Space-Time-Frequency Degrees of Freedom: Fundamental Limits for Spatial Information
<|reference_start|>Space-Time-Frequency Degrees of Freedom: Fundamental Limits for Spatial Information: 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.<|reference_end|>
@article{abhayapala2007space-time-frequency,
    title={Space-Time-Frequency Degrees of Freedom: Fundamental Limits for Spatial
  Information},
    author={Leif Hanlen Thushara Abhayapala},
    journal={arXiv preprint arXiv:cs/0701056},
    year={2007},
    archivePrefix={arXiv},
    eprint={cs/0701056},
    primaryClass={cs.IT math.IT}
}