Bounds on Space-Time-Frequency Dimensionality
<|reference_start|>Bounds on Space-Time-Frequency Dimensionality: 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.<|reference_end|>
@article{hanlen2007bounds,
    title={Bounds on Space-Time-Frequency Dimensionality},
    author={Leif Hanlen, Thushara Abhayapala},
    journal={arXiv preprint arXiv:cs/0701055},
    year={2007},
    archivePrefix={arXiv},
    eprint={cs/0701055},
    primaryClass={cs.IT math.IT}
}