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

arXiv: https://arxiv.org/abs/1905.03183 · HTML: https://mlsanity.com/paper/1905.03183/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 May 2019.

## Built on by (most cited first, 4 of 4)

- [Adaptive Integrate-and-Fire Time Encoding Machine with Quantization](https://mlsanity.com/paper/2403.02992/) (2024)
- [A Time Encoding approach to training Spiking Neural Networks](https://mlsanity.com/paper/2110.06735/) (2021)
- [Time Encoding Quantization of Bandlimited and Finite-Rate-of-Innovation Signals](https://mlsanity.com/paper/2110.01928/) (2021)
- [How Asynchronous Events Encode Video](https://mlsanity.com/paper/2206.04341/) (2022)

## Abstract (arXiv)

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.