Adaptive Filtering Analysis and Design
Adaptive filters are, by design, time-variant and nonlinear systems that adapt to variations in signal statistics and that learn from their interactions with the environment. They have found many applications in signal processing, communications, biomedical engineering,.. etc. The success of their learning mechanism can be measured in terms of how fast they adapt to changes in the signal characteristics and how well they can learn given sufficient time. It is therefore typical to measure the performance of an adaptive filter in terms of both its transient performance and its steady-state performance. The former is concerned with the stability and convergence rate of an adaptive scheme, whereas the latter is concerned with the mean-square error that is left in steady state.
Mean-square Analysis of Adaptive Filters
I performed a unified mean-square analysis of a large class of adaptive algorithms. Analysis unifies and extends earlier analysis approaches; is able to predict stability and learning behavior of many adaptive algorithms very accurately. It allows the user to choose the adaptive algorithm best suited for a given application; applies regardless of type of nonlinearity employed in the algorithm and irrespective of the color or statistics of data driving the adaptive algorithm.
Adaptive Filters with Optimum Nonlinearities
Many LMS type adaptive filters have been suggested in literature with error and data nonlinearities. A recent research problem that I am interested in is to design adaptive filters with optimum error and data nonlinearities given a priori knowledge about the input and noise statistics.