Active noise control filter design methods can be categorized as time-domain or frequency-domain methods. When multiple frequency-dependent constraints need to be specified, such as the enhancement constraint, stability constraint, and robustness constraint, the optimal filter coefficients can be obtained more conveniently by solving a constrained optimization problem formulated using frequency-domain methods. However, the computational load for searching the global optimal solution is significantly high, if the number of channels, filter coefficients, or constraints is large. To improve computational efficiency, some previous work relaxed the traditional formulation to a convex problem, and then reformulated it to a cone programming problem. After this reformulation, efficient algorithms for cone programming problem, e.g., the primal-dual interior-point methods, can be applied to solve the filter design problem. However, some numerical issues may occur when solving the reformulated standard conic form directly. In this paper, the numerical instability issue for active noise control filter design problem is investigated. The original conic form was rearranged via dual formulation and different treatments of free variables are discussed. It is demonstrated that the proposed approach result is equivalent to the standard conic form but numerically more stable.
Active Noise Control, Convex Optimization, Cone Programing, Optimal Filter Design, Duality
Acoustics and Noise Control
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