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

TL;DR

This paper introduces a power-efficient, clockless sampling method for finite-rate-of-innovation signals using an integrate-and-fire time encoding machine, with theoretical guarantees and noise robustness improvements.

Contribution

It provides a novel sampling framework for FRI signals with arbitrary pulse shapes, including design and recovery methods without pulse separation constraints.

Findings

Theoretical guarantees for perfect reconstruction of FRI signals.

A modified kernel improves noise robustness.

Enables low-cost, energy-efficient ADC design for FRI signals.

Abstract

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.