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In this chapter, we consider linear graph filters. Readers can find nonlinear graph filters, like one used in deep learning, in the following chapters, specifically Chapter 10.

Let us denote a graph filter as H ∈ R^N×N, where its elements are typically derived from and x. As in the LTI system, the filtered signal is represented as

[1.7]

The representation of its element y_n is similar to that observed in equation [1.3], i.e.

[1.8]

where [·]_n,k is the n, k-element in the matrix. Similar to discrete-time signals, graph signal filtering may be defined in the vertex and graph frequency domains. These are described in the following.