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

Abstract

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.

Review of active noise control techniques with emphasis on sound quality enhancement

“…In this study, constraints are added to limit the filter gain, filter convergence, and filter output power. Then, the Lagrange multiplier [105] method, which helps the CMD algorithm obtain a faster convergence speed, is used to solve the constrained optimization problem [106]. Fig.…”

An active noise control algorithm with gain and power constraints on the adaptive filter

“…A constraint is added for filter convergence, and a constraint is also added for either the filter gain (coefficient's magnitude in each frequency bin), or the filter output power, depending on which we intend to limit. The method of Lagrange multipliers [11,12] is then used to solve this constrained optimization problem [13].…”