Combinations of Adaptive Filters
Prof. Tõnu Trump
Department of Radio and Telecommunication
Tallinn University of Technology
Abstract: In this talk we consider the combination of two adaptive filters that are simultaneously applied to the same inputs. When designing an adaptive algorithm, one faces a trade–off between the initial convergence speed and the mean–square error in steady state. In case of algorithms belonging to the Least Mean Square (LMS) family this trade–off is controlled by the step-size parameter. Large step size leads to a fast initial convergence but the algorithm also exhibits a large mean–square error in the steady state and in contrary, small step size slows down the convergence but results in a small steady state error.
Recently there has been an interest in a combination scheme that is able to optimize the trade–off between convergence speed and steady state error. The scheme consists of two adaptive filters that are simultaneously applied to the same inputs. One of the filters has a large step size allowing fast convergence and the other one has a small step size for a small steady state error. The outputs of the filters are combined through a mixing parameter.
There are several ways to compute the combination parameter. In our treatment the combination parameter λ is computed from output signals of the individual filters. The scheme is optimal in the sense that it results from minimizing the mean square error of the combination.
The combination of two filters can be applied in different situations. The applications like line enhancement, system identification and beamforming will be examined in detail.
Brief Biography of the Speaker: Tõnu Trump received his Ph.D. degree from Tallinn University of Technology in 1993. He was from 1994 to 2006 with Ericsson AB in Stockholm Sweden, where he reached the position of expert in echo cancellation and voice enhancement devices. From 2002 to 2006 he was also the rapporteur of Question 17, Study Group 16 at International Telecommunication Union (ITU-T) in Geneva Switzerland. Since 2006 he has been the professor of Signal Processing at Tallinn University of Technology in Tallinn, Estonia.
Prof. Trump has published a number of scientific papers and is the author of more than 10 patents.