An iterative quadratic programming method for multirate filter design

An iterative quadratic programming method for multirate filter design is described. The design problem is formulated as a 4th-order nonlinear optimization problem in which the objective function is a weighted sum of a reconstruction term and an aliasing-error term. Constraints on the filter's frequency response in the passband and stopband are imposed as a set of linear inequalities. The optimization problem is solved by iteratively minimizing a quadratic function subject to a set of linear constraints. Explicit formulas for evaluating the minimums of these quadratic functions are described, which lead to an efficient and fast algorithm. An example is included to illustrate the design method.