In this paper, the close relationship among wavelet transform and quadrature mirror filter (QMF) banks and the scattering matrix of wave digital filter (WDF) is analyzed in detail. The parametrization of orth...In this paper, the close relationship among wavelet transform and quadrature mirror filter (QMF) banks and the scattering matrix of wave digital filter (WDF) is analyzed in detail. The parametrization of orthonormal compactly supported wavelet bases that have an arbitrary number of vanishing moment is obtained by building any QMF pair out of elementary factors of the scatteringmatrix. In addition, the optimization of parameter is also presented. As comparison, some examples about orthonormal compactly supported wavelet that has arbitrary number of vanishing moment and the most number of vanishing moment are given respectively. Then we give the efficient lattice structure to implement the transform.展开更多
In this paper the design problem of perfect-reconstruction cosine-modulated QMF banks has been formulated as a quadratic-constrained least-squares (QCLS) minimization problem in which all constrained matrices of the Q...In this paper the design problem of perfect-reconstruction cosine-modulated QMF banks has been formulated as a quadratic-constrained least-squares (QCLS) minimization problem in which all constrained matrices of the QCLS optimization problem are symmetric and positive definite. A cost function which is a convex function of desired prototype filter coefficients is constructed so that this kind of QCLS optimization problems can be efficiently solved. So a global minimizer of this problem can be easily obtained. Results of two design examples are presented to support the derivations and analyses.展开更多
文摘In this paper, the close relationship among wavelet transform and quadrature mirror filter (QMF) banks and the scattering matrix of wave digital filter (WDF) is analyzed in detail. The parametrization of orthonormal compactly supported wavelet bases that have an arbitrary number of vanishing moment is obtained by building any QMF pair out of elementary factors of the scatteringmatrix. In addition, the optimization of parameter is also presented. As comparison, some examples about orthonormal compactly supported wavelet that has arbitrary number of vanishing moment and the most number of vanishing moment are given respectively. Then we give the efficient lattice structure to implement the transform.
基金Climbing Programme-National Key Project for Foundamental Research in China,Grant NSC92097National Natural Science Foundation of China
文摘In this paper the design problem of perfect-reconstruction cosine-modulated QMF banks has been formulated as a quadratic-constrained least-squares (QCLS) minimization problem in which all constrained matrices of the QCLS optimization problem are symmetric and positive definite. A cost function which is a convex function of desired prototype filter coefficients is constructed so that this kind of QCLS optimization problems can be efficiently solved. So a global minimizer of this problem can be easily obtained. Results of two design examples are presented to support the derivations and analyses.
