A SIMPLE GEOMETRICAL STRUCTURE UNDERLYING SPEECH SIGNALS OF THE JAPANESE VOWEL /a/

Abstract

We provide several pieces of evidence for possible chaotic dynamics in the irregular behavior of normal speech signals of the Japanese vowel /a/. First, principal component analysis demonstrates that a simple geometric structure underlying the complex speech signal is well reconstructed in a three-dimensional delay-coordinate space. Observations of the reconstructed speech trajectory at multiple cross sections also display speech dynamics with stretching, folding and compressing. Second, Lyapunov spectrum analysis indicates sensitive dependence on initial conditions with a positive Lyapunov exponent for the speech signals of several different speakers. Third, nonlinear modeling analysis with an artificial neural network shows that the nonlinear dynamics of the vowel sound is well reproduced by a deterministic dynamical model.

Higher‐order correlation analysis of pitch fluctuations in sustained normal vowels by the method of surrogate data

“…Analyses of voice signals based on nonlinear dynamic system theory [6][7][8][9][10] have been carried out extensively. Sato and colleagues [11], Tokuda's group [12][13][14], and Ikeguchi and Aihara [15] have analyzed the nonlinear dynamic structure of the vowels and have investigated their fluctuation models.…”

Chaotic dynamics and simulation of Japanese vowel sounds

“…We do this by transforming each scalar data x i to correspond to one of four different symbols b (1) , b (2) , b (3) , or b (4) . We partition the data so that the probability of each of these symbols occurring is equal, and then apply the transformation x i → b i where b i ∈ {b (1) , b (2) , b (3) , b (4) }. Finally, we apply the Lempel-Ziv algorithm to compute the number of unique symbol sequences.…”

“…Moreover, in four out of five cases we conclude that the deterministic dynamics underlying these vocalisation patterns are aperiodic, bounded and deterministic: sufficient conditions for the existence of chaos. In the fifth case (/u/) we fail to find sufficient evidence to reject the hypothesis that the data is a noise-driven periodic orbit Human vocalisation patterns are, virtually by definition, approximately periodic [1,2]. In [2] Ikeguchi and colleagues presented an analysis of vowel sounds using the methods of nonlinear dynamical system theory (at that time, this meant correlation dimension [3] and linear surrogate tests [4]).…”

Detecting determinism in speech phonemes

“…A number of studies have been conducted to seek evidence of the possible underlying chaotic features in speech phonemes [2][3][4][5][6]. The most commonly used identification method is to calculate the Lyapunov exponent and correlation dimension, which are invariants of a chaotic system.…”

“…Unfortunately, calculating the correlation dimension, the other invariant, may also be misleading as it is susceptible to false positive results [7]. Thus, studies based on numerically evaluating these two invariants have provided evidence that both support and reject the existence of chaos in speech [2][3][4]. This paper presents a discriminating approach to detecting the existence of determinism in speech phonemes using the surrogate data method [8].…”