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

TL;DR

This paper establishes fundamental limits on the maximum number of electromagnetic signals that can be observed within a given space, frequency range, and time interval, indicating a finite information capacity in such regions.

Contribution

It provides a theoretical bound on electromagnetic signals' degrees of freedom in space, frequency, and time, using a series expansion with exponential bounds.

Findings

Finite number of signals observable within specified constraints

Signals can be represented by a bounded series expansion

Implication of finite information capacity in a spatial region

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.