The purpose of this work is to analyse biomedical signals in order to diagnosis some pathologies. More precisely, the thesis report is divided into two subsections. The first one deals with the conception of a new system for sleep staging in ambulatory conditions. In this case, blind source separation methods, developed for instantaneous mixtures, were studied and applied in order to resolve the previous problem. In the second one, the reported investigation aims at extracting the original cardiac sympathetic and parasympathetic nervous activities only from a single-channel observed ECG, or more precisely from two parameters derived from it. In order to solve some encountered mathematical problems, we proposed a new family of phase retrieval algorithms. Then their performances were compared with classical methods. The obtained results show that our algorithms exhibit in general better performances than classical algorithms.