Signal Processing with Pulse Trains: An Algebraic Approach- Part I

TL;DR

This paper introduces an algebraic framework for representing and processing band-limited signals using pulse trains generated by the integrate and fire converter, emphasizing low power and compatibility with modern silicon technology.

Contribution

It defines addition of pulse trains via timing information and proves it forms an Abelian group, linking pulse domain operations to analog signal addition.

Findings

Pulse train addition forms an Abelian group.

Pulse domain addition corresponds to pointwise analog addition.

Representation of signals with arbitrary accuracy using pulse trains.

Abstract

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.