Nonconvex Optimization via Joint Norm Relaxed SQP and Filled Function Method with Application to Minimax Two-Channel Linear Phase FIR QMF Bank Design - Advances in Heuristic Signal Processing and Applications - page 14

Fig. 1.1 Magnitude response
of the filter bank
Fig. 1.2 Magnitude response
of the prototype filter in the
passband
Fig. 1.3 Magnitude response
of the prototype filter in the
stopband
1.5 Conclusions
This chapter proposes a joint norm relaxed sequential quadratic programming and
filled function method for the design of a two-channel linear phase FIR QMF bank
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. In particular, a locally optimal solution of the
optimization problem in each iteration of the filled function method is found by
the norm relaxed sequence quadratic programming method. The globally optimal
solution of the original optimization problem is found by the filled function method.
Computer numerical simulation results show that the proposed method can find the
global minimum of the nonconvex optimization problem efficiently.