SIST EN 301 704 V7.2.1:2003
(Main)Digital cellular telecommunications system (Phase 2+) (GSM); Adaptive Multi-Rate (AMR) speech transcoding (GSM 06.90 version 7.2.1 Release 1998)
- Abstract
Adaptive Multi- Rate (AMR) Speech Transcoding
- 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 301 704 V7.2.1:2003 is the Slovenian adoption of ETSI EN 301 704 Version 7.2.1, published by SIST for GSM digital cellular telecommunications systems. It specifies Adaptive Multi-Rate (AMR) speech transcoding for the GSM Phase 2+ speech codec, including the encoder, decoder, bit allocation and homing procedures used in GSM speech traffic channels.
What does SIST EN 301 704 V7.2.1:2003 specify?
SIST EN 301 704 V7.2.1:2003 specifies the detailed mapping between 160 speech samples in 13-bit uniform Pulse Code Modulation (PCM) and encoded AMR speech blocks, and the reverse mapping back to 160 reconstructed speech samples. It covers the AMR speech transcoding procedure for GSM adaptive multi-rate full-rate and half-rate traffic channels.
The document is organized into:
- scope and references
- definitions, symbols and abbreviations
- an outline description of the codec
- functional description of the encoder
- functional description of the decoder
- detailed bit allocation
- homing sequences
- bibliography
- an informative document change history annex
What are the key requirements of SIST EN 301 704 V7.2.1:2003?
SIST EN 301 704 V7.2.1:2003 defines the codec behavior for eight source codec bit-rates: 12.2, 10.2, 7.95, 7.40, 6.70, 5.90, 5.15 and 4.75 kbit/s. In practice, this tells implementers which mode they must support and what frame sizes they must produce and decode.
Input, frame structure and bitstream format
The encoder takes 160-sample frames at 8 kHz, with 20 ms frame duration and 40-sample subframes. The encoder output is a unique ordered bitstream, and the most significant bit of each codec parameter is sent first. For buyers and integrators, this matters because interoperable equipment must generate and accept the same bit order and frame structure.
Speech analysis and prediction
The encoder applies high-pass filtering and down-scaling before coding, then performs linear prediction (LP) analysis to model the short-term speech spectrum. The 12.2 kbit/s mode performs LP analysis twice per frame, while the other modes perform it once per frame and use interpolation across subframes. This is the core speech-modeling stage, so it determines how well the codec follows changing speech.
LSP quantization and interpolation
The LP coefficients are converted to Line Spectral Pair (LSP) form for quantization and interpolation. The 12.2 kbit/s mode uses split matrix quantization (SMQ), while the other modes use split vector quantization (SVQ), and the interpolated LSPs are converted back to LP coefficients for each subframe. In practice, this is the main mechanism that compresses the spectral envelope into a transmit-friendly representation.
Pitch, adaptive codebook and fixed codebook search
The codec uses open-loop pitch analysis, closed-loop pitch search, an adaptive codebook and an algebraic fixed codebook. Fractional pitch resolution is mode-dependent, and the codec searches for the best excitation by minimizing weighted error between original and synthesized speech. This is important because pitch and excitation coding largely control speech naturalness and robustness.
Gain quantization, post-processing and stability
The adaptive and fixed codebook gains are quantized differently by mode, using scalar or vector quantization. The decoder applies adaptive post-filtering, optional anti-sparseness processing in several modes, adaptive gain control (AGC), and high-pass filtering with up-scaling. The decoder also includes additional instability protection, which is intended to handle overflow conditions in the synthesis filter.
Homing and test behavior
Clause 8 defines encoder homing frames and decoder homing frames for bit-exact testing and reset behavior. This matters for conformance testing and for remote reset through in-band signaling.
What terms does SIST EN 301 704 V7.2.1:2003 define?
- Adaptive Multi-Rate (AMR) codec - The speech and channel codec that operates at half-rate and full-rate channel modes with several codec-mode bit-rates.
- ACELP - Algebraic Code Excited Linear Prediction, the coding scheme used by the multi-rate codec.
- LSP - Line Spectral Pair, a transformed form of LP coefficients used for quantization and interpolation.
- LP - Linear Prediction, the short-term speech model used by the encoder and decoder.
- LTP - Long Term Predictor, the pitch-related part of speech synthesis.
- AGC - Adaptive Gain Control, used to compensate for level differences after synthesis and post-filtering.
- VAD - Voice Activity Detection, referenced as part of the speech processing chain.
Who uses SIST EN 301 704 V7.2.1:2003?
SIST EN 301 704 V7.2.1:2003 is used by designers and implementers of GSM speech codecs, including terminal equipment, network equipment and test systems. It is also relevant to engineers working on channel coding, transcoding, interoperability testing and bit-exact verification of AMR speech processing.
What changed in SIST EN 301 704 V7.2.1:2003 from the previous edition?
The document change history notes these changes:
- introduction of the codec homing procedure
- description of instability protection in AMR
- bit allocation of the adaptive multi-rate codec
- version update to 7.2.1 for publication
Which standards are used with SIST EN 301 704 V7.2.1:2003?
The document cites these companion and referenced standards:
- GSM01.04 - abbreviations and acronyms used in GSM documentation
- GSM03.50 - speech service transmission planning aspects, including out-of-band signals
- GSM05.03 - channel coding, including bit rearrangement before channel encoding
- GSM06.71 - general description of AMR speech processing functions and reference configuration
- GSM06.73 - ANSI-C code for the AMR speech codec, which prevails in case of discrepancy
- GSM06.74 - test sequences for the GSM AMR speech codec
- GSM06.94 - voice activity detection for AMR speech traffic channels
- ITU-T G.711 - A-law and µ-law to linear PCM conversion
- ITU-T G.726 - fixed-point examples for PCM conversion
What does the SIST EN 301 704 V7.2.1:2003 document contain?
The document contains the functional description of the AMR encoder and decoder, including LP analysis, pitch search, codebook search, gain quantization, synthesis and post-filtering. It also contains detailed bit-allocation tables for all AMR modes, showing how each 20 ms frame is packed.
It includes figures for the simplified CELP model and the encoder and decoder block diagrams, which help readers trace signal flow through the codec. Annex A gives the informative document change history.
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Frequently Asked Questions
SIST EN 301 704 V7.2.1:2003 is a standard published by the Slovenian Institute for Standardization (SIST). Its full title is "Digital cellular telecommunications system (Phase 2+) (GSM); Adaptive Multi-Rate (AMR) speech transcoding (GSM 06.90 version 7.2.1 Release 1998)". This standard covers: Adaptive Multi- Rate (AMR) Speech Transcoding
Adaptive Multi- Rate (AMR) Speech Transcoding
SIST EN 301 704 V7.2.1:2003 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 301 704 V7.2.1:2003 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 301 704 V7.2.1:2003 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); 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.:+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 301 704 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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