Graph signal processing on directed graphs is more challenging that on undirected graph, primarily because the graph matrices, e.g., adjacency or Laplacian, associated with the latter is non-symmetric. The eigenvalues that represent the spectral frequencies are therefore complex in general, and the design of spectral filters for complex frequencies presents more challenges. In this work we consider the design of two-channel filter banks for directed bipartite graphs. By decomposing any graph into a series of bipartite graphs, the basic two-channel system can be applied in cascade for arbitrary graphs. The graph filters are constructed using ladder structures. The design of the kernels in the ladder structures is achieved via a least-squares formulation. Analytical formulas are derived for the design of the kernel coefficients.

中文翻译：

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有向二部图上双通道滤波器组的滤波器设计

有向图上的图信号处理比无向图上的图信号处理更具挑战性，主要是因为与后者相关联的图矩阵（例如，邻接或拉普拉斯算子）是非对称的。因此，表示频谱频率的特征值通常是复杂的，复杂频率的频谱滤波器的设计提出了更多挑战。在这项工作中，我们考虑为有向二部图设计双通道滤波器组。通过将任何图分解为一系列二部图，基本的双通道系统可以级联应用于任意图。图过滤器是使用梯形结构构建的。梯形结构中内核的设计是通过最小二乘公式实现的。推导出用于设计核系数的分析公式。