The design problem of cosine modulated QMF banks satisfying the perfect reconstruction property has been formulated as a quadratic constrained least squares（QCLS）optimization problem whose constrained matrices are symmetric and positive definite.In order to efficiently solve this kind of QCLS optimization problems

we construct a cost function which is a convex function of our desired prototype filter coefficients.So a global minimum of this problem can be easily obtained.Results of two digital design examples are presented to support our derivatives and analyses in this paper.