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Abstract:
This work deals with the problem of extracting the underlying
pattern variability from a set of speech movement signals
(wavelets). It is a follow up of previous paper [Lucero, Munhall,
Gracco, and Ramsay, J. Speech Lang. Hear. Res. 40, 1111-1117
(1997)] where a new technique using Functional Data Analysis
(FDA) was applied to extract the pattern from such a set. That
technique was based in a nonlinear transformation of the time
scale (nonlinear time normalization) so as to align the wavelets
in time. The pattern was computed as the average of the
normalized wavelets, and the amplitude variability of the set was
visualized by computing the difference of each normalized wavelet
to their average. Further, the time transformation needed to
align each wavelet was regarded as a representation of the phase
variability of the set. Here, the technique is considered in more
detail using synthetic speech wavelets. The wavelets are
generated using a simple model which consists of a common pattern
and random terms involving amplitude and phase variability. It is
shown that, although the extraction problem is indeterminate
(there is an infinite set of pattern and variability functions
that will reproduce the same set of wavelets), pattern and
variability may be extracted with good accuracy as separate
functions, provided that the wavelets have the same general
shape. The variability functions may then be used to visualize
both the magnitude and distribution of variability along the
pattern length. Indices of phase and amplitude variability are
next defined, and it is shown that they provide a better
assessment of the set variability than previous approaches based
on linear normalization and zero phase transformation. In
general, the results illustrate the potential of FDA for
analyzing patterns and variability in speech signals.
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