Elsabrouty, Maha2013-11-082013-11-0820062006Source: Dissertation Abstracts International, Volume: 67-07, Section: B, page: 3990.http://hdl.handle.net/10393/29291http://dx.doi.org/10.20381/ruor-19681Blind Source Separation is one of the newest and most active research areas in adaptive filtering. It represents the solution for many real situations in the audio, speech processing and telecommunication fields. The word "blind" reflects the fact that neither the source nor the mixing channel is known. This is, clearly, a more difficult situation compared to conventional adaptive filtering problems. Algorithms developed for blind separation reflect this difficulty. They possess a higher degree of sophistication compared with algorithms in other adaptive filtering approaches. The cost functions employed for blind separation are mostly based, implicitly or explicitly, on higher order statistics, while some of the adaptive algorithms developed for blind signal separation witnessed the introduction of the powerful principle of differential geometry to modify the LMS-based algorithms to what is known as the natural-gradient update. The aim of this work is to generalize differential geometry algorithms for different cost functions of blind signal separation and provide new faster converging RLS-based and Newton-based algorithms using the natural gradient update. The thesis starts by providing a thorough review of the existing solutions developed in the literature for blind separation. This is followed by a study of the mathematical basis of Riemannian geometry and providing an engineering insight into the intrinsic geometry of curved spaces and its relation to optimization in adaptive filtering. Several new update algorithms are then developed throughout the thesis. They are structured to perform at faster convergence rates even in difficult mixing situations. These algorithms provide significantly improved performance in comparison with existing algorithms and are suitable for on-line applications.187 p.enEngineering, Electronics and Electrical.Thesis