Professor Fettweis as far back as 1977 published a paper generalizing McClellan transformation to obtain circular symmetry in 2-D and spherical, hyper-spherical symmetries in multidimensional digital filters [1]. This survey paper presents stateof-the-art two-dimensional (2-D) VLSI digital filter architectures possessing various symmetries in the filter magnitude response. Preceding the symmetry structures, a generalized formulation is given that allows the derivation of various new 2-D VLSI filter structures of any order without global broadcast. Following this, two types (namely, Type 1 [20] and Type 3 [21], [25], [26]) of cost-effective 2-D magnitude symmetry filter architectures possessing diagonal, four-fold rotational, quadrantal, and octagonal symmetries with reduced number of multipliers are given. By combining the identities of the Types-1 and 3 symmetry filter structures, multimode 2-D symmetry filters which enable the above four symmetry modes are discussed. The Type-1 and Type-3 multimode filters can result in a 65.3% cost reduction in terms of number of multipliers compared with the sum of the multipliers of the four individual Type-1 symmetry filter structures studied in this paper. Furthermore, Type-3 has shorter critical path than Type-1 multimode filter. The paper is concluded with the presentation of a 2-D filter design example and a corresponding structure.

中文翻译：

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用于二维数字滤波器的 Symmetry Incorporated 高性价比架构

Fettweis 教授早在 1977 年就发表了一篇论文，概括了麦克莱伦变换以获得二维圆对称和多维数字滤波器中的球面、超球面对称性 [1]。这份调查论文介绍了最先进的二维 (2-D) VLSI 数字滤波器架构，在滤波器幅度响应中具有各种对称性。在对称结构之前，给出了一个通用公式，该公式允许推导任何阶的各种新 2-D VLSI 滤波器结构，而无需全局广播。在此之后，两种类型（即类型 1 [20] 和类型 3 [21]、[25]、[26]）具有对角线、四重旋转、象限和给出了乘数减少的八边形对称性。通过结合类型 1 和类型 3 对称滤波器结构的特性，讨论了实现上述四种对称模式的多模二维对称滤波器。与本文研究的四个单独的 Type-1 对称滤波器结构的乘法器之和相比，Type-1 和 Type-3 多模滤波器在乘法器数量方面可以降低 65.3% 的成本。此外，Type-3 的关键路径比 Type-1 多模滤波器短。本文最后介绍了一个二维滤波器设计示例和相应的结构。与本文研究的四个单独的 Type-1 对称滤波器结构的乘法器之和相比，乘法器数量减少了 3%。此外，Type-3 的关键路径比 Type-1 多模滤波器短。本文最后介绍了一个二维滤波器设计示例和相应的结构。与本文研究的四个单独的 Type-1 对称滤波器结构的乘法器之和相比，乘法器数量减少了 3%。此外，Type-3 的关键路径比 Type-1 多模滤波器短。本文最后介绍了一个二维滤波器设计示例和相应的结构。