设计余弦调制QMF组的一种新方法

A New Method for Designing Cosine modulated QMF Bank

通过适当矩阵变换，本文首先将精确重建余弦调制正交镜像滤波器组的设计转化为一种带约束的非线性优化问题。它是一种带二次型约束的最小二乘（ＱＣＬＳ）优化问题。然后，我们提出了一种变参量的罚函数方法来有效求解该类ＱＣＬＳ优化问题。通过直接采用原型滤波器系数为优化变量，我们构造了一个特殊的凸函数作为优化代价函数，故可获得该问题的全局最小点。最后，采用本文提出的设计方法进行了一个具体实例设计，结果表明我们的方法是很有效的。

Though proper matrix transformations, at first, the design of perfect reconstruction cosine modulated QMF banks has been recasted into a constrained nonlinear optimization problem which is of a quadratic constrained least squares (QCLS) optimization problem with symmetric and positive definite constrained matrices. Secondly, we propose a penalty function approach with variable parameter to efficiently tackle this kind of QCLS optimization problems. By directly utilizing the impulse coefficients of the prototype filter as optimizing arguments, we build a special convex function as the cost of the problem in hand. Therefore the global minimizer of this problem can be easily obtained. Finally, a concrete design instance is provided for our claims in this paper.