  Finite impulse response (FIR) graph filters play a crucial role in the field
of signal processing on graphs. However, when the graph signal is time-varying,
the state of the art FIR graph filters do not capture the time variations of
the input signal. In this work, we propose an extension of FIR graph filters to
capture also the signal variations over time. By considering also the past
values of the graph signal, the proposed FIR graph filter extends naturally to
a 2-dimensional filter, capturing jointly the signal variations over the graph
and time. As a particular case of interest we focus on 2-dimensional separable
graph-temporal filters, which can be implemented in a distributed fashion at
the price of higher communication costs. This allows us to give filter
specifications and perform the design independently in the graph and temporal
domain. The work is concluded by analyzing the proposed approach for stochastic
graph signals, where the first and second order moments of the output signal
are characterized.
