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

Leif Hanlen Thushara Abhayapala

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arXiv · cs/0701056

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

Leif Hanlen Thushara Abhayapala

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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.

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Leif Hanlen Thushara Abhayapala. 2007-01-09. Space-Time-Frequency Degrees of Freedom: Fundamental Limits for Spatial Information. https://arxiv.org/abs/cs/0701056

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