Noise Reduction in Multidimensional Digital filters Using High-Order Error Feedback

本文对“高阶误差反馈在多维数字滤波器中的降噪”进行了如下研究：1）对于由二维有理传递函数描述的二维递归数字滤波器，提出了一种设计最优误差反馈的算法。此外，为了降低实现成本和提高处理速度，还提出了次优误差反馈的设计算法，误差反馈系数可以是对称的或反对称的。2）针对由Roesser局部状态空间（LSS）模型表示的二维状态空间数字滤波器，提出了一种最优高阶误差反馈的设计算法。3）对于由Fornasini-Marchesini第二LSS模型表示的2-D状态空间数字滤波器，研究了设计高阶误差反馈的最优算法以及系数矩阵为对角的高阶误差反馈的次优设计算法。4）部分算法已成功地推广到三维有理传递函数描述的三维递归数字滤波器中。5）部分算法已成功地推广到多维状态空间数字滤波器中。从这些结果来看，我们认为我们的研究目标已经充分地达到了。

Stusies on "Noise Reduction in Multidimensional Digital filters Using High-Order Error Feedback" have been carried out as follows.1) For two-dimensional (2-D) recursive digital filters described by 2-D rational transfer functions, an algorithm has been developed for designing the optimal error-feedback. Moreover, algorithm have been presented for designing the suboptimal error-feedback, whose coefficients are symmetric or antisymmetric, in order to reduce the implementation cost and make the processing rate high.2) For 2-D state-space digital filters represented by the Roesser local state-space (LSS) model, an algorithm has been proposed for the design of the optimal high-order error-feedback. Also, algorithms have been explored to design the suboptimal high-order error-feedback with symmetric or antisymmetric coefficients.3) For 2-D state-space digital filters expressed by the Fornasini-Marchesini second LSS model, the optimal algorithm for designing high-order error-feedbacks has been investigated together with the suboptimal design algorithms of high-order error-feedbacks whose coefficient matrices are diagonal.4) A part of the algorithms mentioned above have been successfully extended to three-dimensional (3-D) recursive digital filters described by 3-D rational transfer functions.5) Some of the above algorithms have also been extended to multidimensional state-space digital filters successfully.Judging from these results, we consider that the objective of our study has been achieved sufficiently.