Sampling based on timing: Time encoding machines on shift-invariant subspaces

TL;DR

This paper extends the concept of time encoding machines from band-limited functions to shift-invariant subspaces, demonstrating their potential as non-uniform sampling devices that enable perfect signal reconstruction under certain density conditions.

Contribution

It generalizes time encoding machines to shift-invariant subspaces and proves their effectiveness for perfect signal reconstruction with robustness to timing quantization.

Findings

Time encoding machines can be viewed as non-uniform sampling devices.

Perfect reconstruction is possible under certain density conditions.

The method is robust to timing quantization.

Abstract

Sampling information using timing is a new approach in sampling theory. The question is how to map amplitude information into the timing domain. One such encoder, called time encoding machine, was introduced by Lazar and Toth in [23] for the special case of band-limited functions. In this paper, we extend their result to the general framework of shift-invariant subspaces. We prove that time encoding machines may be considered as non-uniform sampling devices, where time locations are unknown a priori. Using this fact, we show that perfect representation and reconstruction of a signal with a time encoding machine is possible whenever this device satisfies some density property. We prove that this method is robust under timing quantization, and therefore can lead to the design of simple and energy efficient sampling devices.