[Fractal dimension of speech]

Fractal dimension (D) quantifies the roughness of a temporal signal and estimates its degree of freedom, allowing a good approach of its fluctuations and roughness. Using a 16 kHz time sampling and the box-counting method, we studied Ds of some of the main French phonemes, i.e. [a], [e], [i], [o], [y], and consonants in a consonant-vowel context pronounced 4 times by 10 males and 10 females. For D measurement of long phonemes we used the dyadic Box Counting method and its 10 points D measurement (10pD). For plosion part of plosives consonants, we designed a Semi Continuous Box Counting method devoted to D measurement of short single dimension temporal signal. In the aim to approach infinitely small time scales, and to appreciate at least the tendency of these 10 points set, we calculated also the slope of the 3 last points (3pD). Our study consistently demonstrates that vowels are not fractal; plosive consonants are not fractal; long fricative consonants are fractal; males Ds are significantly higher females Ds, as far as only vowels and long voiced consonants are concerned; there is a significant difference (p < 0.01) between 3pD values of vowels (couple [a] [y] excepted), and fricative consonants (couple [[symbol: see text]]] [f] excepted). In case of nasal consonants, this categorisation is efficient using both 3pD and 10pD measurements (p < 0.05). These results will be commented and discussed, in the aim of clinical use, i.e. dysphonia follow up and auditory prosthesis speech signal processing.