  The integrate and fire converter (IFC) enables an alternative to digital
signal processing. IFC converts analog signal voltages into time between pulses
and it is possible to reconstruct the analog signal from the IFC pulses with an
error as small as required. In this paper, we present the definition of
multiplication in pulse trains created by the IFC based on time domain
operations and prove that it constitutes an Abelian group in the space of IFC
pulse trains. We also show that pulse domain multiplication corresponds to
pointwise multiplication of analog signals. It is further proved that pulse
domain multiplication is distributive over pulse domain addition and hence it
forms a field in the space of IFC pulse trains, which is an important property
for linear signal processing.
