---
title: Bounds on Space-Time-Frequency Dimensionality
url: https://www.emergentmind.com/papers/0701055
type: paper
arxiv_id: '0701055'
arxiv_url: https://arxiv.org/abs/0701055
published: '2007-01-09'
categories:
- cs.IT
- math.IT
---

# Bounds on Space-Time-Frequency Dimensionality

## Abstract

We bound the number of electromagnetic signals which may be observed over a frequency range $2W$ for a time $T$ within a region of space enclosed by a radius $R$. Our result implies that broadband fields in space cannot be arbitrarily complex: there is a finite amount of information which may be extracted from a region of space via electromagnetic radiation. Three-dimensional space allows a trade-off between large carrier frequency and bandwidth. We demonstrate applications in super-resolution and broadband communication.