Detection of chaotic behavior in speech signals using Fraser's mutual information algorithm

The apparent irregularity of speech signals is generally considered the effect of pure randomness or of time-varying control. This paper presents a new explanation in terms of deterministic chaos as the underlying model of the temporal fine structure of speech. Within this hypothesis, attractors of sustained vowel articulations are reconstructed using Takens' theorem. Next, Fraser's mutual information algorithm is exploited to estimate the marginal redundancy $R_n^T$ of a signal sample given $n$ past samples with delay time $T$. This results in the optimal choice of the delay time $T_opt$ (in the vicinity of 1 msec), a saturation value of 3 for the embedding dimension and an estimate of the information production rate of roughly one bit per pitch period. This last result together with the independently measured correlation dimension (between 1 and 2) corroborate the chaos hypothesis for speech. The general use of the implemented algorithms of chaos-targetted analyses of natural signals is possible.