This letter analyses the convergence behaviour of the transform domain least mean square (TDLMS) adaptive filtering algorithm which is based on a well known interpretation of the variable stepsize algorithm. With this interpretation, the analysis is considerably simplified. The time varying stepsize is implemented by the modified power estimator to redistribute the spread power after transformation. The main contribution of this letter is the statistical performance analysis in terms of mean and mean squared error of the weight error vector and the decorrelation property of the TDLMS is presented by the lower and upper bound of eigenvalue spread ratio. The theoretical analysis results are validated by Monte Carlo simulation.

This article addresses two issues. Firstly, the convergence property of conjugate gradient (CG) algorithm is investigated by a Chebyshev polynomial approximation. The analysis result shows that its convergence behaviour is affected by an acceleration term over the steepest descent (SD) algorithm. Secondly, a new CG algorithm is proposed in order to boost the tracking capability for time-varying parameters. The proposed algorithm based on re-initialising forgetting factor shows a fast tracking ability and a noise-immunity property when it encounters an unexpected parameter change. A fast tracking capability is verified through a computer simulation in a system identification problem.