3-D Separable-Denominator Digital Filters with Minimum L2-Sensitivity and No Overflow Oscillations

T. Hinamoto, O. I. Omoifo
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Abstract

The problem of minimizing an L2-sensitivity measure subject to L2-norm dynamic-range scaling constraints for three-dimensional (3-D) separable-denominator digital filters is formulated. The constrained optimization problem is converted into an unconstrained optimization problem by using linear-algebraic techniques. Next, an efficient quasi-Newton algorithm is applied with closed-form formula for gradient evaluation to solve the unconstrained optimization problem. The optimal filter structure is then constructed by employing the resulting coordinate transformation matrix that minimizes the L2-sensitivity measure subject to the scaling constraints. A numerical example is presented to illustrate the utility of the proposed technique
具有最小l2灵敏度和无溢出振荡的三维可分分母数字滤波器
提出了三维可分分母数字滤波器在l2范数动态范围标度约束下l2灵敏度最小化问题。利用线性代数技术将约束优化问题转化为无约束优化问题。在此基础上,提出了一种有效的拟牛顿算法,并结合近似公式进行梯度求值,求解无约束优化问题。然后利用得到的坐标变换矩阵来构造最优滤波器结构,该矩阵在尺度约束下使l2灵敏度度量最小化。最后给出了一个数值算例来说明该方法的有效性
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