A central problem in signal processing and communications is to design signals
that are compact both in time and frequency. The variance is believed to be a
good measure of compactness, and with this definition Heisenberg stated that a
given function cannot be arbitrarily compact in time and frequency, defining an
"uncertainty" lower bound. In continuous-time, gaussian functions reach this
bound. For sequences, this is not true; it is known that Heisenberg's bound is
generally unachievable.
For a chosen frequency variance, we formulate the search for maximally compact
sequences as an exactly and efficiently solved  optimization problem, thus
providing a sharp uncertainty principle for sequences.