外文文献翻译 用于近似处理的低能耗数字滤波器Word格式.docx

外文文献翻译 用于近似处理的低能耗数字滤波器Word格式.docx

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专业

学号

班级

指导教师

2010年4月

Ⅰ.INTRODUCTION

TECHNIQUESforreducingpowerconsumptionhavebemultimediadevices.Sincedigitalsignalprocessingispervasiveinsuchapplications,itisusefultoconsiderhowalgorithmicapproachesmaybeexploitedinconstructionlow-powersolution.

AsignificantnumberofDSPfunctioninvolvefrequency-selectivedigitalfilteringinwhichthegoalistorejectoneormorefrequencybandswhilekeepingtheremainingportionsoftheinputspectrumlargelyunaltered.Examplesincludelowpassfilteringforsignalupsamplinganddownsampling,bandpassfilteringforsubbandcoding,andlowpassfilteringforfrequency-divisionmultiplexinganddemultiplexing.Theexplorationoflow-powersolutionsintheseareasisthereforeofsignificantinterest.

Tofirstorder,theaveragepowerconsumption,P,ofadigitalsystemmaybeexpressedas

（1）

WhereCiistheaveragecapacitanceswitchedperoperationoftypei（correspondingtoaddition,multiplication,storage,orbusaccesses）,Niisthenumberofoperationoftypeiperformedpersample,Vddistheoperatingsupplyvoltage,andfsisthesamplefrequency.

Real-timedigitalfilteringisanexampleofaclassofapplicationsinwhichthereisnoadvantageinexceedingaboundedcomputationrate.Forsuchapplications,anarchitecture-drivenvoltagescalingapproachhaspreviouslybeendevelopedinwhichparallelandpipelinedarchitecturescanbeusedtocompensateforincreaseddelaysatreducedvoltages.Thisstrategycanresultinsupplyvoltagesinthe1to1.5Vra-ngebyusingconventionalCMOStechnology.Powersupplyvoltagescanbefurtherscaledusingreducedthresholddevices.Circuitsoperatingatpowersupplyvoltagesaslowas70mV（at300K）and27mV（at77K）havebeendemonstrated.

Oncethepowersupplyvoltageisscaledtothelowestpossiblelevel,thegoalistominimizetheswitchedcapacitanceatalllevelsofthedesignabstraction.Atthelogiclevel,forexample,modulescanbeshutdownataverylowlevelbasedonsignalvalues.Arithmeticstructures（e.g.,ripplecarryversuscarryselect）canalsobeoptimizedtoreducetransi-tionactivity.Architecturaltechniquesincludeoptimizingthesequencingofoperationstominimizetransitionactivity,avoidingtime-multiplexedarchitectureswhichdestroysig-nalcorrelations,usingbalancedpathstominimizeglitchingtransitions,etc.Atthealgorithmiclevel,thecomputationalcomplexityorthedatarepresentationcanbeoptimizedforlowpower.

AnotherapproachtoreducetheswitchedcapacitanceistolowerN,.EffortshavebeenmadetominimizeN,byintelli-gentchoiceofalgorithm,givenaparticularsignalprocessingtask.Inthecaseofconventionalfilterdesign,thefilterorderisfixedbasedonworstcasesignalstatistics,whichisinefficientiftheworstcaseseldomoccurs.Moreflexibilitymaybeincorporatedbyusingadaptivefilteringalgorithms,whicharecharacterizedbytheirabilitytodynamicallyadjusttheprocessingtothedatabyemployingfeedbackmechanisms.Inthispaper,weillustratehowadaptivefilteringconceptsmaybeexploitedtodeveloplow-powerimplementationsfordigitalfiltering.

Adaptivefilteringalgorithmshavegenerallybeenusedtodynamicallychangethevaluesofthefiltercoefficients,whilemaintainingafixedfilterorder.Incontrast,ourapproachnvolvesthedynamicadjustmentofthefilterorder.Thisapproachleadstofilteringsolutionsinwhichthestopbandenergyinthefilteroutputmaybekeptbelowaspecifiedhresholdwhileusingassmallafilterorderaspossible.Sincepowerconsumptionisproportionaltofilterorder,ourapproachachievespowerreductionwithrespecttoafixed-orderfilterwhoseoutputissimilarlyguaranteedtohavestopbandenergybelowthespecifiedthreshold.Powerreductionisachievedbydynamicallyminimizingtheorderofthedigitalfilter.

Theideaofdynamicallyreducingcost（inourcase,powerconsumption）Whilemaintainingadesiredlevelofoutputquality（inourcase,stopbandenergyinthefilteroutput）emanatesfromtheconceptofapproximateprocessingincomputerscience.Whileapproximateprocessingconceptsmaybeusedtodescribeavarietyofexistingtechniquesindigitalsignalprocessingprocessing（DSP）,communications,andotherareas,therehasrecentlybeenprogressinformallyusingtheseconceptstodevelopnewDSPtechnique.Sinceouradaptivefilteringtechniquefallsintothiscategory,werefertoourapproachasadaptiveapproximatefiltering,orsimplyapproximatefiltering.

Ⅱ.DIGITALFILTERINGTRADE-OFFS

Afrequency-selectivedigitalfiltermayhaveeitherafiniteimpulseresponse（FIR）oraninfiniteimpulseresponse（IIR）.ItiswellknownthatIIRfiltersusefewertapsthanFIRfiltersinordertoprovidethesameamountofattenuationinthestopbandregion.However,IIRfiltersintroducenonlinearfrequencydispersionintheoutputsignalswhichisunacceptableinsomeapplication.Forsuchcases,itisdesirabletousesymmetricFIRfiltersbecauseoftherelinearphasecharacteristic.

AnimportantfamilyofsymmetricFIRfilterscorrespondstothesymmetricwindowingoftheimpulseresponsesofcorrespondingidealfilters.Forexample,alowpassfilterofthistypehasanimpulseresponsegivenby

（2）

Where

isasymmetricN-pointwindow.Thisfilterhascutofffrequency

andmaybeimplementedusingatappeddelaylinewithNtaps.Forthepurposesofthispaper,werefertosuchafilterashavingorderN.InFig.1,wedisplaythefrequencyresponsemagnitudesforthreedifferentvaluesofNwhen

isarectangularwindowand

=

.Itshouldbeobservedthatthemeanattenuationbeyondthecutofffrequency

increasewithfilterorder.Furthermore,withrespecttoatappeddelay-lineimplementation（seeFig.2）,thetapsoftheshorterTypeIfilteraresubsetsofthetapsofthelongerTypeIfilters.Thisensuresthatifthefilterorderistobedecreasedwithoutchangingthecutofffrequency,wecansimplypowerdownportionsofthetappeddelaylineforthehigherorderfilter.Thepricepaidforsuchpoweringdownisthatthestopbandattenuationofthefilterdecreases.

ButterworthIIRfilterarecommonlyusedforperformingfrequency-selectivefilteringinapplicationswherefrequencydispersionistolerable.ThefrequencyresponsemagnitudesofsuchfiltersdonotsufferfromtherippleswhichcanbeseeninthefrequencyresponsemagnitudesforFIRfilters.TheseIIRfiltersarecommonlyimplementedascascadeinterconnectionsofsecond-ordersections,eachofwhichconsistoffivemultipliesandfourdelays,asshowninFig.3.AlsoinFig.3isanillustrationofacascadestructureforaneighth-orderIIRfilterasthecascadeoffoursecond-ordersectionForthepurposesofthispaper,weconsidertheorderofaButterworthIIRfiltertobeequaltotwicethenumberofsecond-order

Frequency,

normalized

Fig.1FrequencyresponsemagnitudesforFIRfiltersofordersN=20,80,and140

Fig.2TappeddelaylineofanFIRfilterstructure,andthepoweringdownconceptTopreservephaselinearity,poweringdownmustbeappliedatbothendsofthestructure.

Fig.3CascadeimplementationofanIIRfilterstructure.Thedetailofoneofthesecond-ordersectionisshown.

sectionsinitscascadeimplementation.,AninterestingpropertyofIIRButterworthfiltersisthatifthesecond-ordersectionsareappropriatelyordered,onemaysequentiallypowerdownthelatersecond-ordersectionsandeffectivelydecreasethenetstopbanattenuationofthefilter.

Ⅲ.ADAPTIVEAPPROXIMATEFILTERING

Inthissectionwepresentthedetailsofourapproximateprocessingapproachtolow-powerfrequency-selectivefilter-ing.Asdiscussedearlier,frequency-selectivefiltersareusedinapplicationswherethegoalistoextractcertainfrequencycomponentsfromasignalwhilerejectingothers.Supposeasignal,x[n],consistsofapassbandcomponent,xp[n],andastopbandcomponent,

.Thatis,

（3）

Ifitwerepossibletocost-effectivelymeasurethestrengthofthestopbandcomponent,

fromobservationof

wecoulddeterminehowmuchstopbandattenuationisneededatanyparticulartime.Whentheenergyin

increases,itisdesirabletoincreasethestopbandattenuationofthefilter.Thiscanbeaccomplishedbyusingahigher-orderfilter.Conversely,thefilterordermaybeloweredwhentheenergyin

decreases.Wehavedevelopedapracticaltechnique,baseduponadaptivefilteringprinciples,fordynamicallyestimatingtheenergyfluctuationsinthestopbandcomponent,

andusingthemtoadjusttheorderofafrequency-selectiveFIRorIIRfilter.Asdescribedintheprevioussection,thedecrease

infilterorderenablesthepoweringdownofvarioussegmentsofthefilterstructure.Poweringdownofthehigherordertapshastheeffectofreducingtheswitchedcapacitanceatthecostofdecreasingtheattenuationinthestopband.AssumingthattheFIRdelaylineisimplementedusingSRAM,eventhedatashiftingoperationofthehigherordertapscanbeeliminatedthroughappropriateaddressingschemes.

OuroveralltechniqueisdepictedinFig.4.Thequantityd[n],whichrepresentstheenergydifferentialbetweentheinputandtheoutput,isobtainedas

（4）

where

（5）

and

（6）

Thefilterorderforsampleperiodn,Order[n],isupdatedateachsampleperiod.OneapproachfortheupdateprocessistochooseOrder[n]tobethesmallestpositiveintegerwhichguaranteesthatthestopbandenergy,Q[n],oftheoutputsignalwillbemaintainedbelowaspecifiedthresholdy.Assumingthatthestopbandportionofthe