  Recently we have shown that it is possible to represent continuous amplitude,
continuous time, band limited signals with an error as small as desired using
pulse trains via the integrate and fire converter (IFC). The IFC is an ultra
low power converter and processing with pulse trains is compatible with the
trends in the silicon technology for very low supply voltages. This paper
presents the definition of addition in pulse trains created by the IFC using
exclusively timing information, and proofs that it constitutes an Abelian group
in the space of IFC pulse trains. We also show that pulse domain addition
corresponds to pointwise addition of analog signals.
