A new look at adaptive envelope-constrained filtering via the constraint approximation

The smoothing function used in the constraint approximation plays an important role in the adaptive envelope-constrained (EC) filtering algorithms. In this paper a cubic smoothing function is proposed to implement the constraint approximation and the simplified line search technique is introduced to speed up the convergence rate. It is shown that the performance of the adaptive EC filtering algorithms can be greatly improved due to the use of the cubic constraint approximation and simplified line searches. In particular, the second order convergence is established for the Newton-Raphson type algorithm. Numerical results are included to illustrate the effectiveness of these adaptive EC filtering algorithms.