Error spectrum shaping in two-dimensional recursive digital filters
Error spectrum shaping in two-dimensional recursive digital filters
复制标题
二维递归数字滤波器中的误差频谱整形
DOI：
10.1109/81.795833
复制
发表时间：
1999
影响因子：
5.1
通讯作者：
T. Kuma
中科院分区：
文献类型：
--
作者：
T. Hinamoto;S. Karino;N. Kuroda;T. Kuma
本文用有理传递函数和Roesser局部状态空间模型来描述二维递归数字滤波器的误差谱整形。对于滤波器的每个描述，开发了一种技术来获得最佳误差反馈（EF）系数，使滤波器输出处的噪声方差最小化。最优解可以用一个封闭的形式来表征，该形式最小化了受约束的二次形式，如EF系数的对称性、不对称性、象限对称性或象限不对称性。在无约束情况下，最优EF对应于上述最优解的一种特殊情况。最后，给出了两个数值算例来说明该方法的实用性。在数值算例中，利用已有的离散空间最小二乘优化方法，得到了离散次优系数。
This paper treats error spectrum shaping for two-dimensional recursive digital filters, described by a rational transfer function as well as the Roesser local state-space model. For each description of the filter, a technique is developed for obtaining the optimal error-feedback (EF) coefficients that minimize the noise variance at the filter output. The optimal solution can be characterized in a closed form which minimizes a quadratic form subject to constraints such as symmetry, antisymmetry, quadrantal symmetry, or quadrantal antisymmetry of the EF coefficients. In an unconstrained case, the optimal EF corresponds to a special case of the above optimal solution. Finally, two numerical examples are given to illustrate the utility of the proposed technique. In the numerical examples, the discrete sub-optimal coefficients of the EF are obtained by applying an existing procedure for the least-squares discrete-space optimization.