SIST EN 301 704 V7.2.1:2003

• Abstract:

  Adaptive Multi- Rate (AMR) Speech Transcoding

• 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 301 704 V7.2.1 (2000-05) - Digital cellular telecommunications system (Phase 2+) (GSM); Adaptive Multi-Rate (AMR) speech transcoding (GSM 06.90 version 7.2.1 Release 1998)

Overview

SIST EN 301 704 V7.2.1:2003 defines the specification for adaptive multi-rate (AMR) speech transcoding within the digital cellular telecommunications system (Phase 2+), commonly known as GSM. Developed by the Slovenian Institute for Standardization (SIST) and harmonized with the European EN 301 704 standard, this document provides guidelines for encoding and decoding speech signals over GSM networks using the AMR codec, leveraging multiple bit rates to optimize both quality and network resource usage.

Adaptive Multi-Rate (AMR) speech transcoding plays a crucial role in the GSM framework, enhancing voice quality and spectral efficiency by dynamically adjusting the codec bit rate based on current network conditions and channel quality.

Key Topics

• AMR Speech Transcoding: Enables efficient transmission of speech by mapping input blocks of speech samples to encoded bitstreams at multiple bit rates.
• Codec Flexibility: The AMR codec supports several bit rates, from 4.75 kbit/s to 12.2 kbit/s, providing flexibility to network operators and devices.
• Linear Prediction and Codebooks: The codec applies linear predictive coding (LPC) and combines adaptive and fixed codebooks for efficient speech synthesis and analysis.
• Format Compatibility: Details procedures for handling various Pulse Code Modulation (PCM) formats, including conversion between 13-bit uniform PCM and 8-bit A-law or µ-law formats, in line with ITU-T G.711 recommendations.
• Encoder and Decoder Functions: Outlines functional descriptions for analogue-to-digital (A/D) and digital-to-analogue (D/A) conversions, signal pre-processing, encoding, channel bit allocation, and decoding processes.
• Channel Adaptivity: The standard supports both full-rate and half-rate traffic channels, allowing adaptation to network capacity and signal quality.
• Parameter Mapping and Quality: Ensures that subjective speech quality is maintained by managing the order of importance for encoded parameters for optimal transmission.

Applications

This standard is essential in several practical GSM and mobile telecommunications contexts:

• Mobile Network Operators: Ensures interoperability among devices and network infrastructure by providing a uniform method for speech transcoding. This is especially important for international roaming and vendor diversity.
• Mobile Devices: Mobile phones and communication terminals implement AMR transcoding for improved voice quality and reduced dropped call rates in variable network conditions.
• Voice Services Optimization: AMR maximizes network throughput and call quality, particularly beneficial for users in areas with fluctuating signal strengths or high network congestion.
• Device and Chipset Manufacturing: Manufacturers of GSM handsets, network equipment, and embedded modules reference this standard to meet regulatory and market requirements.

Related Standards

For comprehensive GSM speech codec implementation, SIST EN 301 704 V7.2.1:2003 references and aligns with several other standards:

• GSM 06.90: Defines core adaptive multi-rate speech transcoding requirements.
• GSM 05.03: Channel coding specifications for GSM systems.
• GSM 06.71/06.73: Provides reference configurations and ANSI-C code description for AMR codecs.
• ITU-T G.711: PCM coding for voice frequencies, crucial for PCM format conversions.
• ITU-T G.726: Adaptive differential PCM, used for further speech compression techniques.

Practical Value

Implementing SIST EN 301 704 V7.2.1:2003 ensures:

• Enhanced Speech Quality: Dynamic adaptation to available bandwidth preserves intelligibility and clarity.
• Network Efficiency: Variable bit-rate encoding optimizes bandwidth utilization.
• Interoperability: Adhering to an internationally recognized standard ensures broad compatibility within the GSM ecosystem.
• Scalability: The standard supports both current and future deployments of GSM voice services, ensuring long-term relevance.

By following this standard, stakeholders in the telecommunication sector can achieve efficient, high-quality voice transmission across GSM networks worldwide.

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.Digital cellular telecommunications system (Phase 2+) (GSM); Adaptive Multi-Rate (AMR) speech transcoding (GSM 06.90 version 7.2.1 Release 1998)33.070.50Globalni sistem za mobilno telekomunikacijo (GSM)Global System for Mobile Communication (GSM)ICS:Ta slovenski standard je istoveten z:EN 301 704 Version 7.2.1SIST EN 301 704 V7.2.1:2003en01-december-2003SIST EN 301 704 V7.2.1:2003SLOVENSKI
STANDARD
ETSIEN301704V7.2.1(2000-04)EuropeanStandard(Telecommunicationsseries)Digitalcellulartelecommunicationssystem(Phase2+);AdaptiveMulti-Rate(AMR)speechtranscoding(GSM06.90version7.2.1Release1998)GLOBALSYSTEMFORMOBILECOMMUNICATIONSRSIST EN 301 704 V7.2.1:2003

ETSIETSIEN301704V7.2.1(2000-04)2(GSM06.90version7.2.1Release1998)ReferenceREN/SMG-110690Q7R1KeywordsDigitalcellulartelecommunicationssystem,GlobalSystemforMobilecommunication(GSM),speech,AMRETSI650RoutedesLuciolesF-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 301 704 V7.2.1:2003

ETSIETSIEN301704V7.2.1(2000-04)3(GSM06.90version7.2.1Release1998)ContentsIntellectualPropertyRights.5Foreword.51Scope.62References.63Definitions,symbolsandabbreviations.73.1Definitions.73.2Symbols.93.3Abbreviations.124Outlinedescription.134.1Functionaldescriptionofaudioparts.134.2Preparationofspeechsamples.144.2.1PCMformatconversion.144.3PrinciplesoftheGSMadaptivemulti-ratespeechencoder.144.4PrinciplesoftheGSMadaptivemulti-ratespeechdecoder.164.5Sequenceandsubjectiveimportanceofencodedparameters.175Functionaldescriptionoftheencoder.175.1Pre-processing(allmodes).175.2Linearpredictionanalysisandquantization.175.2.1Windowingandauto-correlationcomputation.185.2.2Levinson-Durbinalgorithm(allmodes).195.2.3LPtoLSPconversion(allmodes).205.2.4LSPtoLPconversion(allmodes).215.2.5QuantizationoftheLSPcoefficients.225.2.6InterpolationoftheLSPs.235.2.7MonitoringresonanceintheLPCspectrum(allmodes).245.3Open-looppitchanalysis.255.4Impulseresponsecomputation(allmodes).285.5Targetsignalcomputation(allmodes).285.6Adaptivecodebook.285.6.1Adaptivecodebooksearch.285.6.2Adaptivecodebookgaincontrol(allmodes).325.7Algebraiccodebook.335.7.1Algebraiccodebookstructure.335.7.2Algebraiccodebooksearch.355.8Quantizationoftheadaptiveandfixedcodebookgains.395.8.1Adaptivecodebookgainlimitationinquantization.395.8.2Quantizationofcodebookgains.395.8.3Updatepastquantizedadaptivecodebookgainbuffer(allmodes).415.9Memoryupdate(allmodes).416Functionaldescriptionofthedecoder.426.1Decodingandspeechsynthesis.426.2Post-processing.456.2.1Adaptivepost-filtering(allmodes).456.2.2High-passfilteringandup-scaling(allmodes).467Detailedbitallocationoftheadaptivemulti-ratecodec.468Homingsequences.518.1Functionaldescription.518.2Definitions.518.3Encoderhoming.528.4Decoderhoming.52SIST EN 301 704 V7.2.1:2003

ETSIETSIEN301704V7.2.1(2000-04)4(GSM06.90version7.2.1Release1998)9Bibliography.56AnnexA(informative):Documentchangehistory.57History.58SIST EN 301 704 V7.2.1:2003

ETSIETSIEN301704V7.2.1(2000-04)5(GSM06.90version7.2.1Release1998)IntellectualPropertyRightsIPRsessentialorpotentiallyessentialtothepresentdocumentmayhavebeendeclaredtoETSI.TheinformationpertainingtotheseessentialIPRs,ifany,ispubliclyavailableforETSImembersandnon-members,andcanbefoundinSR000314:"IntellectualPropertyRights(IPRs);Essential,orpotentiallyEssential,IPRsnotifiedtoETSIinrespectofETSIstandards",whichisavailablefromtheETSISecretariat.LatestupdatesareavailableontheETSIWebserver(http://www.etsi.org/ipr).PursuanttotheETSIIPRPolicy,noinvestigation,includingIPRsearches,hasbeencarriedoutbyETSI.NoguaranteecanbegivenastotheexistenceofotherIPRsnotreferencedinSR000314(ortheupdatesontheETSIWebserver)whichare,ormaybe,ormaybecome,essentialtothepresentdocument.ForewordThisEuropeanStandard(Telecommunicationsseries)hasbeenproducedbytheSpecialMobileGroup(SMG).Thepresentdocumentdescribesthedetailedmappingfrominputblocksof160speechsamplesin13-bituniformPCMformattoencodedblocksof95,103,118,134,148,159,204,and244bitsandfromencodedblocksof95,103,118,134,148,159,204,and244bitstooutputblocksof160reconstructedspeechsampleswithinthedigitalcellulartelecommunicationssystem.ThecontentsofthepresentdocumentissubjecttocontinuingworkwithinSMGandmaychangefollowingformalSMGapproval.ShouldSMGmodifythecontentsofthepresentdocumentitwillbere-releasedwithanidentifyingchangeofreleasedateandanincreaseinversionnumberasfollows:Version7.x.ywhere:7indicatesRelease1998ofGSMPhase2+.xtheseconddigitisincrementedforallchangesofsubstance,i.e.technicalenhancements,corrections,updates,etc.ythethirddigitisincrementedwheneditorialonlychangeshavebeenincorporatedinthespecification.NationaltranspositiondatesDateofadoptionofthisEN:31March2000DateoflatestannouncementofthisEN(doa):30June2000DateoflatestpublicationofnewNationalStandardorendorsementofthisEN(dop/e):31December2000DateofwithdrawalofanyconflictingNationalStandard(dow):31December2000SIST EN 301 704 V7.2.1:2003

ETSIETSIEN301704V7.2.1(2000-04)6(GSM06.90version7.2.1Release1998)1ScopeThepresentdocumentdescribesthedetailedmappingfrominputblocksof160speechsamplesin13-bituniformPCMformattoencodedblocksof95,103,118,134,148,159,204,and244bitsandfromencodedblocksof95,103,118,134,148,159,204,and244bitstooutputblocksof160reconstructedspeechsamples.Thesamplingrateis8000samples/sleadingtoabitratefortheencodedbitstreamof4.75,5.15,5.90,6.70,7.40,7.95,10.2or12.2kbit/s.Thecodingschemeforthemulti-ratecodingmodesistheso-calledAlgebraicCodeExcitedLinearPredictionCoder,hereafterreferredtoasACELP.Themulti-rateACELPcoderisreferredtoasMR-ACELP.Inthecaseofdiscrepancybetweentherequirementsdescribedinthepresentdocumentandthefixedpointcomputationaldescription(ANSI-Ccode)oftheserequirementscontainedinGSM06.73[6],thedescriptioninGSM06.73[6]willprevail.TheANSI-Ccodeisnotdescribedinthepresentdocument,seeGSM06.73[6]foradescriptionoftheANSI-Ccode.Thetranscodingprocedurespecifiedinthepresentdocumentisapplicablefortheadaptivemulti-ratefullrateandhalfratespeechtrafficchannels(TCH)intheGSMsystem.InGSM06.71[5],areferenceconfigurationforthespeechtransmissionchainoftheGSMadaptivemulti-rate(AMR)systemisshown.Accordingtothisreferenceconfiguration,thespeechencodertakesitsinputasa13-bituniformPCMsignaleitherfromtheaudiopartoftheMobileStationoronthenetworkside,fromthePSTNviaan8-bitA-laworµ-lawto13-bituniformPCMconversion.TheencodedspeechattheoutputofthespeechencoderisdeliveredtoachannelencoderunitwhichisspecifiedinGSM05.03[3].Inthereceivedirection,theinverseoperationstakeplace.2ReferencesThefollowingdocumentscontainprovisionswhich,throughreferenceinthistext,constituteprovisionsofthepresentdocument.• Referencesareeitherspecific(identifiedbydateofpublication,editionnumber,versionnumber,etc.)ornon-specific.• Foraspecificreference,subsequentrevisionsdonotapply.• Foranon-specificreference,thelatestversionapplies.• Anon-specificreferencetoanETSshallalsobetakentorefertolaterversionspublishedasanENwiththesamenumber.• ForthisRelease1998document,referencestoGSMdocumentsareforRelease1998versions(version7.x.y).[1]GSM01.04:"Digitalcellulartelecommunicationssystem(Phase2+);Abbreviationsandacronyms".[2]GSM03.50:"Digitalcellulartelecommunicationssystem(Phase2+);TransmissionplanningaspectsofthespeechserviceintheGSMPublicLandMobileNetwork(PLMN)system".[3]GSM05.03:"Digitalcellulartelecommunicationssystem(Phase2+);Channelcoding".[4]GSM06.94:"Digitalcellulartelecommunicationssystem(Phase2+);VoiceActivityDetection(VAD)forAdaptiveMulti-Ratespeechtrafficchannels".[5]GSM06.71:"Digitalcellulartelecommunicationssystem(Phase2+);AdaptiveMulti-Ratespeechprocessingfunctions;Generaldescription".[6]GSM06.73:"Digitalcellulartelecommunicationssystem(Phase2+);ANSI-CcodefortheAdaptiveMulti-Ratespeechcodec".[7]GSM06.74:"Digitalcellulartelecommunicationssystem(Phase2+);TestsequencesfortheGSMAdaptiveMulti-Ratespeechcodec".SIST EN 301 704 V7.2.1:2003

ETSIETSIEN301704V7.2.1(2000-04)7(GSM06.90version7.2.1Release1998)[8]ITU-TRecommendationG.711(1988):"CodingofanaloguesignalsbypulsecodemodulationPulsecodemodulation(PCM)ofvoicefrequencies".[9]ITU-TRecommendationG.726:"40,32,24,16kbit/sadaptivedifferentialpulsecodemodulation(ADPCM)".3Definitions,symbolsandabbreviations3.1DefinitionsForthepurposesofthepresentdocument,thefollowingtermsanddefinitionsapply.adaptivecodebook:Theadaptivecodebookcontainsexcitationvectorsthatareadaptedforeverysubframe.Theadaptivecodebookisderivedfromthelong-termfilterstate.Thelagvaluecanbeviewedasanindexintotheadaptivecodebook.adaptivepostfilter:Thisfilterisappliedtotheoutputoftheshort-termsynthesisfiltertoenhancetheperceptualqualityofthereconstructedspeech.Intheadaptivemulti-ratecodec,theadaptivepostfilterisacascadeoftwofilters:aformantpostfilterandatiltcompensationfilter.AdaptiveMulti-Rate(AMR)codec:Speechandchannelcodeccapableofoperatingatgrossbit-ratesof11.4kbit/s(“half-rate”)and22.8kbit/s(“full-rate”).Inaddition,thecodecmayoperateatvariouscombinationsofspeechandchannelcoding(codecmode)bit-ratesforeachchannelmode.algebraiccodebook:Afixedcodebookwherealgebraiccodeisusedtopopulatetheexcitationvectors(innovationvectors).Theexcitationcontainsasmallnumberofnonzeropulseswithpredefinedinterlacedsetsofpositions.AMRhandover:HandoverbetweentheFRandHRchannelmodestooptimiseAMRoperation.anti-sparsenessprocessing:Anadaptivepost-processingprocedureappliedtothefixedcodebookvectorinordertoreduceperceptualartifactsfromasparsefixedcodebookvector.channelmode:Half-rateorfull-rateoperation.channelmodeadaptation:Thecontrolandselectionofthe(FRorHR)channelmode.channelrepacking:RepackingofHR(andFR)radiochannelsofagivenradiocelltoachievehighercapacitywithinthecell.closed-looppitchanalysis:Thisistheadaptivecodebooksearch,i.e.,aprocessofestimatingthepitch(lag)valuefromtheweightedinputspeechandthelongtermfilterstate.Intheclosed-loopsearch,thelagissearchedusingerrorminimizationloop(analysis-by-synthesis).Intheadaptivemulti-ratecodec,closed-looppitchsearchisperformedforeverysubframe.codecmode:Foragivenchannelmode,thebitpartitioningbetweenthespeechandchannelcodecs.codecmodeadaptation:Thecontrolandselectionofthecodecmodebit-rates.Normally,impliesnochangetothechannelmode.directformcoefficients:Oneoftheformatsforstoringtheshorttermfilterparameters.Intheadaptivemulti-ratecodec,allfilterswhichareusedtomodifyspeechsamplesusedirectformcoefficients.fixedcodebook:Thefixedcodebookcontainsexcitationvectorsforspeechsynthesisfilters.Thecontentsofthecodebookarenon-adaptive(i.e.,fixed).Intheadaptivemulti-ratecodec,thefixedcodebookisimplementedusinganalgebraiccodebook.fractionallags:Asetoflagvalueshavingsub-sampleresolution.Intheadaptivemulti-ratecodecasub-sampleresolutionof1/6thor1/3rdofasampleisused.full-rate(FR):Full-ratechannelorchannelmode.frame:Atimeintervalequalto20ms(160samplesatan8kHzsamplingrate).SIST EN 301 704 V7.2.1:2003

ETSIETSIEN301704V7.2.1(2000-04)8(GSM06.90version7.2.1Release1998)grossbit-rate:Thebit-rateofthechannelmodeselected(22.8kbsor11.4kbs).half-rate(HR):Half-ratechannelorchannelmode.in-bandsignalling:SignallingforDTX,LinkControl,Channelandcodecmodemodification,etc.carriedwithinthetrafficchannel.integerlags:Asetoflagvalueshavingwholesampleresolution.interpolatingfilter:AnFIRfilterusedtoproduceanestimateofsubsampleresolutionsamples,givenaninputsampledwithintegersampleresolution.inversefilter:Thisfilterremovestheshorttermcorrelationfromthespeechsignal.Thefiltermodelsaninversefrequencyresponseofthevocaltract.lag:Thelongtermfilterdelay.Thisistypicallythetruepitchperiod,oritsmultipleorsub-multiple.LineSpectralFrequencies:(seeLineSpectralPair).LineSpectralPair:TransformationofLPCparameters.LineSpectralPairsareobtainedbydecomposingtheinversefiltertransferfunctionA(z)toasetoftwotransferfunctions,onehavingevensymmetryandtheotherhavingoddsymmetry.TheLineSpectralPairs(alsocalledasLineSpectralFrequencies)aretherootsofthesepolynomialsonthez-unitcircle.LPanalysiswindow:Foreachframe,theshorttermfiltercoefficientsarecomputedusingthehighpassfilteredspeechsampleswithintheanalysiswindow.Intheadaptivemulti-ratecodec,thelengthoftheanalysiswindowisalways240samples.Foreachframe,twoasymmetricwindowsareusedtogeneratetwosetsofLPcoefficientinthe12,2kbit/smode.Fortheothermodes,onlyasingleasymmetricwindowisusedtogenerateasinglesetofLPcoefficients.Inthe12,2kbit/smode,nosamplesofthefutureframesareused(nolookahead).Theothermodesusea5mslookahead.LPcoefficients:LinearPrediction(LP)coefficients(alsoreferredasLinearPredictiveCoding(LPC)coefficients)isagenericdescriptivetermfortheshorttermfiltercoefficients.mode:Whenusedalone,referstothesourcecodecmode,i.e.,tooneofthesourcecodecsemployedintheAMRcodec.(Seealsocodecmodeandchannelmode.)open-looppitchsearch:Aprocessofestimatingthenearoptimallagdirectlyfromtheweightedspeechinput.Thisisdonetosimplifythepitchanalysisandconfinetheclosed-looppitchsearchtoasmallnumberoflagsaroundtheopen-loopestimatedlags.Intheadaptivemulti-ratecodec,anopen-looppitchsearchisperformedineveryothersubframe.out-of-bandsignalling:SignallingontheGSMcontrolchannelstosupportlinkcontrol.residual:Theoutputsignalresultingfromaninversefilteringoperation.shorttermsynthesisfilter:Thisfilterintroduces,intotheexcitationsignal,shorttermcorrelationwhichmodelstheimpulseresponseofthevocaltract.perceptualweightingfilter:Thisfilterisemployedintheanalysis-by-synthesissearchofthecodebooks.Thefilterexploitsthenoisemaskingpropertiesoftheformants(vocaltractresonances)byweightingtheerrorlessinregionsneartheformantfrequenciesandmoreinregionsawayfromthem.subframe:Atimeintervalequalto5ms(40samplesat8kHzsamplingrate).vectorquantization:Amethodofgroupingseveralparametersintoavectorandquantizingthemsimultaneously.zeroinputresponse:Theoutputofafilterduetopastinputs,i.e.duetothepresentstateofthefilter,giventhataninputofzerosisapplied.zerostateresponse:Theoutputofafilterduetothepresentinput,giventhatnopastinputshavebeenapplied,i.e.,giventhatthestateinformationinthefilterisallzeroes.SIST EN 301 704 V7.2.1:2003

ETSIETSIEN301704V7.2.1(2000-04)9(GSM06.90version7.2.1Release1998)3.2SymbolsForthepurposesofthepresentdocument,thefollowingsymbolsapply:()AzTheinversefilterwithunquantizedcoefficients()AzTheinversefilterwithquantizedcoefficients()()HzAz=1ThespeechsynthesisfilterwithquantizedcoefficientsaiTheunquantizedlinearpredictionparameters(directformcoefficients)aiThequantifiedlinearpredictionparametersmTheorderoftheLPmodel1Bz()Thelong-termsynthesisfilter()WzTheperceptualweightingfilter(unquantizedcoefficients)γγ12,TheperceptualweightingfactorsFzE()Adaptivepre-filterTTheintegerpitchlagnearesttotheclosed-loopfractionalpitchlagofthesubframeβTheadaptivepre-filtercoefficient(thequantifiedpitchgain)HzAzAzfnd()(/)(/)=γγTheformantpostfilterγnControlcoefficientfortheamountoftheformantpost-filteringγdControlcoefficientfortheamountoftheformantpost-filtering()HztTiltcompensationfilterγtControlcoefficientfortheamountofthetiltcompensationfilteringµγ=tk1'Atiltfactor,withk1'beingthefirstreflectioncoefficient()hnfThetruncatedimpulseresponseoftheformantpostfilterLhThelengthof()hnfrih()Theauto-correlationsof()hnf()AznγTheinversefilter(numerator)partoftheformantpostfilter()1AzdγThesynthesisfilter(denominator)partoftheformantpostfilter()rnTheresidualsignaloftheinversefilter()Aznγ()hntImpulseresponseofthetiltcompensationfilterβscn()TheAGC-controlledgainscalingfactoroftheadaptivepostfilterαTheAGCfactoroftheadaptivepostfilter()Hzh1Pre-processinghigh-passfilterwnI(),wnII()LPanalysiswindowsLI1()LengthofthefirstpartoftheLPanalysiswindowwnI()LI2()LengthofthesecondpartoftheLPanalysiswindowwnI()LII1()LengthofthefirstpartoftheLPanalysiswindowwnII()LII2()LengthofthesecondpartoftheLPanalysiswindowwnII()rkac()Theauto-correlationsofthewindowedspeechsn'()()wilagLagwindowfortheauto-correlations(60Hzbandwidthexpansion)SIST EN 301 704 V7.2.1:2003

ETSIETSIEN301704V7.2.1(2000-04)10(GSM06.90version7.2.1Release1998)f0ThebandwidthexpansioninHzfsThesamplingfrequencyinHzrkac'()Themodified(bandwidthexpanded)auto-correlations()EiLDThepredictionerrorintheithiterationoftheLevinsonalgorithmkiTheithreflectioncoefficientaji()ThejthdirectformcoefficientintheithiterationoftheLevinsonalgorithm()′Fz1SymmetricLSFpolynomial()′Fz2AntisymmetricLSFpolynomial()Fz1Polynomial()′Fz1withrootz=−1eliminated()Fz2Polynomial()′Fz2withrootz=1eliminatedqiThelinespectralpairs(LSPs)inthecosinedomainqAnLSPvectorinthecosinedomain()qinThequantifiedLSPvectorattheithsubframeoftheframenωiThelinespectralfrequencies(LSFs)Txm()AmthorderChebyshevpolynomialfifi12(),()ThecoefficientsofthepolynomialsFz1()andFz2()fifi12''(),()Thecoefficientsofthepolynomials()′Fz1and()′Fz2fi()Thecoefficientsofeither()Fz1or()Fz2()CxSumpolynomialoftheChebyshevpolynomialsxCosineofangularfrequencyωλkRecursioncoefficientsfortheChebyshevpolynomialevaluationfiThelinespectralfrequencies(LSFs)inHz[]ftfff=1210ThevectorrepresentationoftheLSFsinHz()z()1n,()z()2nThemean-removedLSFvectorsatframen()r()1n,()r()2nTheLSFpredictionresidualvectorsatframenp()nThepredictedLSFvectoratframen()()r21n−ThequantifiedsecondresidualvectoratthepastframefkThequantifiedLSFvectoratquantizationindexkELSPTheLSPquantizationerrorwii,,,,=110LSP-quantizationweightingfactorsdiThedistancebetweenthelinespectralfrequenciesfi+1andfi−1()hnTheimpulseresponseoftheweightedsynthesisfilterOkThecorrelationmaximumofopen-looppitchanalysisatdelaykOiti,,,=13Thecorrelationmaximaatdelaystii,,,=13()Mtiii,,,,=13ThenormalizedcorrelationmaximaMiandthecorrespondingdelaystii,,,=13HzWzAzAzAz()()(/)()(/)=γγ12Theweightedsynthesisfilter()Azγ1Thenumeratoroftheperceptualweightingfilter()12AzγThedenominatoroftheperceptualweightingfilterSIST EN 301 704 V7.2.1:2003

ETSIETSIEN301704V7.2.1(2000-04)11(GSM06.90version7.2.1Release1998)T1Theintegernearesttothefractionalpitchlagoftheprevious(1stor3rd)subframesn'()Thewindowedspeechsignal()snwTheweightedspeechsignal()snReconstructedspeechsignal()′snThegain-scaledpost-filteredsignal()snfPost-filteredspeechsignal(beforescaling)()xnThetargetsignalforadaptivecodebooksearch()xn2,x2tThetargetsignalforalgebraiccodebooksearchresnLP()TheLPresidualsignal()cnThefixedcodebookvector()vnTheadaptivecodebookvectorynvnhn()=()()∗Thefilteredadaptivecodebookvector()ynkThepastfilteredexcitation()unTheexcitationsignal()unTheemphasizedadaptivecodebookvector'()unThegain-scaledemphasizedexcitationsignalTopThebestopen-looplagtminMinimumlagsearchvaluetmaxMaximumlagsearchvalue()RkCorrelationtermtobemaximizedintheadaptivecodebooksearchb24TheFIRfilterforinterpolatingthenormalizedcorrelationterm()Rk()RktTheinterpolatedvalueof()Rkfortheintegerdelaykandfractiontb60TheFIRfilterforinterpolatingthepastexcitationsignal()untoyieldtheadaptivecodebookvector()vnAkCorrelationtermtobemaximizedinthealgebraiccodebooksearchatindexkCkThecorrelationinthenumeratorofAkatindexkEDkTheenergyinthedenominatorofAkatindexkdHx=t2Thecorrelationbetweenthetargetsignal()xn2andtheimpulseresponse()hn,i.e.,backwardfilteredtargetHThelowertriangularToeplizconvolutionmatrixwithdiagonal()h0andlowerdiagonals()()hh139,,Φ=HHtThematrixofcorrelationsof()hndn()Theelementsofthevectordφ(,)ijTheelementsofthesymmetricmatrixΦckTheinnovationvectorCThecorrelationinthenumeratorofAkmiThepositionoftheithpulseϑiTheamplitudeoftheithpulseNpThenumberofpulsesinthefixedcodebookexcitationEDTheenergyinthedenominatorofAkSIST EN 301 704 V7.2.1:2003

ETSIETSIEN301704V7.2.1(2000-04)12(GSM06.90version7.2.1Release1998)()resnLTPThenormalizedlong-termpredictionresidual()bnThesignalusedforpresettingthesignsinalgebraiccodebooksearch()snbThesignsignalforthealgebraiccodebooksearch()′dnSignextendedbackwardfilteredtargetφ'(,)ijThemodifiedelementsofthematrixΦ,includingsigninformationzt,()znThefixedcodebookvectorconvolvedwith()hn()EnThemean-removedinnovationenergy(indB)EThemeanoftheinnovationenergy()~EnThepredictedenergy[]bbbb1234TheMApredictioncoefficients()RkThequantifiedpredictionerroratsubframekEIThemeaninnovationenergyRn()Thepredictionerrorofthefixed-codebookgainquantizationEQThequantizationerrorofthefixed-codebookgainquantizationen()Thestatesofthesynthesisfilter()1Az()enwTheperceptuallyweightederroroftheanalysis-by-synthesissearchηThegainscalingfactorfortheemphasizedexcitationgcThefixed-codebookgain′gcThepredictedfixed-codebookgaingcThequantifiedfixedcodebookgaingpTheadaptivecodebookgaingpThequantifiedadaptivecodebookgainγgcccgg=′Acorrectionfactorbetweenthegaingcandtheestimatedone′gcγgcTheoptimumvalueforγgcγscGainscalingfactor3.3AbbreviationsForthepurposesofthepresentdocument,thefollowingabbreviationsapply.FurtherGSMrelatedabbreviationsmaybefoundinGSM01.04[1].ACELPAlgebraicCodeExcitedLinearPredictionAGCAdaptiveGainControlAMRAdaptiveMulti-RateCELPCodeExcitedLinearPredictionEFREnhancedFullRateFIRFiniteImpulseResponseFRFullRateHRHalfRateISPPInterleavedSingle-PulsePermutationLPLinearPredictionLPCLinearPredictiveCodingLSFLineSpectralFrequencyLSPLineSpectralPairLTPLongTermPredictor(orLongTermPrediction)MAMovingAverageSIST EN 301 704 V7.2.1:2003

ETSIETSIEN301704V7.2.1(2000-04)13(GSM06.90version7.2.1Release1998)4OutlinedescriptionThepresentdocumentisstructuredasfollows:Section4.1containsafunctionaldescriptionoftheaudiopartsincludingtheA/DandD/Afunctions.Section4.2describestheconversionbetween13-bituniformand8-bitA-laworµ-lawsamples.Sections4.3and4.4presentasimplifieddescriptionoftheprinciplesoftheAMRcodecencodinganddecodingprocessrespectively.Insubclause4.5,thesequenceandsubjectiveimportanceofencodedparametersaregiven.Section5presentsthefunctionaldescriptionoftheAMRcodecencoding,whereasclause6describesthedecodingprocedures.Insection7,thedetailedbitallocationoftheAMRcodecistabulated.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-bitA-laworµ-lawcompoundedformat,basedonastandardA-laworµ-lawcodec/filteraccordingtoITU-TRecommendationsG.711[8]andG.714,followedbythe8-bitto13-bitconversionasspecifiedinsubclause4.2.1.FortheD/Aoperation,theinverseoperationstakeplace.InthelattercaseitshouldbenotedthatthespecificationsinITU-TG.714(supersededbyG.712)areconcernedwithPCMequipmentlocatedinthecentralpartsofthenetwork.Whenusedintheterminalequipment,thepresentdocumentdoesnotonitsownensuresufficientout-of-bandattenuation.Thespecificationofout-of-bandsignalsisdefinedinGSM03.50[2]inclause2.SIST EN 301 704 V7.2.1:2003

ETSIETSIEN301704V7.2.1(2000-04)14(GSM06.90version7.2.1Release1998)4.2PreparationofspeechsamplesTheencoderisfedwithdatacomprisingofsampleswitharesolutionof13bitsleftjustifiedina16-bitword.Thethreeleastsignificantbitsaresetto'0'.Thedecoderoutputsdatainthesameformat.Outsidethespeechcodecfurtherprocessingmustbeappliedifthetrafficdataoccursinadifferentrepresentation.4.2.1PCMformatconversionTheconversionbetween8-bitA-Laworµ-lawcompresseddataandlineardatawith13-bitresolutionatthespeechencoderinputshallbeasdefinedinITU-TRec.G.711[8].ITU-TRec.G.711[8]specifiestheA-Laworµ-lawtolinearconversionandviceversabyprovidingtableentries.Examplesonhowtoperformtheconversionbyfixed-pointarithmeticcanbefoundinITU-TRec.G.726[9].Section4.2.1ofG.726[9]describesA-Laworµ-lawtolinearexpansionandsubclause4.2.8ofG.726[9]providesasolutionforlineartoA-Laworµ-lawcompression.4.3PrinciplesoftheGSMadaptivemulti-ratespeechencoderTheAMRcodecuseseightsourcecodecswithbit-ratesof12.2,10.2,7.95,7.40,6.70,5.90,5.15and4.75kbit/s.Thecodecisbasedonthecode-excitedlinearpredictive(CELP)codingmodel.A10thorderlinearprediction(LP),orshort-term,synthesisfilterisusedwhichisgivenby:()()HzAzaziiim==+−=1111,(1)where,,,,aimi=1arethe(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=.(forthe12.2and10.2kbit/smode)or94.01=γ(forallothermodes)andγ206=.areused.TheweightingfilterusestheunquantizedLPparameters.Thecoderoperatesonspeechframesof20mscorrespondingto160samplesatthesamplingfrequencyof8000sample/s.Ateach160speechsamples,thespeechsignalisanalysedtoextracttheparametersoftheCELPmodel(LPfiltercoefficients,adaptiveandfixedcodebooks'indicesandgains).Theseparametersareencodedandtransmitted.AtSIST EN 301 704 V7.2.1:2003

ETSIETSIEN301704V7.2.1(2000-04)15(GSM06.90version7.2.1Release1998)thedecoder,theseparametersaredecodedandspeechissynthesizedbyfilteringthereconstructedexcitationsignalthroughtheLPsynthesisfilter.Thesignalflowattheencoderisshowninfigure3.LPanalysisisperformedtwiceperframeforthe12.2kbit/smodeandoncefortheothermodes.Forthe12.2kbit/smode,thetwosetsofLPparametersareconvertedtolinespectrumpairs(LSP)andjointlyquantizedusingsplitmatrixquantization(SMQ)with38bits.Fortheothermodes,thesinglesetofLPparametersisconvertedtolinespectrumpairs(LSP)andvectorquantizedusingsplitvectorquantization(SVQ).Thespeechframeisdividedinto4subframesof5mseach(40samples).Theadaptiveandfixedcodebookparametersaretransmittedeverysubframe.ThequantizedandunquantizedLPparametersortheirinterpolatedversionsareuseddependingonthesubframe.Anopen-looppitchlagisestimatedineveryothersubframe(exceptforthe5.15and4.75kbit/smodesforwhichitisdoneonceperframe)basedontheperceptuallyweightedspeechsignal.Thenthefollowingoperationsarerepeatedforeachsubframe:Thetargetsignal()xniscomputedbyfilteringtheLPresidualthroughtheweightedsynthesisfilter()()WzHzwiththeinitialstatesofthefiltershavingbeenupdatedbyfilteringtheerrorbetweenLPresidualandexcitation(thisisequivalenttothecommonapproachofsubtractingthezeroinputresponseoftheweightedsynthesisfilterfromtheweightedspeechsignal).Theimpulseresponse,()hnoftheweightedsynthesisfilteriscomputed.Closed-looppitchanalysisisthenperformed(tofindthepitchlagandgain),usingthetarget()xnandimpulseresponse()hn,bysearchingaroundtheopen-looppitchlag.Fractionalpitchwith1/6thor1/3rdofasampleresolution(dependingonthemode)isused.Thetargetsignal()xnisupdatedbyremovingtheadaptivecodebookcontribution(filteredadaptivecodevector),andthisnewtarget,()xn2,isusedinthefixedalgebraiccodebooksearch(tofindtheoptimuminnovation).Thegainsoftheadaptiveandfixedcodebookarescalarquantifiedwith4and5bitsrespectivelyorvectorquantifiedwith6-7bits(withmovingaverage(MA)predictionappliedtothefixedcodebookgain).Finally,thefiltermemoriesareupdated(usingthedeterminedexcitationsignal)forfindingthetargetsignalinthenextsubframe.ThebitallocationoftheAMRcodecmodesisshownintable1.Ineach20msspeechframe,95,103,118,134,148,159,204or244bitsareproduced,correspondingtoabit-rateof4.75,5.15,5.90,6.70,7.40,7.95,10.2or12.2kbit/s.Moredetailedbitallocationamongthecodecparametersisgivenintables9a-9h.Notethatthemostsignificantbits(MSB)arealwayssentfirst.SIST EN 301 704 V7.2.1:2003

ETSIETSIEN301704V7.2.1(2000-04)16(GSM06.90version7.2.1Release1998)Table1:BitallocationoftheAMRcodingalgorithmfor20msframeModeParameter1stsubframe2ndsubframe3rdsubframe4thsubframetotalperframe2LSPsets3812.2kbit/sPitchdelay969630(GSMEFR)Pitchgain444416Algebraiccode35353535140Codebookgain555520Total244LSPset2610.2kbit/sPitchdelay858526Algebraiccode31313131124Gains777728Total204LSPsets277.95kbit/sPitchdelay868628Pitchgain444416Algebraiccode1717171768Codebookgain555520Total159LSPset267.40kbit/sPitchdelay858526(DAMPSEFR)Algebraiccode1717171768Gains777728Total148LSPset266.70kbit/sPitchdelay848424Algebraiccode1414141456Gains777728Total134LSPset265.90kbit/sPitchdelay848424Algebraiccode1111111144Gains666624Total118LSPset235.15kbit/sPitchdelay844420Algebraiccode999936Gains666624Total103LSPset234.75kbit/sPitchdelay844420Algebraiccode999936Gains8816Total954.4PrinciplesoftheGSMadaptivemulti-ratespeechdecoderThesignalflowatthedecoderisshowninfigure4.Atthedecoder,basedonthechosenmode,thetransmittedindicesareextractedfromthereceivedbitstream.Theindicesaredecodedtoobtainthecoderparametersateachtransmissionframe.TheseparametersaretheLSPvectors,thefractionalpitchlags,theinnovativecodevectors,andthepitchandinnovativegains.TheLSPvectorsareconvertedtotheLPfiltercoefficientsandinterpolatedtoobtainLPfiltersateachsubframe.Then,ateach40-samplesubframe:-theexcitationisconstructedbyaddingtheadaptiveandinnovativecodevectorsscaledbytheirrespectivegains;-thespeechisreconstructedbyfilteringtheexcitationthroughtheLPsynthesisfilter.SIST EN 301 704 V7.2.1:2003

ETSIETSIEN301704V7.2.1(2000-04)17(GSM06.90version7.2.1Release1998)Finally,thereconstructedspeechsignalispassedthroughanadaptivepostfilter.4.5SequenceandsubjectiveimportanceofencodedparametersTheencoderwillproducetheoutputinformationinauniquesequenceandformat,andthedecodermustreceivethesameinformationinthesameway.Intable9a-9h,thesequenceofoutputbitsandthebitallocationforeachparameterisshown.Thedifferentparametersoftheencodedspeechandtheirindividualbitshaveunequalimportancewithrespecttosubjectivequality.Beforebeingsubmittedtothechannelencodingfunctionthebitshavetoberearrangedinthesequenceofimportanceasgivenin05.03[3].5FunctionaldescriptionoftheencoderInthisclause,thedifferentfunctionsoftheencoderrepresentedinfigure3aredescribed.5.1Pre-processing(allmodes)Twopre-processingfunctionsareappliedpriortotheencodingprocess:high-passfilteringandsignaldown-scaling.Down-scalingconsistsofdividingtheinputbyafactorof2toreducethepossibilityofoverflowsinthefixed-pointimplementation.Thehigh-passfilterservesasaprecautionagainstundesiredlowfrequencycomponents.Afilterwithacutofffrequencyof80Hzisused,anditisgivenby:21211911376953.0906005859.11927246903.08544941.1927246093.0)(−−−−+−+−=zzzzzHh.(4)Down-scalingandhigh-passfilteringarecombinedbydividingthecoefficientsatthenumeratorof()Hzh1by2.5.2Linearpredictionanalysisandquantization12.2kbit/smodeShort-termprediction,orlinearprediction(LP),analysisisperformedtwiceperspeechframeusingtheauto-correlationapproachwith30msasymmetricwindows.Nolookaheadisusedintheauto-correlationcomputation.Theauto-correlationsofwindowedspeechareconvertedtotheLPcoefficientsusingtheLevinson-Durbinalgorithm.ThentheLPcoefficientsaretransformedtotheLineSpectralPair(LSP)domainforquantizationandinterpolationpurposes.TheinterpolatedquantifiedandunquantizedfiltercoefficientsareconvertedbacktotheLPfiltercoefficients(toconstructthesynthesisandweightingfiltersateachsubframe).10.2,7.95,7.40,6.70,5.90,5.15,4.75kbit/smodesShort-termprediction,orlinearprediction(LP),analysisisperformedonceperspeechframeusingtheauto-correlationapproachwith30msasymmetricwindows.Alookaheadof40samples(5ms)isusedintheauto-correlationcomputation.Theauto-correlationsofwindowedspeechareconvertedtotheLPcoefficientsusingtheLevinson-Durbinalgorithm.ThentheLPcoefficientsaretransformedtotheLineSpectralPair(LSP)domainforquantizationandinterpolationpurposes.TheinterpolatedquantifiedandunquantizedfiltercoefficientsareconvertedbacktotheLPfiltercoefficients(toconstructthesynthesisandweightingfiltersateachsubframe).SIST EN 301 704 V7.2.1:2003

ETSIETSIEN301704V7.2.1(2000-04)18(GSM06.90version7.2.1Release1998)5.2.1Windowingandauto-correlationcomputation12.2kbit/smodeLPanalysisisperformedtwiceperframeusingtwodifferentasymmetricwindows.ThefirstwindowhasitsweightconcentratedatthesecondsubframeanditconsistsoftwohalvesofHammingwindowswithdifferentsizes.Thewindowisgivenby:wnnLnLnLLnLLLIIIIIIII().46,,,,.46(),,,.()()()()()()()=−−=−+−−=+−05401010540111112112coscosππ(5)ThevaluesLI1160()=andLI280()=areused.Thesecondwindowhasitsweightconcentratedatthefourthsubframeanditconsistsoftwoparts:thefirstpartishalfaHammingwindowandthesecondpartisaquarterofacosinefunctioncycle.Thewindowisgivenby:wnnLnLnLLnLLLIIIIIIIIIIIIIIII().46,,,,(),,,()()()()()()()=−−=−−−=+−05402210124111112112coscosππ(6)wherethevaluesLII1232()=andLII28()=areused.NotethatbothLPanalysesareperformedonthesamesetofspeechsamples.Thewindowsareappliedto80samplesfrompastspeechframeinadditiontothe160samplesofthepresentspeechframe.Nosamplesfromfutureframesareused(nolookahead).AdiagramofthetwoLPanalysiswindowsisdepictedbelow.20ms5msframe(160samples)subframe(40samples)framen-1framentIw(n)IIw(n)Figure1:LPanalysiswindowsTheauto-correlationsofthewindowedspeech()′=snn,,0239,arecomputedby:SIST EN 301 704 V7.2.1:2003

ETSIETSIEN301704V7.2.1(2000-04)19(GSM06.90version7.2.1Release1998)rksnsnkkacnk()'()'(),,,,=−==239010(7)anda60Hzbandwidthexpansionisusedbylagwindowingtheauto-correlationsusingthewindow:()wififilags=−=exp,,12211002π,(8)wheref060=Hzisthebandwidthexpansionandfs=8000Hzisthesamplingfrequency.Further,rac()0ismultipliedbythewhitenoisecorrectionfactor1.0001whichisequivalenttoaddinganoisefloorat-40dB.10.2,7.95,7.40,6.70,5.90,5.15,4.75kbit/smodesLPanalysisisperformedonceperframeusinganasymmetricwindow.Thewindowhasitsweightconcentratedatthefourthsubframeanditconsistsoftwoparts:thefirstpartishalfaHammingwindowandthesecondpartisaquarterofacosinefunctioncycle.Thewindowisgivenbyequation(6)wherethevalues2001=Land402=Lareused.Theauto-correlationsofthewindowedspeech()′=snn,,0239,arecomputedbyequation(7)anda60Hzbandwidthexpansionisusedbylagwindowingtheauto-correlationsusingthewindowofequation(8).Further,rac()0ismultipliedbythewhitenoisecorrectionfactor1.0001whichisequivalenttoaddinganoisefloorat-40dB.5.2.2Levinson-Durbinalgorithm(allmodes)Themodifiedauto-correlationsrracac'().()0100010=andrkrkwkkacaclag'()()(),,,==110areusedtoobtainthedirectformLPfiltercoefficientsakk,,,,=110bysolvingthesetofequations.()arikriikackac''(),,,.−=−==110110(9)Thesetofequationsin(9)issolvedusingtheLevinson-Durbinalgorithm.Thisalgorithmusesthefollowingrecursion:[]EriakarijEiakjiaakaEikEiLDaciijiacjiLDiiijijiiijiLDiLD()'()'()/()()()()()()()()()()0011011111101101112====−−−==−=+=−−−−=−−−−fortodofortodoendendThefinalsolutionisgivenasaajjj==(),,,10110.TheLPfiltercoefficientsareconvertedtothelinespectralpair(LSP)representationforquantizationandinterpolationpurposes.TheconversionstotheLSPdomainandbacktotheLPfiltercoefficientdomainaredescribedinthenextclause.SIST EN 301 704 V7.2.1:2003

ETSIETSIEN301704V7.2.1(2000-04)20(GSM06.90version7.2.1Release1998)5.2.3LPtoLSPconversion(allmodes)TheLPfiltercoefficientsakk,,,=110,areconvertedtothelinespectralpair(LSP)representationforquantizationandinterpolationpurposes.Fora10thorderLPfilter,theLSPsaredefinedastherootsofthesumanddifferencepolynomials:()()()′=+−−FzAzzAz1111(10)and()()()′=−−−FzAzzAz2111,(11)respectively.Thepolynomial()′Fz1and()′Fz2aresymmetricandanti-symmetric,respectively.Itcanbeproventhatallrootsofthesepolynomialsareontheunitcircleandtheyalternateeachother.()′Fz1hasarootz=−1(ωπ=)and()′Fz2hasarootz=1(ω=0).Toeliminatethesetworoots,wedefinethenewpolynomials:()()()FzFzz1111=′+−(12)and()()()FzFzz2211=′−−(13)Eachpolynomialhas5conjugaterootsontheunitcircle()eji±ω,therefore,thepolynomialscanbewrittenas()()Fzqzzii11213912=−+−−=∏,,,(14)and()()Fzqzzii212241012=−+−−=∏,,,,(15)where()qii=cosωwithω ibeingthelinespectralfrequencies(LSF)andtheysatisfytheorderingproperty01210<<<<<ωωωπ.WerefertoqiastheLSPsinthecosinedomain.Sincebothpolynomials()Fz1and()Fz2aresymmetriconlythefirst5coefficientsofeachpolynomialneedtobecomputed.Thecoefficientsofthesepolynomialsarefoundbytherecursiverelations(fori=0to4):()()()()fiaafifiaafiimiimi11121211+=+−+=−++−+−(16)wherem=10isthepredictororder.TheLSPsarefoundbyevaluatingthepolynomials()Fz1and()Fz2at60pointsequallyspacedbetween0andπ andcheckingforsignchanges.Asignchangesignifiestheexistenceofarootandthesignchangeintervalisthendivided4timestobettertracktheroot.TheChebyshevpolynomialsareusedtoevaluate()Fz1and()Fz2.Inthismethodtherootsarefounddirectlyinthecosinedomain{}qi.Thepolynomials()Fz1or()Fz2evaluatedatzej=ωcanbewrittenas:()()FeCxjωω=−25,SIST EN 301 704 V7.2.1:2003

ETSIETSIEN301704V7.2.1(2000-04)21(GSM06.90version7.2.1Release1998)with:()()()()()()()()()()()CxTxfTxfTxfTxfTxf=+++++54321123452,(17)where()()Txmm=cosωisthemthorderChebyshevpolynomial,and()fii,,,=15arethecoefficientsofeither()Fz1or()Fz2,computedusingtheequationsin(16).Thepolynomial()Cxisevaluatedatacertainvalueof()x=cosωusingtherecursiverelation:fordowntoendkxfkCxxfkkk=−+−=−+=++4125521212λλλλλ()()()/,withinitialvaluesλ51=andλ60=.ThedetailsoftheChebyshevpolynomialevaluationmethodarefoundinP.KabalandR.P.Ramachandran[6].5.2.4LSPtoLPconversion(allmodes)OncetheLSPsarequantifiedandinterpolated,theyareconvertedbacktotheLPcoefficientdomain{}ak.TheconversiontotheLPdomainisdoneasfollows.Thecoefficientsof()Fz1or()Fz2arefoundbyexpandingequations(14)and(15)knowingthequantifiedandinterpolatedLSPsqii,=,,110.Thefollowingrecursiverelationisusedtocompute()fi1:()()()()()()()fortofordowntoendendifiqfifijifjfjqfjfjii==−−+−=−=−−+−−−1521221121212111112111withinitialvalues()f101=and()f110−=.Thecoefficients()fi2arecomputedsimilarlybyreplacingqi21−byqi2.Oncethecoefficients()fi1and()fi2arefound,()Fz1and()Fz2aremultipliedby11+−zand11−−z,respectively,toobtain()′Fz1and()′Fz2;thatis:()()()()()()′=+−=′=−−=fififiifififii111222115115,,,,,,.(18)FinallytheLPcoefficientsarefoundby:()()()(
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