Speech Signal Representations

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1、SpeechSignalRepresentationsPart1:DigitalSignalProcessingHsin-minWangReferences:1X.Huangetal.,SpokenLanguageProcessing,Chapters5-62J.R.Delleretal.,Discrete-TimeProcessingofSpeechSignals,Chapters4-63J.W.Picone,“Signalmodelingtechniquesinspeechrecognition,”proceedingso

2、ftheIEEE,September1993,pp.1215-12471Introduction¢Currentspeechrecognitionsystemsaremainlycomposedof:−Afront-endfeatureextractor(featureextractionmodule)•Discoversalientcharacteristicssuitedforclassification•Basedonscientificand/orheuristicknowledgeaboutpatternstorec

3、ognize−Aback-endclassifier(classificationmodule)•Setclassboundariesaccuratelyinthefeaturespace•StatisticallydesignedaccordingtothefundamentalBayes’decisiontheory2AnalogSignaltoDigitalSignalAnalogSignalDigitalSignal:Discrete-timeDiscrete-timeSignalorDigitalSignalsign

4、alwithdiscreteamplitudex[n]=x(nT),T:samplingperiod;at=nTsamplingperiod=125μsF=1samplingrate=>samplingrate=8kHzsT3TwoMainApproachestoDigitalSignalProcessing¢FilteringSignalinSignaloutFilterx[]ny[n]Amplifyorattenuatesomefrequencycomponentsofx[n]¢ParameterExtractionSig

5、nalinParameterParameteroutx[]nExtractionccc1121L1e.g.:c12c22cL21.SpectrumEstimation2.ParameterforRecognitionccc1m2mLm45.1DigitalSignalsandSystems5SinusoidalSignalsx[n]=Acos(ωn+φ)f:normalizedfrequency0≤f≤1−A:amplitude(振

6、幅)−ω:angularfrequency(角頻率),fω=2π−:phase(相角)φ[]πperiod:T=25samplesxn=Acosωn−2frequency:f=0.046SinusoidalSignals–periodicvs.non-periodicx[n]isperiodicwithperiodNifandonlyifx[n+N]=x[n]Acos()ω(n+N)+φ=Acos(ωn+φ)2πωN=2πω=NAcos()ωn+φisnotperiodicforallvaluesofw¢Examp

7、les−x[]n=cos(πn/4)isperiodicwithperiodN=81−x[]n=cos(3πn/8)isperiodicwithperiodN=162−x[]n=cos(n)isnotperiodic37SinusoidalSignals–periodicvs.non-periodic(cont.)x1[n]=cos()πn/4πππ=cos(n+N1)=cosn+N1444π⇒N1=2π⋅k⇒N1=8k(bothN2andkareintergers)4∴periodN1=8x2[n]=

8、cos(3πn/8)3π3π3π=cos(n+N2)=cosn+N28883π16⇒N2=2π⋅k⇒N2=k(bothN2andkareintergers)83∴periodN2=16x3[n]=cos()n=cos(n+N3)⇒N3=2π⋅kcan'