Data approximation with time-frequency invariant systems

BARBIERI, DAVIDE; CABRELLI, CARLOS; HERNÁNDEZ, EUGENIO; MOLTER, URSULA

Landscapes of Time-Frequency Analysis, Vol.2

Birkhäuser

Lugar: Washington DC; Año: 2020;

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