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In this paper, we present a novel convolution theorem which encompasses thewell known convolution theorem in (graph) signal processing as well as the onerelated to time-varying filters. Specifically, we show how a node-wiseconvolution for signals supported on a graph can be expressed as anothernode-wise convolution in a frequency domain graph, different from the originalgraph. This is achieved through a parameterization of the filter coefficientsfollowing a basis expansion model. After showing how the presented theorem isconsistent with the already existing body of literature, we discuss itsimplications in terms of non-stationarity. Finally, we propose a data-drivenalgorithm based on subspace fitting to learn the frequency domain graph, whichis then corroborated by experimental results on synthetic and real data.

A Generalization of the Convolution Theorem and its Connections to Non-Stationarity and the Graph Frequency Domain