Cubic constraint approximation based adaptive algorithms for envelope-constrained filtering

The design of envelope-constrained filters is formulated as a constrained o ptimization problem. In this paper the constraint approximation is realized through a cubic natural spline, which results in an unconstrained optimiza tion problem for envelope-constrained filter design. The solution of this u nconstrained problem is suitable for real-time update. It is shown that, co mpared with the previously used quadratic natural spline, the cubic natural spline leads to the establishment of the adaptive algorithms with much mov e desirable performance. In particular, the step size of the cubic constrai nt approximation based adaptive algorithms can be chosen in a more flexible manner so as to achieve faster convergence. Numerical examples illustrate the main results.