Synthesis of 2-D separable denominator digital filters with minimum roundoff noise and no overflow oscillations
Synthesis of 2-D separable denominator digital filters with minimum roundoff noise and no overflow oscillations
复制标题
具有最小舍入噪声和无溢出振荡的二维可分离分母数字滤波器的合成
DOI：
10.1109/tcs.1986.1085931
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发表时间：
1986
期刊：
影响因子：
--
通讯作者：
T. Higuchi
中科院分区：
文献类型：
--
作者：
M. Kawamata;T. Higuchi
本文给出了用Roesser局部状态空间模型描述的2-D可分分母数字滤波器中循环噪声方差的新表达式。在1_2范数尺度下，得到了分析循环噪声方差所需的协方差矩阵和噪声矩阵，作为Liapunov方程的解。在1_2范数尺度下，给出了二维可分离分母数字滤波器的最小噪声综合问题。在1维情况下，应用圆噪声最小化技术，给出了1_2模尺度下2维最小噪声实现的综合方法。此外，它表明，2-D最小噪声实现旋转和缩放平衡实现。利用这一性质，证明了在零输入条件下，如果二维最小噪声实现的二阶模式是不同的，则它们不会产生溢出振荡。
This paper presents a new expression of the variance of roundoff noise in 2-D separable denominator digital filters described by Roesser's local state-space model. The covariance matrices and noise matrices necessary to analyze the variance of roundoff noise under the 1_2 norm scaling are obtained as the solutions of Liapunov equations. The synthesis problem of 2-D separable denominator digital filters with minimum roundoff noise are formulated under the 1_2 norm scaling. The synthesis method of 2-D minimum noise realizations under the 1_2 norm scaling is proposed by applying the minimization technique of roundoff noise in the 1-D case. Furthermore, it is shown that 2-D minimum noise realizations are rotated and scaled balanced realizations. Using this property, 2-D minimum noise realizations are proved to be free of overflow oscillations under zero input conditions, if their second-order modes are distinct.