The transform-domain forward-backward LMS adaptive filter with applications

The authors present the transform-domain forward-backward least-mean-squares (LMS) (TFBLMS) adaptive algorithm, its properties, and applications. The authors demonstrate that the TFBLMS adaptive line enhancer (ALE) gives significantly improved convergence speed for various applications with colored noise inputs and same level of reduced misadjustment as the forward-backward LMS (FBLMS) ALE for a given convergence factor (adaptive step size). The authors examine the impacts of the backward prediction error and forward prediction error individually on the total misadjustment in both the FBLMS and TFBLMS algorithms. The choice of a suitable transform is discussed as an implementation issue for the TFBLMS algorithm