Reply to “Comments on ‘A Recursive Least M-Estimate Algorithm for Robust Adaptive Filtering in Impulsive Noise: Fast Algorithm and Convergence Performance Analysis’”

We appreciate the comments by Bershad [ldquoComments on `A Recursive Least M-Estimate Algorithm for Robust Adaptive Filtering in Impulsive Noise: Fast Algorithm and Convergence Performance Analysis,´rdquo IEEE Transactions on Signal Processing, vol. 57, no. 1, January 2009] on an assumption of our paper [ldquoA Recursive Least M-Estimate Algorithm for Robust Adaptive Filtering in Impulsive Noise: Fast Algorithm and Convergence Performance Analysis,rdquo IEEE Transactions on Signal Processing, vol. 52, no. 4, April 2004]. In this reply, we elaborate further on this assumption, which was originally introduced as an approximation to simplify the performance analysis. Modifications and references to a related extension of Price´s theorem for independent mixtures are outlined. We wish this will clarify the issues raised.