Design of QMF banks and nonlinear optimization

This paper considers the design of quadrature mirror filter (QMF) banks whose analysis and synthesis filters have linear phase and are of FIR. An iterative algorithm for minimizing the reconstruction error of QMF banks as well as the stopband error of the prototype filter has been developed in the literature. the authors' results provide new derivations for an explicit expression of the error function to be minimized and the necessary condition for minimality. These results offer new insight to the design of QMF banks and relates it to a more general nonlinear optimization problem. Moreover a new iterative algorithm is proposed that generalizes the one from Chen and Lee (1992). It is shown that this new algorithm is a descending one and is essentially a modified Newton's algorithm. Thus the iterative algorithm not only converges, but also admits a fast convergent rate.