This article develops a new adaptive filter algorithm intended for use in active noise control systems where it is required to place gain or power constraints on the filter output to prevent overdriving the transducer, or to maintain a specified system power budget. When the frequency-domain version of the least-mean-square algorithm is used for the adaptive filter, this limiting can be done directly in the frequency domain, allowing the adaptive filter response to be reduced in frequency regions of constraint violation, with minimal effect at other frequencies. We present the development of a new adaptive filter algorithm that uses a penalty function formulation to place multiple constraints on the filter directly in the frequency domain. The new algorithm performs better than existing ones in terms of improved convergence rate and frequency-selective limiting.

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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.