Abstract
A study of several properties of a wave function representation for speech analysis/synthesis, developed by Culler at UCSB is presented. Starting from the formulation ü(t) + (2π/S)2(t − C)u̇(t) + (2π/S)2(N − 1/2)u(t) = 0, asymptotic time and frequency domain solutions are obtained which can then be used as the basis elements for fitting linear combinations to the filtered speech wave. Requirements for obtaining a wave function representation are discussed and algorithms for extracting wave function parameters from speech are presented. To obtain a better understanding of how the wave function parameters relate to the formant parameters of speech, several algorithms are presented for transforming the wavefunction parameters {A,S,C,φ,F} into the formant parameters {Fn,Bn}.
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