Convergence analysis of a frequency domain adaptive filter with constraints on the output weights

The least-mean-square (LMS) algorithm is very popular in adaptive filtering applications due to its robustness and efficiency. The frequency domain implementation of the LMS algorithm offers advantages in both reduced computational complexity for long filter lengths, and improved convergence performance. The frequency response of the filter can also be tailored to specific requirements, for example limiting the magnitude response. In this paper, we present a development, convergence analysis, and mean and mean square stability bounds for a new algorithm that uses a penalty function to limit the adaptive filter magnitude response at any given frequency. This algorithm performed better than existing ones in terms of convergence and gain limiting, especially in colored noise environments.