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Design Of Adaptive Envelope-Constrained Filters Using the Cubic Smoothing Function

The design of envelope-constrained filters is formulated as a constrained optimization problem. The constraint approximation is realized through a cubic smoothing function, which results in an unconstrained optimization problem for envelope-constrained filter design. The solution of this unconstrained problem is suitable for real-time update. It is shown that compared to the previously used quadratic smoothing function, the cubic smoothing function leads to the establishment of the adaptive algorithms with much more desirable performance. In particular, the step size of the cubic constraint approximation based adaptive algorithms can also be chosen in a more flexible manner. Numerical examples illustrate the main results.