Design of Minimum-Phase Filters Using Optimization

Abstract

A method for the design of minimum-phase finite-duration impulse response digital filters using spectral factorization is described. In the proposed method, the required digital filter is designed by formulating a set of nonlinear equations that represent the design problem at hand and then solving it by using the Levenberg–Marquardt optimization method. By using an exact formulation for the Jacobian and Hessian matrix in the Levenberg–Marquardt method, significant performance improvement and fast convergence is achieved. Comparisons show that the new method leads to a significant reduction in the maximum value and the $L_{2}$ norm of the residual error relative to those in state-of-the-art competing methods.