• K.M.MURALEEDHARAN
• R.K.SUNIL KUMAR
• BIBISH KUMAR .K.T
• SUNIL JOHN

Abstract : Aim of this work is to optimise the time delay and embedding dimension for the process of phase space reconstruction from the time series of speech signals to analyse nonlinear behaviour of human vocal tract. According to Taken’s theorem, the underlying dynamics of a non linear deterministic system can be identified from the Reconstructed Phase Space (RPS) of the system, if the phase space is reconstructed with optimum delay and dimensions. The delay and dimensions of RPS are optimised using five Malayalam vowel phonemes uttered by fifty female and fifty male speakers of the three different age groups. Each vowel sound is recorded ten times and time series corresponding to each sound is recorded in two sampling frequencies 16 kHz and 44.1 kHz. The optimum time delay for RPS of speech time series is estimated using Mutual Information (MI) method and the optimum dimension is determined using False Nearest Neighbour (FNN) method. The analysis shows that the optimum delay hasn’t any noticeable dependence on gender and age. But the time delay increases almost linearly with sampling frequency. The embedding dimension of the reconstructed attractor is found to be same for all vowel utterances for all speakers at the studied sampling frequencies. The embedding dimension is directly related with the actual state space dimension of the vocal tract system and it will not vary with age, gender and sampling frequency. The feature extraction in the optimised delay and dimension from reconstructed phase space will help in a better understanding of the inherent non linear properties of vocal tract system. Further studies need to be carried out by reconstructing phase space with the optimised time delay and embedding dimension and to model the speech samples to analyse the dynamical behaviour of vocal tract system.

Non linear dynamics-Reconstructed phase space-Mutual Information-False Nearest Neighbour.

"Analysis of Time delay and Embedding dimension of Reconstructed phase space of Human vocal tract using Malayalam vowels", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.6, Issue 5, page no.549-556, May-2019, Available :http://www.jetir.org/papers/JETIR1905684.pdf

"Analysis of Time delay and Embedding dimension of Reconstructed phase space of Human vocal tract using Malayalam vowels", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.6, Issue 5, page no. pp549-556, May-2019, Available at : http://www.jetir.org/papers/JETIR1905684.pdf