Nonconvex Optimization via Joint Norm Relaxed SQP and Filled Function Method with Application to Minimax Two-Channel Linear Phase FIR QMF Bank Design

Abstract

In this chapter, a two-channel linear phase finite impulse response (FIR) quadrature mirror filter (QMF) bank minimax design problem is formulated as a nonconvex optimization problem so that a weighted sum of the maximum amplitude distortion of the filter bank, the maximum passband ripple magnitude, and the maximum stopband ripple magnitude of the prototype filter is minimized subject to specifications on these performances. A joint norm relaxed sequential quadratic programming and filled function method is proposed for finding the global minimum of the nonconvex optimization problem. Computer numerical simulations show that our proposed design method is efficient and effective.