---
title: 'Space-Time-Frequency Degrees of Freedom: Fundamental Limits for Spatial Information'
url: https://www.emergentmind.com/papers/0701056
type: paper
arxiv_id: '0701056'
arxiv_url: https://arxiv.org/abs/0701056
published: '2007-01-09'
categories:
- cs.IT
- math.IT
---

# Space-Time-Frequency Degrees of Freedom: Fundamental Limits for Spatial Information

## Abstract

We bound the number of electromagnetic signals which may be observed over a frequency range $[F-W,F+W]$ a time interval $[0,T]$ within a sphere of radius $R$. We show that the such constrained signals may be represented by a series expansion whose terms are bounded exponentially to zero beyond a threshold. Our result implies there is a finite amount of information which may be extracted from a region of space via electromagnetic radiation.