SIST EN 301 245 V4.1.1:2003

• Abstract:

  SUBJECT Corrections to GSM 06.60

• Status: Published
• Publication Date: 30-Nov-2003
• ICS: 33.070.50 - Global System for Mobile Communication (GSM)
• Technical Committee: SS EIT - Technical Board for the electrotechnical, information technology and telecommunications fields
• Current Stage: 6060 - National Implementation/Publication (Adopted Project)
• Start Date: 01-Dec-2003
• Due Date: 01-Dec-2003
• Completion Date: 01-Dec-2003
• Mandate: T-172
• Ref Project: ETSI EN 301 245 V4.1.1 (2000-08) - Digital cellular telecommunications system (Phase 2) (GSM); Enhanced Full Rate (EFR) speech transcoding (GSM 06.60 version 4.1.1)

Overview

SIST EN 301 245 V4.1.1:2003 sets out the requirements for Enhanced Full Rate (EFR) speech transcoding within the Digital Cellular Telecommunications System (GSM Phase 2). Developed by the Slovenski inštitut za standardizacijo (SIST), this standard aligns with the European Norm EN 301 245 and is based on GSM 06.60 version 4.1.1. It details how speech signals in GSM networks are encoded and decoded, focusing on corrections and enhancements to existing transcoding specifications.

The EFR codec improves speech quality in GSM networks by providing advanced speech compression and decompression methods. These enhancements are crucial for maintaining call clarity and efficient spectrum use across mobile networks worldwide.

Keywords: GSM, Enhanced Full Rate (EFR), speech transcoding, digital cellular telecommunications, speech codec, SIST, EN 301 245

Key Topics

• Scope and Purpose: The document provides detailed mapping between input blocks of 160 speech samples (13-bit uniform PCM) and encoded blocks of 244 bits, and vice versa. It specifies the conversion between A-law PCM and 13-bit uniform PCM, as well as performance requirements important for transcoder functionality.
• Speech Codec Model: Based on Algebraic Code Excited Linear Prediction (ACELP), the EFR speech codec ensures high-quality speech at a bit rate of 12.2 kbit/s, optimizing for both clarity and bandwidth use.
• Encoding and Decoding: The encoding process converts speech to a compressed digital format for transmission over GSM networks, while the decoding process reconstructs speech accurately at the receiving end.
• Parameter Mapping: The standard describes sequence and subjective importance of encoded parameters, ensuring the most critical bits for perceived speech quality are protected during transmission.
• Test and Verification: Provides test sequences to verify compliance, allowing for high confidence in implementation by network manufacturers and operators.

Applications

SIST EN 301 245 V4.1.1:2003 is fundamental in the following areas within telecommunications:

• Mobile Network Infrastructure: Essential for the design and deployment of GSM mobile base stations and switches, enabling them to handle EFR-coded speech traffic.
• Mobile Devices: Integrates into mobile handsets and terminals to provide end-users with improved voice quality.
• Network Interworking: Facilitates compatibility between mobile stations and the core network, including Public Switched Telephone Network (PSTN) gateways, through standardized PCM conversions.
• Device Certification and Testing: Enables network operators and manufacturers to test and certify equipment for compliance with EFR requirements using standardized test sequences.

By adhering to this standard, telecom operators ensure interoperable, reliable voice services consistent with global GSM requirements, enhancing customer satisfaction through improved audio clarity.

Related Standards

The standard references several key documents and standards for comprehensive implementation and best practices:

• GSM 06.51 (EN 301 243): Enhanced Full Rate speech processing functions
• GSM 06.53 (EN 301 244): ANSI-C code for the GSM EFR speech codec
• GSM 06.54 (EN 301 250): Test vectors for EFR speech codec verification
• GSM 05.03 (ETS 300 575): Channel coding for GSM networks
• ITU-T G.711 & G.726: PCM and ADPCM standards for audio encoding and conversion

Conclusion

SIST EN 301 245 V4.1.1:2003 plays a vital role in ensuring high-quality speech transmission in GSM mobile networks. By providing standardized methods for Enhanced Full Rate speech transcoding, the standard supports operational efficiency, vendor interoperability, and improved end-user experience in digital cellular telecommunications. Businesses and engineers involved in GSM infrastructure benefit from compliance with this robust specification.

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.Digital cellular telecommunications system (Phase 2) (GSM); Enhanced Full Rate (EFR) speech transcoding (GSM 06.60 version 4.1.1)33.070.50Globalni sistem za mobilno telekomunikacijo (GSM)Global System for Mobile Communication (GSM)ICS:Ta slovenski standard je istoveten z:EN 301 245 Version 4.1.1SIST EN 301 245 V4.1.1:2003en01-december-2003SIST EN 301 245 V4.1.1:2003SLOVENSKI
STANDARD
ETSIEN301245V4.1.1(2000-08)EuropeanStandard(Telecommunicationsseries)Digitalcellulartelecommunicationssystem(Phase2);EnhancedFullRate(EFR)speechtranscoding(GSM06.60version4.1.1)GLOBALSYSTEMFORMOBILECOMMUNICATIONSRSIST EN 301 245 V4.1.1:2003

ETSIETSIEN301245V4.1.1(2000-08)2(GSM06.60version4.1.1)ReferenceREN/SMG-110660PR1KeywordsEFR,digitalcellulartelecommunicationssystem,GlobalSystemforMobilecommunications(GSM),speechETSI650RoutedesLuciolesF-06921SophiaAntipolisCedex-FRANCETel.:[phone]Fax:[phone]SiretN°34862356200017-NAF742CAssociationàbutnonlucratifenregistréeàlaSous-PréfecturedeGrasse(06)N°7803/88ImportantnoticeIndividualcopiesofthepresentdocumentcanbedownloadedfrom:http://www.etsi.orgThepresentdocumentmaybemadeavailableinmorethanoneelectronicversionorinprint.Inanycaseofexistingorperceiveddifferenceincontentsbetweensuchversions,thereferenceversionisthePortableDocumentFormat(PDF).Incaseofdispute,thereferenceshallbetheprintingonETSIprintersofthePDFversionkeptonaspecificnetworkdrivewithinETSISecretariat.Usersofthepresentdocumentshouldbeawarethatthedocumentmaybesubjecttorevisionorchangeofstatus.InformationonthecurrentstatusofthisandotherETSIdocumentsisavailableathttp://www.etsi.org/tb/status/Ifyoufinderrorsinthepresentdocument,sendyourcommentto:[e-mail]opartmaybereproducedexceptasauthorizedbywrittenpermission.Thecopyrightandtheforegoingrestrictionextendtoreproductioninallmedia.©EuropeanTelecommunicationsStandardsInstitute2000.Allrightsreserved.SIST EN 301 245 V4.1.1:2003

ETSIETSIEN301245V4.1.1(2000-08)3(GSM06.60version4.1.1)ContentsIntellectualPropertyRights.4Foreword.41Scope.52References.53Definitions,symbolsandabbreviations.63.1Definitions.63.2Symbols.73.3Abbreviations.124Outlinedescription.134.1Functionaldescriptionofaudioparts.134.2Preparationofspeechsamples.134.2.1PCMformatconversion.144.3PrinciplesoftheGSMenhancedfullratespeechencoder.144.4PrinciplesoftheGSMenhancedfullratespeechdecoder.154.5Sequenceandsubjectiveimportanceofencodedparameters.165Functionaldescriptionoftheencoder.165.1Pre-processing.165.2Linearpredictionanalysisandquantization.165.2.1Windowingandauto-correlationcomputation.165.2.2Levinson-Durbinalgorithm.175.2.3LPtoLSPconversion.185.2.4LSPtoLPconversion.195.2.5QuantizationoftheLSPcoefficients.205.2.6InterpolationoftheLSPs.215.3Open-looppitchanalysis.215.4Impulseresponsecomputation.225.5Targetsignalcomputation.225.6Adaptivecodebooksearch.235.7Algebraiccodebookstructureandsearch.245.8Quantizationofthefixedcodebookgain.275.9Memoryupdate.276Functionaldescriptionofthedecoder.286.1Decodingandspeechsynthesis.286.2Post-processing.306.2.1Adaptivepost-filtering.306.2.2Up-scaling.317Variables,constantsandtablesintheC-codeoftheGSMEFRcodec.317.1DescriptionoftheconstantsandvariablesusedintheCcode.318Homingsequences.348.1Functionaldescription.348.2Definitions.348.3Encoderhoming.368.4Decoderhoming.368.5Encoderhomestate.378.6Decoderhomestate.389Bibliography.43AnnexA(informative):Documentchangehistory.44History.45SIST EN 301 245 V4.1.1:2003

ETSIETSIEN301245V4.1.1(2000-08)4(GSM06.60version4.1.1)IntellectualPropertyRightsIPRsessentialorpotentiallyessentialtothepresentdocumentmayhavebeendeclaredtoETSI.TheinformationpertainingtotheseessentialIPRs,ifany,ispubliclyavailableforETSImembersandnon-members,andcanbefoundinETSISR000314:"IntellectualPropertyRights(IPRs);Essential,orpotentiallyEssential,IPRsnotifiedtoETSIinrespectofETSIstandards",whichisavailablefromtheETSISecretariat.LatestupdatesareavailableontheETSIWebserver(http://www.etsi.org/ipr).PursuanttotheETSIIPRPolicy,noinvestigation,includingIPRsearches,hasbeencarriedoutbyETSI.NoguaranteecanbegivenastotheexistenceofotherIPRsnotreferencedinETSISR000314(ortheupdatesontheETSIWebserver)whichare,ormaybe,ormaybecome,essentialtothepresentdocument.ForewordThisEuropeanStandard(Telecommunicationsseries)hasbeenproducedbyETSITechnicalCommitteeSpecialMobileGroup(SMG).Thepresentdocumentdescribesthedetailedmappingbetweeninputblocksof160speechsamplesin13-bituniformPCMformattoencodedblocksof244bitsandfromencodedblocksof244bitstooutputblocksof160reconstructedspeechsampleswithinthedigitalcellulartelecommunicationssystem.NationaltranspositiondatesDateofadoptionofthisEN:30October1998DateoflatestannouncementofthisEN(doa):31January1999DateoflatestpublicationofnewNationalStandardorendorsementofthisEN(dop/e):31July1999DateofwithdrawalofanyconflictingNationalStandard(dow):31July1999SIST EN 301 245 V4.1.1:2003

ETSIETSIEN301245V4.1.1(2000-08)5(GSM06.60version4.1.1)1ScopeThepresentdocumentdescribesthedetailedmappingbetweeninputblocksof160speechsamplesin13-bituniformPCMformattoencodedblocksof244bitsandfromencodedblocksof244bitstooutputblocksof160reconstructedspeechsamples.Thesamplingrateis8000sample/sleadingtoabitratefortheencodedbitstreamof12,2kbit/s.Thecodingschemeistheso-calledAlgebraicCodeExcitedLinearPredictionCoder,hereafterreferredtoasACELP.ThisENalsospecifiestheconversionbetweenA-lawPCMand13-bituniformPCM.Performancerequirementsfortheaudioinputandoutputpartsareincludedonlytotheextentthattheyaffectthetranscoderperformance.Thispartalsodescribesthecodecdowntothebitlevel,thusenablingtheverificationofcompliancetotheparttoahighdegreeofconfidencebyuseofasetofdigitaltestsequences.ThesetestsequencesaredescribedinGSM06.54[7]andareavailableondisks.IncaseofdiscrepancybetweentherequirementsdescribedinthisENandthefixedpointcomputationaldescription(ANSI-Ccode)oftheserequirementscontainedinGSM06.53[6],thedescriptioninGSM06.53[6]willprevail.ThetranscodingprocedurespecifiedinthisENisapplicablefortheenhancedfullratespeechtrafficchannel(TCH)intheGSMsystem.InGSM06.51[5],areferenceconfigurationforthespeechtransmissionchainoftheGSMenhancedfullrate(EFR)systemisshown.Accordingtothisreferenceconfiguration,thespeechencodertakesitsinputasa13-bituniformPCMsignaleitherfromtheaudiopartoftheMobileStationoronthenetworkside,fromthePSTNviaan8-bit/A-lawto13-bituniformPCMconversion.TheencodedspeechattheoutputofthespeechencoderisdeliveredtoachannelencoderunitwhichisspecifiedinGSM05.03[3].Inthereceivedirection,theinverseoperationstakeplace.2ReferencesThefollowingdocumentscontainprovisionswhich,throughreferenceinthistext,constituteprovisionsofthepresentdocument.• Referencesareeitherspecific(identifiedbydateofpublication,editionnumber,versionnumber,etc.)ornon-specific.• Foraspecificreference,subsequentrevisionsdonotapply.• Foranon-specificreference,thelatestversionapplies.• Anon-specificreferencetoanETSshallalsobetakentorefertolaterversionspublishedasanENwiththesamenumber.[1]GSM01.04(ETR100):"Digitalcellulartelecommunicationssystem(Phase2);Abbreviationsandacronyms".[2]GSM03.50(ETS300540):"Digitalcellulartelecommunicationssystem(Phase2);TransmissionplanningaspectsofthespeechserviceintheGSMPublicLandMobileNetwork(PLMN)system".[3]GSM05.03(ETS300575):"Digitalcellulartelecommunicationssystem(Phase2);Channelcoding".[4]GSM06.32(ETS300580-6):"Digitalcellulartelecommunicationssystem(Phase2);VoiceActivityDetection(VAD)".[5]GSM06.51(EN301243):"Digitalcellulartelecommunicationssystem(Phase2);EnhancedFullRate(EFR)speechprocessingfunctionsGeneraldescription".[6]GSM06.53(EN301244):"Digitalcellulartelecommunicationssystem(Phase2);ANSI-CcodefortheGSMEnhancedFullRate(EFR)speechcodec".[7]GSM06.54(EN301250):"Digitalcellulartelecommunicationssystem(Phase2);TestvectorsfortheGSMEnhancedFullRate(EFR)speechcodec".SIST EN 301 245 V4.1.1:2003

ETSIETSIEN301245V4.1.1(2000-08)6(GSM06.60version4.1.1)[8]ITU-TRecommendationG.711(1988):"CodingofanaloguesignalsbypulsecodemodulationPulsecodemodulation(PCM)ofvoicefrequencies".[9]ITU-TRecommendationG.726:"40,32,24,16kbit/sadaptivedifferentialpulsecodemodulation(ADPCM)".3Definitions,symbolsandabbreviations3.1DefinitionsForthepurposesofthepresentdocument,thefollowingtermsanddefinitionsapply:adaptivecodebook:Theadaptivecodebookcontainsexcitationvectorsthatareadaptedforeverysubframe.Theadaptivecodebookisderivedfromthelongtermfilterstate.Thelagvaluecanbeviewedasanindexintotheadaptivecodebook.adaptivepostfilter:Thisfilterisappliedtotheoutputoftheshorttermsynthesisfiltertoenhancetheperceptualqualityofthereconstructedspeech.IntheGSMenhancedfullratecodec,theadaptivepostfilterisacascadeoftwofilters:aformantpostfilterandatiltcompensationfilter.algebraiccodebook:Afixedcodebookwherealgebraiccodeisusedtopopulatetheexcitationvectors(innovationvectors).Theexcitationcontainsasmallnumberofnonzeropulseswithpredefinedinterlacedsetsofpositions.closed-looppitchanalysis:Thisistheadaptivecodebooksearch,i.e.,aprocessofestimatingthepitch(lag)valuefromtheweightedinputspeechandthelongtermfilterstate.Intheclosed-loopsearch,thelagissearchedusingerrorminimizationloop(analysis-by-synthesis).IntheGSMenhancedfullratecodec,closed-looppitchsearchisperformedforeverysubframe.directformcoefficients:Oneoftheformatsforstoringtheshorttermfilterparameters.IntheGSMenhancedfullratecodec,allfilterswhichareusedtomodifyspeechsamplesusedirectformcoefficients.fixedcodebook:Thefixedcodebookcontainsexcitationvectorsforspeechsynthesisfilters.Thecontentsofthecodebookarenon-adaptive(i.e.,fixed).IntheGSMenhancedfullratecodec,thefixedcodebookisimplementedusinganalgebraiccodebook.fractionallags:Asetoflagvalueshavingsub-sampleresolution.IntheGSMenhancedfullratecodecasub-sampleresolutionof1/6thofasampleisused.frame:Atimeintervalequalto20ms(160samplesatan8kHzsamplingrate).integerlags:Asetoflagvalueshavingwholesampleresolution.interpolatingfilter:AnFIRfilterusedtoproduceanestimateofsub-sampleresolutionsamples,givenaninputsampledwithintegersampleresolution.inversefilter:Thisfilterremovestheshorttermcorrelationfromthespeechsignal.Thefiltermodelsaninversefrequencyresponseofthevocaltract.lag:Thelongtermfilterdelay.Thisistypicallythetruepitchperiod,oramultipleorsub-multipleofit.LineSpectralFrequencies:(seeLineSpectralPair).LineSpectralPair:TransformationofLPCparameters.LineSpectralPairsareobtainedbydecomposingtheinversefiltertransferfunctionA(z)toasetoftwotransferfunctions,onehavingevensymmetryandtheotherhavingoddsymmetry.TheLineSpectralPairs(alsocalledasLineSpectralFrequencies)aretherootsofthesepolynomialsonthez-unitcircle).LPanalysiswindow:Foreachframe,theshorttermfiltercoefficientsarecomputedusingthehighpassfilteredspeechsampleswithintheanalysiswindow.IntheGSMenhancedfullratecodec,thelengthoftheanalysiswindowis240samples.Foreachframe,twoasymmetricwindowsareusedtogeneratetwosetsofLPcoefficients.Nosamplesofthefutureframesareused(nolookahead).SIST EN 301 245 V4.1.1:2003

ETSIETSIEN301245V4.1.1(2000-08)7(GSM06.60version4.1.1)LPcoefficients:LinearPrediction(LP)coefficients(alsoreferredasLinearPredictiveCoding(LPC)coefficients)isagenericdescriptivetermfordescribingtheshorttermfiltercoefficients.open-looppitchsearch:Aprocessofestimatingthenearoptimallagdirectlyfromtheweightedspeechinput.Thisisdonetosimplifythepitchanalysisandconfinetheclosed-looppitchsearchtoasmallnumberoflagsaroundtheopen-loopestimatedlags.IntheGSMenhancedfullratecodec,open-looppitchsearchisperformedevery10ms.residual:Theoutputsignalresultingfromaninversefilteringoperation.shorttermsynthesisfilter:Thisfilterintroduces,intotheexcitationsignal,shorttermcorrelationwhichmodelstheimpulseresponseofthevocaltract.perceptualweightingfilter:Thisfilterisemployedintheanalysis-by-synthesissearchofthecodebooks.Thefilterexploitsthenoisemaskingpropertiesoftheformants(vocaltractresonances)byweightingtheerrorlessinregionsneartheformantfrequenciesandmoreinregionsawayfromthem.subframe:Atimeintervalequalto5ms(40samplesatan8kHzsamplingrate).vectorquantization:Amethodofgroupingseveralparametersintoavectorandquantizingthemsimultaneously.zeroinputresponse:Theoutputofafilterduetopastinputs,i.e.duetothepresentstateofthefilter,giventhataninputofzerosisapplied.zerostateresponse:Theoutputofafilterduetothepresentinput,giventhatnopastinputshavebeenapplied,i.e.,giventhestateinformationinthefilterisallzeroes.3.2SymbolsForthepurposesofthepresentdocument,thefollowingsymbolsapply:()AzTheinversefilterwithunquantizedcoefficients()$AzTheinversefilterwithquantifiedcoefficients()()HzAz=1$ThespeechsynthesisfilterwithquantifiedcoefficientsaiTheunquantizedlinearpredictionparameters(directformcoefficients)$aiThequantifiedlinearpredictionparametersmTheorderoftheLPmodel1Bz()Thelong-termsynthesisfilter()WzTheperceptualweightingfilter(unquantizedcoefficients)γγ12,TheperceptualweightingfactorsFzE()Adaptivepre-filterTThenearestintegerpitchlagtotheclosed-loopfractionalpitchlagofthesubframeβTheadaptivepre-filtercoefficient(thequantifiedpitchgain)HzAzAzfnd()$(/)$(/)=γγTheformantpostfilterSIST EN 301 245 V4.1.1:2003

ETSIETSIEN301245V4.1.1(2000-08)8(GSM06.60version4.1.1)γnControlcoefficientfortheamountoftheformantpost-filteringγdControlcoefficientfortheamountoftheformantpost-filteringHzt()TiltcompensationfilterγtControlcoefficientfortheamountofthetiltcompensationfilteringµγ=tk1'Atiltfactor,withk1'beingthefirstreflectioncoefficienthnf()ThetruncatedimpulseresponseoftheformantpostfilterLhThelengthofhnf()rih()Theauto-correlationsofhnf()$(/)AznγTheinversefilter(numerator)partoftheformantpostfilter1/$(/)AzdγThesynthesisfilter(denominator)partoftheformantpostfilter$()rnTheresidualsignaloftheinversefilter$(/)Aznγhzt()Impulseresponseofthetiltcompensationfilterβscn()TheAGC-controlledgainscalingfactoroftheadaptivepostfilterαTheAGCfactoroftheadaptivepostfilterHzh1()Pre-processinghigh-passfilterwnI(),wnII()LPanalysiswindowsLI1()LengthofthefirstpartoftheLPanalysiswindowwnI()LI2()LengthofthesecondpartoftheLPanalysiswindowwnI()LII1()LengthofthefirstpartoftheLPanalysiswindowwnII()LII2()LengthofthesecondpartoftheLPanalysiswindowwnII()rkac()Theauto-correlationsofthewindowedspeechsn'()wilag()Lagwindowfortheauto-correlations(60Hzbandwidthexpansion)f0ThebandwidthexpansioninHzfsThesamplingfrequencyinHzrkac'()Themodified(bandwidthexpanded)auto-correlations()EiLDThepredictionerrorintheithiterationoftheLevinsonalgorithmkiTheithreflectioncoefficientSIST EN 301 245 V4.1.1:2003

ETSIETSIEN301245V4.1.1(2000-08)9(GSM06.60version4.1.1)aji()ThejthdirectformcoefficientintheithiterationoftheLevinsonalgorithmFz1'()SymmetricLSFpolynomialFz2'()AntisymmetricLSFpolynomialFz1()Polynomial()Fz1′withrootz=−1eliminatedFz2()Polynomial()Fz2′withrootz=1eliminatedqiThelinespectralpairs(LSPs)inthecosinedomainqAnLSPvectorinthecosinedomain$()qinThequantifiedLSPvectorattheithsubframeoftheframenωiThelinespectralfrequencies(LSFs)Txm()AmthorderChebyshevpolynomialfifi12(),()ThecoefficientsofthepolynomialsFz1()andFz2()fifi12''(),()Thecoefficientsofthepolynomials()Fz1′and()Fz2′fi()ThecoefficientsofeitherFz1()orFz2()Cx()SumpolynomialoftheChebyshevpolynomialsxCosineofangularfrequencyωλkRecursioncoefficientsfortheChebyshevpolynomialevaluationfiThelinespectralfrequencies(LSFs)inHz[]ftfff=1210KThevectorrepresentationoftheLSFsinHzz()()1n,z()()2nThemean-removedLSFvectorsatframenr()()1n,r()()2nTheLSFpredictionresidualvectorsatframenp()nThepredictedLSFvectoratframen$()()r21n−Thequantifiedsecondresidualvectoratthepastframe$fkThequantifiedLSFvectoratquantizationindexkELSPTheLSPquantizationerrorwii,,,,=110KLSP-quantizationweightingfactorsdiThedistancebetweenthelinespectralfrequenciesfi+1andfi−1SIST EN 301 245 V4.1.1:2003

ETSIETSIEN301245V4.1.1(2000-08)10(GSM06.60version4.1.1)hn()TheimpulseresponseoftheweightedsynthesisfilterOkThecorrelationmaximumofopen-looppitchanalysisatdelaykOiti,,,=13KThecorrelationmaximaatdelaystii,,,=13K()Mtiii,,,,=13KThenormalizedcorrelationmaximaMiandthecorrespondingdelaystii,,,=13KHzWzAzAzAz()()(/)$()(/)=γγ12TheweightedsynthesisfilterAz(/)γ1Thenumeratoroftheperceptualweightingfilter12/(/)AzγThedenominatoroftheperceptualweightingfilterT1Thenearestintegertothefractionalpitchlagoftheprevious(1stor3rd)subframesn'()Thewindowedspeechsignalsnw()Theweightedspeechsignal$()snReconstructedspeechsignal$()′snThegain-scaledpost-filteredsignal$()snfPost-filteredspeechsignal(beforescaling)xn()Thetargetsignalforadaptivecodebooksearchxn2(),x2tThetargetsignalforalgebraiccodebooksearchresnLP()TheLPresidualsignalcn()Thefixedcodebookvectorvn()Theadaptivecodebookvectorynvnhn()=()()∗Thefilteredadaptivecodebookvectorynk()Thepastfilteredexcitationun()Theexcitationsignal()$unTheemphasizedadaptivecodebookvector$'()unThegain-scaledemphasizedexcitationsignalTopThebestopen-looplagtminMinimumlagsearchvaluetmaxMaximumlagsearchvalue()RkCorrelationtermtobemaximizedintheadaptivecodebooksearchSIST EN 301 245 V4.1.1:2003

ETSIETSIEN301245V4.1.1(2000-08)11(GSM06.60version4.1.1)b24TheFIRfilterforinterpolatingthenormalizedcorrelationterm()Rk()RktTheinterpolatedvalueof()Rkfortheintegerdelaykandfractiontb60TheFIRfilterforinterpolatingthepastexcitationsignalun()toyieldtheadaptivecodebookvectorvn()AkCorrelationtermtobemaximizedinthealgebraiccodebooksearchatindexkCkThecorrelationinthenumeratorofAkatindexkEDkTheenergyinthedenominatorofAkatindexkdHx=t2Thecorrelationbetweenthetargetsignal()xn2andtheimpulseresponse()hn,i.e.,backwardfilteredtargetHThelowertriangularToeplizconvolutionmatrixwithdiagonal()h0andlowerdiagonals()()hh139,,KΦ=HHtThematrixofcorrelationsof()hndn()Theelementsofthevectordφ(,)ijTheelementsofthesymmetricmatrixΦckTheinnovationvectorCThecorrelationinthenumeratorofAkmiThepositionoftheithpulseϑiTheamplitudeoftheithpulseNpThenumberofpulsesinthefixedcodebookexcitationEDTheenergyinthedenominatorofAk()resnLTPThenormalizedlong-termpredictionresidualbn()Thesumofthenormalized()dnvectorandnormalizedlong-termpredictionresidual()resnLTPsnb()Thesignsignalforthealgebraiccodebooksearchdn'()Signextendedbackwardfilteredtargetφ'(,)ijThemodifiedelementsofthematrixΦ,includingsigninformationzt,()znThefixedcodebookvectorconvolvedwithhn()En()Themean-removedinnovationenergy(indB)SIST EN 301 245 V4.1.1:2003

ETSIETSIEN301245V4.1.1(2000-08)12(GSM06.60version4.1.1)EThemeanoftheinnovationenergy~()EnThepredictedenergy[]bbbb1234TheMApredictioncoefficients$()RkThequantifiedpredictionerroratsubframekEIThemeaninnovationenergyRn()Thepredictionerrorofthefixed-codebookgainquantizationEQThequantizationerrorofthefixed-codebookgainquantizationen()Thestatesofthesynthesisfilter1/$()Azenw()Theperceptuallyweightederroroftheanalysis-by-synthesissearchηThegainscalingfactorfortheemphasizedexcitationgcThefixed-codebookgaingc'Thepredictedfixed-codebookgain$gcThequantifiedfixedcodebookgaingpTheadaptivecodebookgain$gpThequantifiedadaptivecodebookgainγgcccgg=/'Acorrectionfactorbetweenthegaingcandtheestimatedonegc'$γgcTheoptimumvalueforγgcγscGainscalingfactor3.3AbbreviationsForthepurposesofthepresentdocument,thefollowingabbreviationsapply.FurtherGSMrelatedabbreviationsmaybefoundinGSM01.04[1].ACELPAlgebraicCodeExcitedLinearPredictionAGCAdaptiveGainControlCELPCodeExcitedLinearPredictionFIRFiniteImpulseResponseISPPInterleavedSingle-PulsePermutationLPLinearPredictionLPCLinearPredictiveCodingLSFLineSpectralFrequencyLSPLineSpectralPairLTPLongTermPredictor(orLongTermPrediction)MAMovingAverageSIST EN 301 245 V4.1.1:2003

ETSIETSIEN301245V4.1.1(2000-08)13(GSM06.60version4.1.1)4OutlinedescriptionThepresentdocumentisstructuredasfollows:Section4.1containsafunctionaldescriptionoftheaudiopartsincludingtheA/DandD/Afunctions.Section4.2describestheconversionbetween13-bituniformand8-bitA-lawsamples.Sections4.3and4.4presentasimplifieddescriptionoftheprinciplesoftheGSMEFRencodinganddecodingprocessrespectively.Insubclause4.5,thesequenceandsubjectiveimportanceofencodedparametersaregiven.Section5presentsthefunctionaldescriptionoftheGSMEFRencoding,whereasclause6describesthedecodingprocedures.Section7describesvariables,constantsandtablesoftheC-codeoftheGSMEFRcodec.4.1FunctionaldescriptionofaudiopartsTheanalogue-to-digitalanddigital-to-analogueconversionwillinprinciplecomprisethefollowingelements:1)AnaloguetouniformdigitalPCM−microphone;−inputleveladjustmentdevice;−inputanti-aliasingfilter;−sample-holddevicesamplingat8kHz;−analogue−to−uniformdigitalconversionto13−bitrepresentation.Theuniformformatshallberepresentedintwo'scomplement.2)UniformdigitalPCMtoanalogue−conversionfrom13−bit/8kHzuniformPCMtoanalogue;−aholddevice;−reconstructionfilterincludingx/sin(x)correction;−outputleveladjustmentdevice;−earphoneorloudspeaker.Intheterminalequipment,theA/Dfunctionmaybeachievedeither−bydirectconversionto13-bituniformPCMformat;−orbyconversionto8-bit/A-lawcompoundedformat,basedonastandardA-lawcodec/filteraccordingtoITU-TRecommendationsG.711[8]andG.714,followedbythe8-bitto13-bitconversionasspecifiedinsubclause4.2.1.FortheD/Aoperation,theinverseoperationstakeplace.InthelattercaseitshouldbenotedthatthespecificationsinITU-TG.714(supersededbyG.712)areconcernedwithPCMequipmentlocatedinthecentralpartsofthenetwork.Whenusedintheterminalequipment,thisENdoesnotonitsownensuresufficientout-of-bandattenuation.Thespecificationofout-of-bandsignalsisdefinedinGSM03.50[2]inclause2.4.2PreparationofspeechsamplesTheencoderisfedwithdatacomprisingofsampleswitharesolutionof13bitsleftjustifiedina16-bitword.Thethreeleastsignificantbitsaresetto'0'.Thedecoderoutputsdatainthesameformat.Outsidethespeechcodecfurtherprocessingmustbeappliedifthetrafficdataoccursinadifferentrepresentation.SIST EN 301 245 V4.1.1:2003

ETSIETSIEN301245V4.1.1(2000-08)14(GSM06.60version4.1.1)4.2.1PCMformatconversionTheconversionbetween8-bitA-Lawcompresseddataandlineardatawith13-bitresolutionatthespeechencoderinputshallbeasdefinedinITU-TRec.G.711[8].ITU-TRec.G.711[8]specifiestheA-Lawtolinearconversionandviceversabyprovidingtableentries.Examplesonhowtoperformtheconversionbyfixed-pointarithmeticcanbefoundinITU-TRec.G.726[9].Section4.2.1ofG.726[9]describesA-Lawtolinearexpansionandsubclause4.2.7ofG.726[9]providesasolutionforlineartoA-Lawcompression.4.3PrinciplesoftheGSMenhancedfullratespeechencoderThecodecisbasedonthecode-excitedlinearpredictive(CELP)codingmodel.A10thorderlinearprediction(LP),orshort-term,synthesisfilterisusedwhichisgivenby:HzAzazimii()$()$,==+=−∑1111(1)where$,,,,aimi=1Karethe(quantified)linearprediction(LP)parameters,andm=10isthepredictororder.Thelong-term,orpitch,synthesisfilterisgivenby:111BzgzpT(),=−−(2)whereTisthepitchdelayandgpisthepitchgain.Thepitchsynthesisfilterisimplementedusingtheso-calledadaptivecodebookapproach.TheCELPspeechsynthesismodelisshowninfigure2.Inthismodel,theexcitationsignalattheinputoftheshort-termLPsynthesisfilterisconstructedbyaddingtwoexcitationvectorsfromadaptiveandfixed(innovative)codebooks.Thespeechissynthesizedbyfeedingthetwoproperlychosenvectorsfromthesecodebooksthroughtheshort-termsynthesisfilter.Theoptimumexcitationsequenceinacodebookischosenusingananalysis-by-synthesissearchprocedureinwhichtheerrorbetweentheoriginalandsynthesizedspeechisminimizedaccordingtoaperceptuallyweighteddistortionmeasure.Theperceptualweightingfilterusedintheanalysis-by-synthesissearchtechniqueisgivenby:WzAzAz()(/)(/),=γγ12(3)where()AzistheunquantizedLPfilterand0121<<≤γγaretheperceptualweightingfactors.Thevaluesγ109=.andγ206=.areused.TheweightingfilterusestheunquantizedLPparameterswhiletheformantsynthesisfilterusesthequantifiedones.Thecoderoperatesonspeechframesof20mscorrespondingto160samplesatthesamplingfrequencyof8000sample/s.Ateach160speechsamples,thespeechsignalisanalysedtoextracttheparametersoftheCELPmodel(LPfiltercoefficients,adaptiveandfixedcodebooks'indicesandgains).Theseparametersareencodedandtransmitted.Atthedecoder,theseparametersaredecodedandspeechissynthesizedbyfilteringthereconstructedexcitationsignalthroughtheLPsynthesisfilter.Thesignalflowattheencoderisshowninfigure3.LPanalysisisperformedtwiceperframe.ThetwosetsofLPparametersareconvertedtolinespectrumpairs(LSP)andjointlyquantifiedusingsplitmatrixquantization(SMQ)with38bits.Thespeechframeisdividedinto4subframesof5mseach(40samples).Theadaptiveandfixedcodebookparametersaretransmittedeverysubframe.ThetwosetsofquantifiedandunquantizedLPfiltersareusedforthesecondandfourthsubframeswhileinthefirstandthirdsubframesinterpolatedLPfiltersareused(bothquantifiedandunquantized).Anopen-looppitchlagisestimatedtwiceperframe(every10ms)basedontheperceptuallyweightedspeechsignal.SIST EN 301 245 V4.1.1:2003

ETSIETSIEN301245V4.1.1(2000-08)15(GSM06.60version4.1.1)Thenthefollowingoperationsarerepeatedforeachsubframe:Thetargetsignalxn()iscomputedbyfilteringtheLPresidualthroughtheweightedsynthesisfilterWzHz()()withtheinitialstatesofthefiltershavingbeenupdatedbyfilteringtheerrorbetweenLPresidualandexcitation(thisisequivalenttothecommonapproachofsubtractingthezeroinputresponseoftheweightedsynthesisfilterfromtheweightedspeechsignal).Theimpulseresponse,hn()oftheweightedsynthesisfilteriscomputed.Closed-looppitchanalysisisthenperformed(tofindthepitchlagandgain),usingthetargetxn()andimpulseresponsehn(),bysearchingaroundtheopen-looppitchlag.Fractionalpitchwith1/6thofasampleresolutionisused.Thepitchlagisencodedwith9bitsinthefirstandthirdsubframesandrelativelyencodedwith6bitsinthesecondandfourthsubframes.Thetargetsignalxn()isupdatedbyremovingtheadaptivecodebookcontribution(filteredadaptivecodevector),andthisnewtarget,xn2(),isusedinthefixedalgebraiccodebooksearch(tofindtheoptimuminnovation).Analgebraiccodebookwith35bitsisusedfortheinnovativeexcitation.Thegainsoftheadaptiveandfixedcodebookarescalarquantifiedwith4and5bitsrespectively(withmovingaverage(MA)predictionappliedtothefixedcodebookgain).Finally,thefiltermemoriesareupdated(usingthedeterminedexcitationsignal)forfindingthetargetsignalinthenextsubframe.Thebitallocationofthecodecisshownintable1.Ineach20msspeechframe,244bitsareproduced,correspondingtoabitrateof12.2kbit/s.Moredetailedbitallocationisavailableintable6.Notethatthemostsignificantbits(MSB)arealwayssentfirst.Table1:Bitallocationofthe12.2kbit/scodingalgorithmfor20msframeParameter1st&3rdsubframes2nd&4thsubframestotalperframe2LSPsets38Pitchdelay9630Pitchgain4416Algebraiccode3535140Codebookgain5520Total2444.4PrinciplesoftheGSMenhancedfullratespeechdecoderThesignalflowatthedecoderisshowninfigure4.Atthedecoder,thetransmittedindicesareextractedfromthereceivedbitstream.Theindicesaredecodedtoobtainthecoderparametersateachtransmissionframe.TheseparametersarethetwoLSPvectors,the4fractionalpitchlags,the4innovativecodevectors,andthe4setsofpitchandinnovativegains.TheLSPvectorsareconvertedtotheLPfiltercoefficientsandinterpolatedtoobtainLPfiltersateachsubframe.Then,ateach40-samplesubframe:-theexcitationisconstructedbyaddingtheadaptiveandinnovativecodevectorsscaledbytheirrespectivegains;-thespeechisreconstructedbyfilteringtheexcitationthroughtheLPsynthesisfilter.Finally,thereconstructedspeechsignalispassedthroughanadaptivepostfilter.SIST EN 301 245 V4.1.1:2003

ETSIETSIEN301245V4.1.1(2000-08)16(GSM06.60version4.1.1)4.5SequenceandsubjectiveimportanceofencodedparametersTheencoderwillproducetheoutputinformationinauniquesequenceandformat,andthedecodermustreceivethesameinformationinthesameway.Intable6,thesequenceofoutputbitss1tos244andthebitallocationforeachparameterisshown.Thedifferentparametersoftheencodedspeechandtheirindividualbitshaveunequalimportancewithrespecttosubjectivequality.Beforebeingsubmittedtothechannelencodingfunctionthebitshavetoberearrangedinthesequenceofimportanceasgivenintable6in05.03[3].5FunctionaldescriptionoftheencoderInthisclause,thedifferentfunctionsoftheencoderrepresentedinfigure3aredescribed.5.1Pre-processingTwopre-processingfunctionsareappliedpriortotheencodingprocess:high-passfilteringandsignaldown-scaling.Down-scalingconsistsofdividingtheinputbyafactorof2toreducethepossibilityofoverflowsinthefixed-pointimplementation.Thehigh-passfilterservesasaprecautionagainstundesiredlowfrequencycomponents.Afilterwithacutofffrequencyof80Hzisused,anditisgivenby:.9114024.09059465.1192727435.08544941.192727435.0)(21211−−−−+−+−=zzzzzHh(4)Down-scalingandhigh-passfilteringarecombinedbydividingthecoefficientsatthenumeratorofHzh1()by2.5.2LinearpredictionanalysisandquantizationShort-termprediction,orlinearprediction(LP),analysisisperformedtwiceperspeechframeusingtheauto-correlationapproachwith30msasymmetricwindows.Nolookaheadisusedintheauto-correlationcomputation.Theauto-correlationsofwindowedspeechareconvertedtotheLPcoefficientsusingtheLevinson-Durbinalgorithm.ThentheLPcoefficientsaretransformedtotheLineSpectralPair(LSP)domainforquantizationandinterpolationpurposes.TheinterpolatedquantifiedandunquantizedfiltercoefficientsareconvertedbacktotheLPfiltercoefficients(toconstructthesynthesisandweightingfiltersateachsubframe).5.2.1Windowingandauto-correlationcomputationLPanalysisisperformedtwiceperframeusingtwodifferentasymmetricwindows.ThefirstwindowhasitsweightconcentratedatthesecondsubframeanditconsistsoftwohalvesofHammingwindowswithdifferentsizes.Thewindowisgivenby:wnnLnLnLLnLLLIIIIIIII().46,,,,.46(),,,.()()()()()()()=−−=−+−−=+−05401010540111112112coscosππKK(5)ThevaluesLI1160()=andLI280()=areused.Thesecondwindowhasitsweightconcentratedatthefourthsubframeanditconsistsoftwoparts:thefirstpartishalfaHammingwindowandthesecondpartisaquarterofacosinefunctioncycle.Thewindowisgivenby:SIST EN 301 245 V4.1.1:2003

ETSIETSIEN301245V4.1.1(2000-08)17(GSM06.60version4.1.1)wnnLnLnLLnLLLIIIIIIIIIIIIIIII().46,,,,(),,,()()()()()()()=−−=−−−=+−05402210124111112112coscosππKK(6)wherethevaluesLII1232()=andLII28()=areused.NotethatbothLPanalysesareperformedonthesamesetofspeechsamples.Thewindowsareappliedto80samplesfrompastspeechframeinadditiontothe160samplesofthepresentspeechframe.Nosamplesfromfutureframesareused(nolookahead).AdiagramofthetwoLPanalysiswindowsisdepictedbelow.20ms5msframe(160samples)subframe(40samples)framen-1framentIw(n)IIw(n)Figure1:LPanalysiswindowsTheauto-correlationsofthewindowedspeechsnn'(),,,=0239K,arecomputedby:rksnsnkkacnk()'()'(),,,,=−==∑239010K(7)anda60Hzbandwidthexpansionisusedbylagwindowingtheauto-correlationsusingthewindow:wififilags(),,,,=−=exp12211002πK(8)wheref060=Hzisthebandwidthexpansionandfs=8000Hzisthesamplingfrequency.Further,rac()0ismultipliedbythewhitenoisecorrectionfactor1.0001whichisequivalenttoaddinganoisefloorat-40dB.5.2.2Levinson-DurbinalgorithmThemodifiedauto-correlationsrracac'().()0100010=andrkrkwkkacaclag'()()(),,,==110KareusedtoobtainthedirectformLPfiltercoefficientsakk,,,,=110Kbysolvingthesetofequations.()arikriikackac''(),,,.−=−==∑110110K(9)Thesetofequationsin(9)issolvedusingtheLevinson-Durbinalgorithm.Thisalgorithmusesthefollowingrecursion:SIST EN 301 245 V4.1.1:2003

ETSIETSIEN301245V4.1.1(2000-08)18(GSM06.60version4.1.1)[]EriakarijEiakjiaakaEikEiLDaciijiacjiLDiiijijiiijiLDiLD()'()'()/()()()()()()()()()()0011011111101101112====−−−==−=+=−−−−=−−−−∑fortodofortodoendendThefinalsolutionisgivenasaajjj==(),,,10110K.TheLPfiltercoefficientsareconvertedtothelinespectralpair(LSP)representationforquantizationandinterpolationpurposes.TheconversionstotheLSPdomainandbacktotheLPfiltercoefficientdomainaredescribedinthenextclause.5.2.3LPtoLSPconversionTheLPfiltercoefficientsakk,,,=110K,areconvertedtothelinespectralpair(LSP)representationforquantizationandinterpolationpurposes.Fora10thorderLPfilter,theLSPsaredefinedastherootsofthesumanddifferencepolynomials:FzAzzAz1111'()()()=+−−(10)andFzAzzAz2111'()()()=−−−,(11)respectively.ThepolynomialFz1'()andFz2'()aresymmetricandanti-symmetric,respectively.Itcanbeproventhatallrootsofthesepolynomialsareontheunitcircleandtheyalternateeachother.Fz1'()hasarootz=−=1()ωπandFz2'()hasarootz==10()ω.Toeliminatethesetworoots,wedefinethenewpolynomials:FzFzz1111()()/()'=+−(12)andFzFzz2211()()/()'=−−.(13)Eachpolynomialhas5conjugaterootsontheunitcircle()eji±ω,therefore,thepolynomialscanbewrittenas()Fzqzzii11213912(),,,=−+−−=∏(14)and()Fzqzzii212241012(),,,=−+−−=∏,(15)SIST EN 301 245 V4.1.1:2003

ETSIETSIEN301245V4.1.1(2000-08)19(GSM06.60version4.1.1)where()qii=cosωwithω ibeingthelinespectralfrequencies(LSF)andtheysatisfytheorderingproperty01210<<<<<ωωωπK.WerefertoqiastheLSPsinthecosinedomain.SincebothpolynomialsFz1()andFz2()aresymmetriconlythefirst5coefficientsofeachpolynomialneedtobecomputed.Thecoefficientsofthesepolynomialsarefoundbytherecursiverelations(fori=0to4):fiaafifiaafiimiimi11121211()(),()()+=+−+=−++−+−,(16)wherem=10isthepredictororder.TheLSPsarefoundbyevaluatingthepolynomialsFz1()andFz2()at60pointsequallyspacedbetween0andπ andcheckingforsignchanges.Asignchangesignifiestheexistenceofarootandthesignchangeintervalisthendivided4timestobettertracktheroot.TheChebyshevpolynomialsareusedtoevaluateFz1()andFz2().Inthismethodtherootsarefounddirectlyinthecosinedomain{}qi.ThepolynomialsFz1()orFz2()evaluatedatzej=ωcanbewrittenas:FeCxj()(),ωω=−25with:CxTxfTxfTxfTxfTxf()()()()()()()()()()()/=+++++54321123452,(17)whereTxmm()cos()=ωisthemthorderChebyshevpolynomial,andfii(),,,,=15KarethecoefficientsofeitherFz1()orFz2(),computedusingtheequationsin(16).ThepolynomialCx()isevaluatedatacertainvalueofx=cos()ωusingtherecursiverelation:fordowntoendkxfkCxxfkkk=−+−=−+=++4125521212λλλλλ()()()/,withinitialvaluesλ51=andλ60=.ThedetailsoftheChebyshevpolynomialevaluationmethodarefoundinP.KabalandR.P.Ramachandran[6].5.2.4LSPtoLPconversionOncetheLSPsarequantifiedandinterpolated,theyareconvertedbacktotheLPcoefficientdomain{}ak.TheconversiontotheLPdomainisdoneasfollows.ThecoefficientsofFz1()orFz2()arefoundbyexpandingequations(14)and(15)knowingthequantifiedandinterpolatedLSPsqii,=,,110K.Thefollowingrecursiverelationisusedtocomputefi1():fortofordowntoendendifiqfifijifjfjqfjfjii==−−+−=−=−−+−−−1521221121212111112111()()()()()()()SIST EN 301 245 V4.1.1:2003

ETSIETSIEN301245V4.1.1(2000-08)20(GSM06.60version4.1.1)withinitialvalues()f101=and()f110−=.Thecoefficients()fi2arecomputedsimilarlybyreplacingqi21−byqi2.Oncethecoefficientsfi1()andfi2()arefound,Fz1()andFz2()aremultipliedby11+−zand11−−z,respectively,toobtainFz1'()andFz2'();thatis:fififiifififii111222115115''()()(),,,,()()(),,,.=+−==−−=KK(18)FinallytheLPcoefficientsarefoundby:afifiififiii=+=−−−=050515051105116101212.().(),,,,.().(),,,.''''KK(19)Thisisdirectlyderivedfromtherelation()AzFzFz()()()/''=+122,andconsideringthefactthatFz1'()andFz2'()aresymmetricandanti-symmetricpolynomials,respectively.5.2.5QuantizationoftheLSPcoefficientsThetwosetsofLPfiltercoefficientsperframearequantifiedusingtheLSPrepresentationinthefrequencydomain;thatis:()ffqiisi==2110πarccos,,,,K(20)wherefiarethelinespectralfrequencies(LSF)inHz[0,4000]andfs=8000isthesamplingfrequency.TheLSFvectorisgivenby[]ftfff=1210K,withtdenotingtranspose.A1storderMApredictionisapplied,andthetworesidualLSFvectorsarejointlyquantifiedusingsplitmatrixquantization(SMQ).Thepredictionandquantizationareperformedasfollows.Letz()()1nandz()()2ndenotethemean-removedLSFvectorsatframen.Thepredictionresidualvectorsr()()1nandr()()2naregivenby:rzprzp()()()()()()(),()()(),1122nnnnnn=−=−and(21)wherep()nisthepredictedLSFvectoratframen.Firstordermoving-average(MA)predictionisusedwhere:()pr().$()nn=−06512(22)where$()()r21n−isthequantifiedsecondresidualvectoratthepastframe.ThetwoLSFresidualvectorsr()1andr()2arejointlyquantifiedusingsplitmatrixquantization(SMQ).Thematrix()rr()()12issplitinto5submatricesofdimension2x2(twoelementsfromeachvector).Forexample,thefirstsubmatrixconsistsoftheelementsrrr112112()()(),,,andr22().The5submatricesarequantifiedwith7,8,8+1,8,and6bits,respectively.Thethirdsubmatrixusesa256-entrysignedcodebook(8-bitindexplus1-bitsign).SIST EN 301 245 V4.1.1:2003

ETSIETSIEN301245V4.1.1(2000-08)21(GSM06.60version4.1.1)AweightedLSPdistortionmeasureisusedinthequantizationprocess.Ingeneral,foraninputLSPvectorfandaquantifiedvectoratindexk,$fk,thequantizationisperformedbyfindingtheindexkwhichminimizes:[]EfwfwLSPiiikii=−=∑$.1102(23)Theweightingfactorswii,,,=110K,aregivenby()wdddiiii=−<−33471547450450450.,for=1.8-0.81050otherwise,(24)wheredffiii=−+−11withf00=andf114000=.Here,twosetsofweightingcoefficientsarecomputedforthetwoLSFvectors.Inthequantizationofeachsubmatrix,twoweightingcoefficientsfromeachsetareusedwiththeircorrespondingLSFs.5.2.6InterpolationoftheLSPsThetwosetsofquantified(andunquantized)LPparametersareusedforthesecondandfourthsubframeswhereasthefirstandthirdsubframesusealinearinterpolationoftheparametersintheadjacentsubframes.TheinterpolationisperformedontheLSPsintheqdomain.Let$()q4nbetheLSPvectoratthe4thsubframeofthepresentframen,$()q2nbetheLSPvectoratthe2ndsubframeofthepresentframen,and$()q41n−theLSPvectoratthe4thsubframeofthepastframen−1.TheinterpolatedLSPvectorsatthe1stand3rdsubframesaregivenby:$.$.$,$.$.$.()()()()()()qqqqqq141232405050505nnnnnn=+=+−(25)TheinterpolatedLSPvectorsareusedtocomputeadifferentLPfilterateachsubframe(bothquantifiedandunquantizedcoefficients)usingtheLSPtoLPconversionmethoddescribedinsubclause5.2.4.5.3Open-looppitchanalysisOpen-looppitchanalysisisperformedtwiceperframe(each10ms)tofindtwoestimatesofthepitchlagineachframe.Thisisdoneinordertosimplifythepitchanalysisandconfinetheclosed-looppitchsearchtoasmallnumberoflagsaroundtheopen-loopestimatedlags.Open-looppitchestimationisbasedontheweightedspeechsignalsnw()whichisobtainedbyfilteringtheinputspeechsignalthroughtheweightingfilterWzAzAz()(/)(/)=γγ12.Thatis,inasubframeofsizeL,theweightedspeechisgivenby:snsnasniasninLwiiiiiiw()()()(),,,.=+−−−=−==∑∑γγ1110211001K(26)Open-looppitchanalysisisperformedasfollows.Inthefirststep,3maximaofthecorrelation:SIST EN 301 245 V4.1.1:2003

ETSIETSIEN301245V4.1.1(2000-08)22(GSM06.60version4.1.1)Osnsnkkwwn=−=∑()()079(27)arefoundinthethreeranges:iii===321:::1835367172143,,,,,,,,.KKKTheretainedmaximaOiti,,,=13K,arenormalizedbydividingbysntiwin2(),−=∑1,,3K,respectively.Thenormalizedmaximaandcorrespondingdelaysaredenotedby()Mtiii,,,,=13K.Thewinner,Top,amongthethreenormalizedcorrelationsisselectedbyfavouringthedelayswiththevaluesinthelowerrange.Thisisperformedbyweightingthenormalizedcorrelationscorrespondingtothelongerdelays.Thebestopen-loopdelayTopisdeterminedasfollows:()()()()()TtMTMifMMTMTMTtendifMMTMTMTtendopopopopopopopop==>==>==11222333085085.Thisprocedureofdividingthedelayrangeinto3clausesandfavouringthelowerclausesisusedtoavoidchoosingpitchmultiples.5.4ImpulseresponsecomputationTheimpulseresponse,hn(),oftheweightedsynthesisfilter[]HzWzAzAzAz()()(/)/$()(/)=γγ12iscomputedeachsubframe.Thisimpulseresponseisneededforthesearchofadaptiveandfixedcodebooks.Theimpulseresponsehn()iscomputedbyfilteringthevectorofcoefficientsofthefilterAz(/)γ1extendedbyzerosthroughthetwofilters1/$()Azand12/(/)Azγ.5.5TargetsignalcomputationThetargetsignalforadaptivecodebooksearchisusuallycomputedbysubtractingthezeroinputresponseoftheweightedsynthesisfilter[]HzWzAzAzAz()()(/)/$()(/)=γγ12fromtheweightedspeechsignalsnw().Thisisperformedonasubframebasis.Anequivalentprocedureforcomputingthetargetsignal,whichisusedinthisstandard,isthefilteringoftheLPresidualsignalresnLP()throughthecombinationofsynthesisfilter1/$()AzandtheweightingfilterAzAz(/)/(/)γγ12.Afterdeterminingtheexcitationforthesubframe,theinitialstatesofthesefiltersareupdatedSIST EN 301 245 V4.1.1:2003

ETSIETSIEN301245V4.1.1(2000-08)23(GSM06.6
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