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# 4 Hidden Dynamic Model Implemented Using Piece-wise Linear Approximation

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4 Hidden Dynamic Model Implemented Using Piece-wise Linear Approximation book

# 4 Hidden Dynamic Model Implemented Using Piece-wise Linear Approximation

DOI link for 4 Hidden Dynamic Model Implemented Using Piece-wise Linear Approximation

4 Hidden Dynamic Model Implemented Using Piece-wise Linear Approximation book

## ABSTRACT

After the general nonlinear mapping in Eq. 10.41 from hidden dynamic variables to acoustic observational variables is approximated by a piecewise linear relationship, a new, discrete random variable m is introduced to provide the "region" (i.e., the mixturecomponent index) in the piecewise linear mapping. The conditional PDF for the output acoustic variables o(k) given the input hidden variables x(k) (for the fixed region m at time frame k) is:

P[o(k)lx(k), mk] = N[o(k); Ey]. (10.45) This is due to the Gaussian assumption for the observational noise vm(k). The conditional PDF related to the state equation for the fixed region m at time frame k is

P[x(k +1)1x(k), t(k), sk , mk] = N[x(k +1); (I'sk ,mk x(k)— (I-4'sk,mk)t(k), Ewl. (10.46)

This is due to the Gaussian assumption for the state noise wm(k).