||322 , Sala conferenze, 3 piano
||Kac II: Can you hear the shape of the vocal tract?
||Professor E R Pike - F.R.S.
||Clerk Maxwell Professor of Theoretical Physics King's College, London
Using methods of inverse problems, which are widely applied in optical
superresolution and other modern theoretical studies,
we will outline advances we have made in the last three years in the
development of a new theoretical basis for the study of speech. By analysis
of the acoustical Klein-Gordon equation, known slightly in the field of
musical acoustics but scarcely referred to elsewhere, and not at all in
speech acoustics, it has been possible to develop a wave-mechanical theory
of speech in exact analogy with quantum-mechanical inverse scattering
This work leads to major new insights and simplification of long-standing,
apparently intractable, problems in plane-wave speech acoustics. In
particular, a time-independent perturbation analysis of the straight-tract
solutions of the Klein-Gordon equation shows that it is precisely the
variation in local potential energy that defines correctly the perturbation.
Consequentially, it appears that a somewhat inaccurate definition of an
acoustical `many-to-one' mappings problem currently exists, the inverse
solution of which has been an unsolved problem for researchers worldwide
for over half a century.
Our analysis indicates a method for the ultimate compression of the
speech wave and all 28 vowels in the main phonetic alphabet have been
simulated using a bitwise-parameterisation of the potential function. Such
a compression has been the goal of researchers since the advent of digital
signal processing, and is inextricably linked to the question of `acoustic
invariance' and the development of more robust commercial speech systems for
recognition and other applications.