1995.

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