Encoding and Decoding Mixed Bandlimited Signals using Spiking Integrate-and-Fire Neurons

TL;DR

This paper explores biologically-inspired sampling using integrate-and-fire neurons to encode and decode mixed bandlimited signals, providing conditions for perfect recovery and an algorithm for reconstruction.

Contribution

It introduces a novel sampling scheme using IF-TEMs for mixed signals and establishes conditions for perfect decoding in noiseless environments.

Findings

Conditions for perfect signal recovery are derived.

An algorithm for signal reconstruction from spike times is proposed.

The method demonstrates potential for biologically-inspired signal processing.

Abstract

Conventional sampling focuses on encoding and decoding bandlimited signals by recording signal amplitudes at known time points. Alternately, sampling can be approached using biologically-inspired schemes. Among these are integrate-and-fire time encoding machines (IF-TEMs). They behave like simplified versions of spiking neurons and encode their input using spike times rather than amplitudes. Moreover, when multiple of these neurons jointly process a set of mixed signals, they form one layer in a feedforward spiking neural network. In this paper, we investigate the encoding and decoding potential of such a layer. We propose a setup to sample a set of bandlimited signals, by mixing them and sampling the result using different IF-TEMs. We provide conditions for perfect recovery of the set of signals from the samples in the noiseless case, and suggest an algorithm to perform the reconstruction.