Uncertainty principles for signal concentrations

Uncertainty principles for concentration of signals into truncated subspaces are considered. The "classic" uncertainty principle is explored as a special case of a more general operator framework. The time-bandwidth concentration problem is shown as a similar special case. A spatial concentration of radio signals example is provided, and it is shown that an uncertainty principle exists for concentration of single-frequency signals for regions in space. We show that the uncertainty is related to the volumes of the spatial regions