SIST EN 301 245 V4.1.1:2003
(Main)Digital cellular telecommunications system (Phase 2) (GSM); Enhanced Full Rate (EFR) speech transcoding (GSM 06.60 version 4.1.1)
- Abstract
SUBJECT Corrections to GSM 06.60
- Status
- Published
- Publication Date
- 30-Nov-2003
- 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
SIST EN 301 245 V4.1.1:2003 is the Slovenian adoption of ETSI EN 301 245 V4.1.1 for Digital cellular telecommunications system (Phase 2) (GSM) Enhanced Full Rate (EFR) speech transcoding. It specifies the GSM EFR speech codec at bit level, including the 160-sample to 244-bit mapping, the reverse decoding path, PCM conversion, and the procedures used to verify bit-exact implementations.
What does SIST EN 301 245 V4.1.1:2003 specify?
SIST EN 301 245 V4.1.1:2003 specifies corrections to GSM 06.60 for the GSM Enhanced Full Rate speech transcoder. It covers the transcoder for the enhanced full rate speech traffic channel in GSM, and it also describes the codec down to the bit level so that implementations can be checked with digital test sequences.
The document is organized into scope, references, definitions/symbols/abbreviations, outline description, encoder description, decoder description, C-code variables and tables, homing sequences, bibliography, and Annex A informative change history.
What are the key requirements of SIST EN 301 245 V4.1.1:2003?
Clause 4 defines the core transcoding function: 160 speech samples at 8 kHz in 13-bit uniform PCM are mapped to 244-bit coded frames, and the coded frames are mapped back to 160 reconstructed speech samples. In practice, this is the interface that encoder and decoder implementations must match.
Clause 4.1 allows terminal equipment to use either direct 13-bit uniform PCM or an 8-bit A-law path based on ITU-T G.711 and G.714. This matters when the codec is connected to an analog speech path or to PSTN-style interfaces.
Clause 5.2 uses two linear prediction (LP) analyses per frame, asymmetric analysis windows, the Levinson-Durbin algorithm, and Line Spectral Pair (LSP) conversion and interpolation. In practice, this fixes the speech model used to build the synthesis and weighting filters.
Clauses 5.3 to 5.7 define open-loop pitch analysis, closed-loop pitch search, adaptive codebook search, and algebraic codebook search. The codec uses fractional pitch resolution of 1/6 sample, so implementation accuracy here directly affects voiced speech quality.
Clause 5.8 defines fixed codebook gain quantization using moving average prediction, and Clause 5.9 defines the memory update after each subframe. These state updates must be preserved from subframe to subframe or the decoded speech will drift.
Clause 6 reconstructs speech from the decoded LP parameters, adaptive codebook vector, innovative codebook vector, and their gains, then applies adaptive post-filtering and up-scaling. This is the part that shapes the audible output.
Clause 4.5 and Table 6 define the order of transmitted bits and their relative subjective importance, and the bits are rearranged before channel coding in GSM05.03. This matters for interoperability and for test equipment that checks bit ordering.
Clause 8 defines encoder and decoder homing frames and homestate behavior. These special frames let implementations be reset in-band and support bit-exact testing and type approval.
What terms does SIST EN 301 245 V4.1.1:2003 define?
- Algebraic Code Excited Linear Prediction (ACELP) - The coding scheme used here, where the excitation is built from an adaptive codebook and an algebraic fixed codebook.
- Adaptive codebook - A codebook of excitation vectors adapted for each subframe from the long-term filter state, used to model pitch periodicity.
- Algebraic codebook - The fixed codebook used for innovation excitation, built from a small number of pulses at predefined positions.
- Line Spectral Pair (LSP) - The representation used for LP coefficient quantization and interpolation because it is well suited to stable filter handling.
- Frame - A 20 ms block, equal to 160 samples at 8 kHz.
- Subframe - A 5 ms block, equal to 40 samples at 8 kHz.
- Homing frame - A special frame used to drive the encoder or decoder into homestate for reset and test purposes.
- Adaptive Gain Control (AGC) - The scaling used to compensate level differences after post-filtering.
Who uses SIST EN 301 245 V4.1.1:2003?
SIST EN 301 245 V4.1.1:2003 is used by GSM speech codec implementers, mobile station and network equipment designers, baseband software developers, test laboratories, and conformance or type-approval teams. Buyers and quality managers use it when they need to check that an EFR implementation, a speech path, or a test setup matches the GSM codec behavior expected for interoperability.
What changed in SIST EN 301 245 V4.1.1:2003 from the previous edition?
Annex A records the change history and identifies this version as a publication update to 4.1.1 with the subject “Corrections to GSM 06.60”.
Which standards are used with SIST EN 301 245 V4.1.1:2003?
- GSM01.04 - Provides GSM abbreviations and acronyms.
- GSM03.50 - Covers transmission planning aspects of the speech service in the GSM PLMN system.
- GSM05.03 - Defines channel coding, including the bit ordering used after speech encoding.
- GSM06.32 - Provides Voice Activity Detection (VAD), which is referenced for encoder state handling.
- GSM06.51 - Gives the general description of the GSM EFR speech processing chain.
- GSM06.53 - Provides the ANSI-C code for the GSM EFR speech codec; if there is a discrepancy, this description prevails.
- GSM06.54 - Provides the test vectors used to verify codec behavior.
- ITU-T Recommendation G.711 - Defines A-law to linear PCM conversion and the reverse.
- ITU-T Recommendation G.726 - Provides fixed-point examples for A-law to linear conversion and compression.
- ITU-T Recommendation G.714 - Is used with G.711 in the terminal equipment A-law path described in Clause 4.1.
What does the SIST EN 301 245 V4.1.1:2003 document contain?
The document contains the functional description of the audio path, the encoder, the decoder, and the homing procedure, plus diagrams of the CELP speech model and encoder/decoder signal flow. Clause 7 and Tables 3 to 6 collect fixed-point constants, variables, fixed tables, and the output bit allocation for the 244-bit speech frame.
It also contains the detailed methods used for LP analysis, LSP quantization, pitch search, codebook search, gain quantization, and post-filtering. Tables 7 to 9 define the homing frame parameters and the initial state values used for encoder and decoder homestate operation, which are important for reset and bit-exact test runs.
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Frequently Asked Questions
SIST EN 301 245 V4.1.1:2003 is a standard published by the Slovenian Institute for Standardization (SIST). Its full title is "Digital cellular telecommunications system (Phase 2) (GSM); Enhanced Full Rate (EFR) speech transcoding (GSM 06.60 version 4.1.1)". This standard covers: SUBJECT Corrections to GSM 06.60
SUBJECT Corrections to GSM 06.60
SIST EN 301 245 V4.1.1:2003 is classified under the following ICS (International Classification for Standards) categories: 33.070.50 - Global System for Mobile Communication (GSM). The ICS classification helps identify the subject area and facilitates finding related standards.
SIST EN 301 245 V4.1.1:2003 is associated with the following European legislation: Standardization Mandates: T-172. When a standard is cited in the Official Journal of the European Union, products manufactured in conformity with it benefit from a presumption of conformity with the essential requirements of the corresponding EU directive or regulation.
SIST EN 301 245 V4.1.1:2003 is available in PDF format for immediate download after purchase. The document can be added to your cart and obtained through the secure checkout process. Digital delivery ensures instant access to the complete standard document.
Standards Content (Sample)
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.:+33492944200Fax:+33493654716SiretN°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:editor@etsi.frCopyrightNotificationNopartmaybereproducedexceptasauthorizedbywrittenpermission.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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