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本文以对称理论为基础,进行二维递归数字滤波器的优化设计。首先,讨论了如何满足稳定性条件和保证稳定性的措施,使繁琐的稳定性判别得到简化。然后给出直接用于设计的N阶系数矩阵的通用公式,从而使Rajan和Swamy的对称理论更便于实际应用。最后,对全响应对称理论进行了适当的修改,并把它引入到幅度响应的对称关系中,以扩大幅度响应的对称范围,使二维递归的矩形滤波器的设计得到进一步简化。
In this paper, based on symmetry theory, two-dimensional recursive digital filter optimization design. First of all, it discusses how to satisfy the stability conditions and ensure the stability of the measures, so that cumbersome stability discrimination is simplified. Then, a general formula of the N-th order matrix directly used in the design is given, so that the symmetrical theory of Rajan and Swamy can be more conveniently applied. Finally, the full response symmetry theory is modified appropriately, and introduced into the symmetrical relation of amplitude response to enlarge the symmetrical range of amplitude response so that the design of two-dimensional recursive rectangular filter can be further simplified.