The least mean squares (LMS) algorithm has been widely used for adaptive filtering because of easily implementing at a computational complexity of O(2N) where N is the number of taps. The drawback of the LMS algorithm is that its performance is sensitive to the scaling of the input. The normalized LMS (NLMS) algorithm solves this problem on the LMS algorithm by normalizing with the sliding-window power of the input; however, this normalization increases the computational cost to O(3N) per iteration. In this work, we derive a new formula to strictly perform the NLMS algorithm at a computational complexity of O(2N), that is referred to as the C-NLMS algorithm. The derivation of the C-NLMS algorithm uses the H∞ framework presented previously by one of the authors for creating a unified view of adaptive filtering algorithms. The validity of the C-NLMS algorithm is verified using simulations.

In this paper, we propose a real-time BSS (Blind Source Separation) system with two microphones that extracts only desired sound sources. Under the assumption that the desired sound sources are close to the microphones, the proposed BSS system suppresses distant sound sources as undesired sound sources. We previously developed a BSS system that can estimate the distance from a microphone to a sound source and suppress distant sound sources, but it was not a real-time processing system. The proposed BSS system is a real-time version of our previous BSS system. To develop the proposed BSS system, we simplify some BSS procedures of the previous system. Simulation results showed that the proposed system can effectively suppress the distant source signals in real-time and has almost the same capability as the previous system.