Statistical signal analysis in Lp space

Extending the signal analysis to the L
^p
space offers new properties of the statistical operators. Low order statistics (LOS) based on centered moments of order p, when p ϵ N
⁺
and p<;2, are less affected by outliers than that high order moments when p ϵ N and p>2, used in high order statistics (HOS). Independent components analysis (ICA) problems are solved using an algorithm based only on LOS. Using a particular independence condition, an ultra fast ICA algorithm has been obtained. A generalized correlation coefficient defined on the Lp space, for p<;2, is less affected by outliers than that defined by Pearson, and in the case of normal distributed random variables, it gives the same numerical values for any p. These new operators have been used for detection of the sleep stages using a 3D camera.