Design of perfect reconstruction cosine-modulated QMF banks

The design problem of cosine-modulated QMF banks that satisfying the perfect-reconstruction (PR) property has been formulated as an quadratic-constrained least-squares (QCLS) minimization problem in which all constrained matrices of the QCLS optimization problem are symmetry and positive definite. In order to efficiently solve this QCLS optimization problem, we construct a cost function which is convex function of our desired prototype filter coefficients. so, all its minimizers are global minimizers. Results of computer simulations are presented to support our derivatives and analyses.