Detection of s and Spectral Envelopes

図: An example of the overfitted model of harmonic structure where corresponds to of the true

[keepaspectratio=true,width=.95]/lab/common/publications/kameoka/Fig/2003ICA04overfit.eps

In the previous process, the ML procedure allows to aqcuire local optimal solutions of without distinction of the true s, harmonics or subharmonics. Therefore, the true s must somehow be discovered by replacing each by each to their multiples. Consider now that is fixed and a degree of freedom is given to every and consequently allows to extract the spectral envelope, i.e., the relative amplitudes of the partials. If the ML estimate of after the previous peocess corresponds to subharmonics, the ML model must overfit the given spectrum. For example, if is of true , the model should form a harmonic structure whose odd ordered harmonics are extremly small in comparison with even ordered ones (Fig 3). From this point of view, the problem of obtaining the true s and the spectral envelope can also be handled with the information criterion. The process shown below is done with all remaining harmonic-GMMs after the previous process.

1. Replace the representative means to where is an integer number whose initial value is 1. The number of Gaussians limited below the Nyquist log-frequency is denoted as .
   
2. Estimate the ML model parameters by EM algorithm. Here we only update and should be updated to
   

   (14)

   
   
   
   
3. Calculate AIC with equation (10). The number of free parameters here is . If the AIC increases, the process should be interrupted and the is considered as the detected , and if not, add to and return to step1.

図: Detected contour of a single speaker
図: Reference contour corresponding to figure 3

表 1: Results for a single speaker

	Accuracy(%)
Speech file	Cepstrum	Proposed
`myisda01'	88.2	98.0
`myisda02'	88.4	99.0
`myisda03'	84.8	98.1
`myisda04'	85.1	92.4
`myisda05'	76.8	93.7
`fymsda01'	86.3	98.5
`fymsda02'	87.1	97.5
`fymsda03'	83.3	95.8
`fymsda04'	86.7	96.8
`fymsda05'	85.2	96.0