  In this paper, we present a novel convolution theorem which encompasses the
well known convolution theorem in (graph) signal processing as well as the one
related to time-varying filters. Specifically, we show how a node-wise
convolution for signals supported on a graph can be expressed as another
node-wise convolution in a frequency domain graph, different from the original
graph. This is achieved through a parameterization of the filter coefficients
following a basis expansion model. After showing how the presented theorem is
consistent with the already existing body of literature, we discuss its
implications in terms of non-stationarity. Finally, we propose a data-driven
algorithm based on subspace fitting to learn the frequency domain graph, which
is then corroborated by experimental results on synthetic and real data.
