# Reconstructing Classes of Non-bandlimited Signals from Time Encoded Information

## TL;DR

This paper explores reconstructing non-bandlimited signals from time-encoded samples using filtering and non-uniform sampling, introducing new algorithms and conditions for perfect recovery, even with noisy data.

## Contribution

It introduces a novel framework for reconstructing non-bandlimited signals from time encoding, focusing on exponential and polynomial spline filters, with algorithms for perfect recovery.

## Key findings

- Sampling by timing is equivalent to non-uniform sampling.
- Fundamental properties of filters are locally preserved in non-uniform sampling.
- Proposed algorithms achieve perfect reconstruction under certain conditions.

## Abstract

We investigate time encoding as an alternative method to classical sampling, and address the problem of reconstructing classes of non-bandlimited signals from time-based samples. We consider a sampling mechanism based on first filtering the input, before obtaining the timing information using a time encoding machine. Within this framework, we show that sampling by timing is equivalent to a non-uniform sampling problem, where the reconstruction of the input depends on the characteristics of the filter and on its non-uniform shifts. The classes of filters we focus on are exponential and polynomial splines, and we show that their fundamental properties are locally preserved in the context of non-uniform sampling. Leveraging these properties, we then derive sufficient conditions and propose novel algorithms for perfect reconstruction of classes of non-bandlimited signals such as: streams of Diracs, sequences of pulses and piecewise constant signals. Next, we extend these methods to operate with arbitrary filters, and also present simulation results on synthetic noisy data.