  In the work of Donoho and Stark, they study a manifestation of the
uncertainty principle in signal recovery. They conjecture that, for a function
with support of bounded size T, the maximum concentration of its Fourier
transform in the low frequencies [-W/2,W/2] is achieved when the support of the
function is an interval. They are able to prove a positive result under the
extra assumption that WT $\leq$ 0.8, using an inequality with symmetric
rearrangements. In our work, we present a more elementary proof of their
result, while also relaxing the required bound to WT $\leq$ 1. Finally, we also
study a discrete version of the problem, by considering complex polynomials and
their concentration on subsets of the unit circle, and we prove an analogous
problem. Lastly, this result is used to improve an inequality by Montgomery.
