Separation of Speech Signals for Nonlinear Mixtures C.G.Puntonet, M.R.Alvarez, A.Prieto, B.Prieto Departamento de Arquitectura y Tecnologfa de Computadores Universidad de Granada. 18071-Granada. Spain E-mail: carios@atc.ugr.es Abstract. This paper shows an approach to recover original speech signals from their nonlinear mixtures. Using a geometric method that makes a piecewise linear approximation of the nonlinear mixing space, and the fact that the speech distributions are Laplacian or Gamma type, a set of slopes is obtained as a set of linear mixtures. 1 Introduction The problem of blind separation of sources [1] involves obtaining the signals generated by p sources, sj, j=l ..... p, from the mixtures detected by p sensors, ej, i=l ..... p. The mixture of the signals takes place in the medium in which they are propagated, and: ei(t ) = Fi(sl(t) ..... sj(t) ..... sp(t)) , i = 1..... p (1) where Fi: flt~ is a function of p variables from the s-space to the e-space, represented by one matrix, Apx p. The goal of source separation is to obtain p functions, Lj, such that: sj(t) = Lj~.e.l~t~ ) ..... ei(t ) ..... ep(t)) , j= 1 ..... p (2) where Lj: ~P-3t is a function from the e-space to the s-space. The source separation is considered solved when signals yj(t) are obtained from matrix Wpxp(similar to A) [2], and: W -l . A -- D.P ; Dc {diagonal mat.} ,Pc {permutation mat.} (3) We have proposed various procedures that are based on geometrical properties of source vectors, S (t), and of mixtures, E(t), from the hypothesis that the sources are bounded [3,4], since the real signals (speech, biomedical) are limited in amplitude. The present paper aims to extend this method to a type of nonlinear mixture that approximately models the non linearities introduced in sensors. We believe, in agreement with other authors [5], that an adequate mixture model is the post-nonlinear (PNL) model. Thus, (1) may be expressed as" ei(t ) = Fi( f~ aij.sj(t )) ; i = l ..... p (4) j=l Nevertheless, there exists a great variety of sensors [6] whose transfer characteristics are modelled by diverse functions. Thus, we can also consider a more general nonlinear model whenever the F~ transformation is a continuous nonlinear function, since in this way, it is