A frequency domain adaptive filter algorithm 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 an algorithm formulated in the frequency domain based on the principle of minimum disturbance, with a penalty function incorporated 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. Simulation results are provided to illustrate the performance of this algorithm in comparison to other algorithms that limit the filter magnitude response.