# FRI-TEM: Time Encoding Sampling of Finite-Rate-of-Innovation Signals

arXiv: https://arxiv.org/abs/2106.05564 · HTML: https://mlsanity.com/paper/2106.05564/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jun 2021.

## Built on by (most cited first, 5 of 5)

- [Adaptive Integrate-and-Fire Time Encoding Machine with Quantization](https://mlsanity.com/paper/2403.02992/) (2024)
- [Baseline Drift Tolerant Signal Encoding for ECG Classification with Deep Learning](https://mlsanity.com/paper/2405.00724/) (2024)
- [Low-Bit Data Processing Using Multiple-Output Spiking Neurons with Non-linear Reset Feedback](https://mlsanity.com/paper/2508.06292/) (2025)
- [A Non-Uniform Quantization Framework for Time-Encoding Machines](https://mlsanity.com/paper/2511.02728/) (2025)
- [Time Encoding Quantization of Bandlimited and Finite-Rate-of-Innovation Signals](https://mlsanity.com/paper/2110.01928/) (2021)

## Abstract (arXiv)

Classical sampling is based on acquiring signal amplitudes at specific points in time, with the minimal sampling rate dictated by the degrees of freedom in the signal. The samplers in this framework are controlled by a global clock that operates at a rate greater than or equal to the minimal sampling rate. At high sampling rates, clocks are power-consuming and prone to electromagnetic interference. An integrate-and-fire time encoding machine (IF-TEM) is an alternative power-efficient sampling mechanism which does not require a global clock. Here, the samples are irregularly spaced threshold-based samples. In this paper, we investigate the problem of sampling finite-rate-of-innovation (FRI) signals using an IF-TEM. We provide theoretical recovery guarantees for an FRI signal with arbitrary pulse shape and without any constraint on the minimum separation between the pulses. In particular, we show how to design a sampling kernel, IF-TEM, and recovery method such that the FRI signals are perfectly reconstructed. We then propose a modification to the sampling kernel to improve noise robustness. Our results enable designing low-cost and energy-efficient analog-to-digital converters for FRI signals.