### ASA 126th Meeting Denver 1993 October 4-8

## 2pSP4. Duration modeling with hidden Markov models.

**L. F. M. ten Bosch
X. Wang
L. C. W. Pols
**

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*Inst. for Phonetic Sci., Univ. of Amsterdam, Herengracht 338, 1016 CG
Amsterdam, The Netherlands
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In hidden Markov modeling (HMM) of speech signals, the statistics of
speech characteristics are represented by HMM parameters after the HMM
training. This procedure is purely statistical. This study concerns the
incorporation of explicit knowledge into the HMM training. Therefore one
specific parameter, i.e., segment duration, was selected. In order to study the
relation between duration and HMM modeling, three types of duration PDFs
(DPDFs) are distinguished: (A) the DPDF defined by the segmented database used
(the actual duration histogram); (B) the DPDF defined by the trained Markov
model (i.e., by the transition matrix), and (C) the DPDF based on the HMM
segmentation. While PDF (A) is based on data and PDF (B) is based on the
trained model, PDF (C) combines both features and is based on the available set
of observation sequences. First, an explicit relation is formulated between
topology of the PLU, the three DPDFs, and the so-called Pade expansion. By
using the generating function of the PDPT, it is possible to relate topological
properties of PLUs on the one hand and algebraic properties of the DPDF on the
other. Second, relations between those PDFs are presented by using two
databases containing identical texts, but read aloud with a normal and fast
speaking rate. This procedure allows a comparison between variations in the
phonetic segment duration and the HMM parameters.