Joint modeling and maximum-likelihood estimation of pitch and linear prediction coefficient parameters David Burshtein
Tel-AvivUniversity, Department ofElectricalEngineering--Systems, Tel-Aviv69978,Israel
(Received8 November1990;revised7 October1991;accepted20 October1991)
The well-knownspeechproductionmodelis considered, wherethe speechsignalis modeledas theoutputof an all-polefilterdriveneitherby somewhitenoisesequence (unvoicedspeech)or by the sumof a periodicexcitationanda noisesequence (voicedspeech).Approximate maximum-likelihood (ML) estimationalgorithmsfor the unvoicedcaseare well known.The ML estimatorof the parameters is obtainedfor the voicedspeechmodel.Theseparameters consistof theparameters of the periodicexcitation(pitchparameters)andthe parameters of thefilter [linearpredictioncoefficient (LPC) parameters ]. The resultsof the applicationof the algorithmon simulatedand on real speechdata are presented. PACS numbers:43.60.Cg,43.60.Gk, 43.70.Bk
INTRODUCTION
Considerthe well-knownspeechproductionmodel,• wherethe speechsignalis modeledasthe responseof an allpole filter to either somewhite noisesequence(unvoiced speech),or to the sumof a periodicexcitationand a noise sequence(voiced speech). Approximate maximum-likelihood (ML) estimationof the filter parameters(i.e., the linear predictioncoefficient(LPC) parameters),underthe unvoiced assumption,has been dealt with extensivelyin the
literature. 2 ThesestandardLPC-processing algorithms include the covariance
and autocorrelation
methods.
How-
ever,assumingthe speechsegmentis voiced,a largenumber of parameters(the period,phase,and amplitudeof the periodic excitation,in additionto the LPC parameters)haveto be estimated.Therefore, insteadof usingthe ML estimator for the detailed model for voiced speech,one usually estimatesthe LPC parametersseparatelyfrom the pitch. In Ref. 3, knowledgeof the pitch valueof a givenvoicedsegment,is used to enhancethe estimationof the spectralcontentsof that speechsegment,howeverthe pitch valueis determined apart from the estimationof the spectrum. In thisstudy,we developa maximum-likelihoodestimation algorithm for joint estimationof the pitch and LPC parameters,and assessthe proposedmethod on simulated and on real speechdata. Unlike Ref. 3, our approachis parametric. We simultaneouslyobtain both the pitch and LPC parametersof the givenvoicedspeechsegment.
dc[t-
gc(t)=
(k + •b)TAr]
at t = nat, n .... , -- 2, -- 1,0,1,2,...; i.e.,
gn=gc(nAr)=
•
dn_kr_•r,
where dn : dc(nAt). Here, Ar is the samplingperiod, •bis the phaseof the periodicsequence(0
Tel-AvivUniversity, Department ofElectricalEngineering--Systems, Tel-Aviv69978,Israel
(Received8 November1990;revised7 October1991;accepted20 October1991)
The well-knownspeechproductionmodelis considered, wherethe speechsignalis modeledas theoutputof an all-polefilterdriveneitherby somewhitenoisesequence (unvoicedspeech)or by the sumof a periodicexcitationanda noisesequence (voicedspeech).Approximate maximum-likelihood (ML) estimationalgorithmsfor the unvoicedcaseare well known.The ML estimatorof the parameters is obtainedfor the voicedspeechmodel.Theseparameters consistof theparameters of the periodicexcitation(pitchparameters)andthe parameters of thefilter [linearpredictioncoefficient (LPC) parameters ]. The resultsof the applicationof the algorithmon simulatedand on real speechdata are presented. PACS numbers:43.60.Cg,43.60.Gk, 43.70.Bk
INTRODUCTION
Considerthe well-knownspeechproductionmodel,• wherethe speechsignalis modeledasthe responseof an allpole filter to either somewhite noisesequence(unvoiced speech),or to the sumof a periodicexcitationand a noise sequence(voiced speech). Approximate maximum-likelihood (ML) estimationof the filter parameters(i.e., the linear predictioncoefficient(LPC) parameters),underthe unvoiced assumption,has been dealt with extensivelyin the
literature. 2 ThesestandardLPC-processing algorithms include the covariance
and autocorrelation
methods.
How-
ever,assumingthe speechsegmentis voiced,a largenumber of parameters(the period,phase,and amplitudeof the periodic excitation,in additionto the LPC parameters)haveto be estimated.Therefore, insteadof usingthe ML estimator for the detailed model for voiced speech,one usually estimatesthe LPC parametersseparatelyfrom the pitch. In Ref. 3, knowledgeof the pitch valueof a givenvoicedsegment,is used to enhancethe estimationof the spectralcontentsof that speechsegment,howeverthe pitch valueis determined apart from the estimationof the spectrum. In thisstudy,we developa maximum-likelihoodestimation algorithm for joint estimationof the pitch and LPC parameters,and assessthe proposedmethod on simulated and on real speechdata. Unlike Ref. 3, our approachis parametric. We simultaneouslyobtain both the pitch and LPC parametersof the givenvoicedspeechsegment.
dc[t-
gc(t)=
(k + •b)TAr]
at t = nat, n .... , -- 2, -- 1,0,1,2,...; i.e.,
gn=gc(nAr)=
•
dn_kr_•r,
where dn : dc(nAt). Here, Ar is the samplingperiod, •bis the phaseof the periodicsequence(0
