Third Degree Volterra Kernel for Newborn Cry Estimation Gibran Etcheverry 1 , Efra´ ın L´ opez-Damian 2 , and Carlos A. Reyes-Garc´ ıa 3 1 DIFUS-USON, Encinas y Rosales S/N, 83000, Hermosillo, Mexico gibran.etcheve@difus.uson.mx 2 FIME-CIIDIT-UANL, Mechatronics Department, PIIT, 66600, Apodaca, Nuevo Le´on, Mexico efrain.lopezdm@uanl.edu.mx 3 INAOE, Department of Computer Science, Enrique Erro 1, 72840, Tonantzintla, Mexico kargaxxi@ccc.inaoep.mx Abstract. Newborn cry analysis is a difficult task due to its nonsta- tionary nature, combined to the presence of nonlinear behavior as well. Therefore, an adaptive hereditary optimization algorithm is implemented in order to avoid the use of windowing nor overlapping to capture the transient signal behavior. Identification of the linear part of this par- ticular time series is carried out by employing an Autorregresive Mov- ing Average (ARMA) structure; then, the resultant estimation error is approched by a Nonlinear Autorregresive Moving Average (NARMA) model, which realizes a Volterra cubic kernel by means of a bilinear homo- geneous structure in order to capture burst behavior. Normal, deaf, asfixia, pain, and uncommon newborn cries are inspected for differentation. 1 Introduction The newborn cry represents the heart-breathing coordination activity with the muscular larynx. The cry is an acoustics event that contains information about the central nerves system functioning as well. It is one of the most important natural ways of communication that a newborn has to interact with his/her en- vironment; through crying, the newborn babies express their needs and basic feelings like hungry or pain. Crying is the only non visual option that neonatol- ogists or pediatricians have for disease or malaise recognition. The Golub [1] crying model is divided into four parts. The first part is the glottal system that is in charge to develop the pressure under the glottis necessary to drive the vocal folds. The second part is the source of sound located at the larynx. This sound source can be described mathematically, in frequency domain, as a periodic source or like noisy source. All these sources can work in an isolated or simultaneous way. Both acoustics sources are originated in the vocal folds. The periodic source is produced by the vocal folds vibration. The noise is seen as a turbulence and is the result of the forced air passing through a small opening J.A. Carrasco-Ochoa et al. (Eds.): MCPR 2010, LNCS 6256, pp. 230–239, 2010. c  Springer-Verlag Berlin Heidelberg 2010