  In this paper we prove the existence of a time-frequency space that best
approximates a given finite set of data. Here best approximation is in the
least square sense, among all time-frequency spaces with no more than a
prescribed number of generators. We provide a formula to construct the
generators from the data and give the exact error of approximation. The setting
is in the space of square integrable functions defined on a second countable
LCA group and we use the Zak transform as the main tool.
