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1SpeechSignalProcessing—Lecture9HomomorphicSpeechProcessing
2BasicSpeechModelshortsegmentofspeechcanbemodeledashavingbeengeneratedbyexcitinganLTIsystemeitherbyaquasi-periodicimpulsetrain,orarandomnoisesignalspeechanalysis=estimateparametersofthespeechmodel,measuretheirvariations(andperhapseventheirstatisticalvariability-forquantization)withtimespeech=excitation*systemresponse=wanttodeconvolvespeechintoexcitationandsystemresponse=dothisusinghomomorphicfilteringmethods
3SuperpositionPrinciple
4GeneralizedSuperpositionforConvolution
5HomomorphicFilter
6CanonicFormforHomomorphicConvolution
7FrequencyDomainCanonicForm
8CharacteristicSystemsforHomomorphicDeconvolution
9CharacteristicSystemsforHomomorphicDeconvolution+
10IssueswithLogarithms
11ComplexandRealCepstrum
12TheComplexCepstrum
13TheCepstrum
14ComplexCepstrumExamples
15ComplexCepstrumExamples
16ComplexCepstrumfor2PulsesNp2Np3Np
17ComplexCepstrumofSpeechmodelofspeech:voicedspeechproducedbyaquasi-periodicpulsetrainexcitingslowlytime-varyinglinearsystem=p(n)convolvedwithhv(n)unvoicedspeechproducedbyrandomnoiseexcitingslowlytime-varyinglinearsystem=u(n)convolvedwithhv(n)timetoexaminefullmodelandseewhatthecomplexcepstrumofspeechlookslike
18ComplexCepstrumforSpeech
19ComplexCepstrumforSpeech
20ComplexCepstrumforVoicedSpeecha:HWvoicedspeechsegmentb:logmagnitudeofDFT(periodiccomponent)c:principalvalueofphase=rapidlydiscontinuousd:unwrappedphasee:complexcepstrum(basedonbandd)-pitchpeaksforbothpositiveandnegativenf:cepstrum-samegeneralproperties
HomomorphicFilteringofVoicedSpeechgoalistoseparateouttheexcitationimpulsesfromtheremainingcomponentsofthecomplexcepstrumusecepstralwindow,l(n),toseparateexcitationpulsesfromcombinedvocaltractl
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