Application of cubic constraint approximation in the recursive design of FIR filters subject to output envelope constraints

The smoothing function used in the constraint approximation plays an import ant role in the adaptive envelope-constrained (EC) filtering algorithms pre sented in [10]. In this paper, a cubic smoothing function is proposed to im plement the constraint approximation and the simplified line search techniq ue is introduced to speed up the convergence rate. It is shown that the per formance of the adaptive EC filtering algorithms can be greatly improved du e to the use of the cubic constraint approximation and simplified line sear ches. In particular, the second-order convergence is established for the Ne wton-Raphson type algorithm. Numerical results are included to illustrate t he effectiveness of these adaptive EC filtering algorithms.