  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.
