Variable bandwidth via Wilson basis

19.05.2023 09:45 - 11:15

Beatrice Andreolli (University of Vienna)

Bandlimited functions are functions whose Fourier transform has bounded support, which means that if the bandwidth of a function is  Ω > 0, then Ω is the maximal frequency contributing to f.In contrast to bandlimited functions, which are entire functions of time and represent infinite signals, real-world signals are time-limited and therefore require a description that accounts for this fact. As a result, the concept of variable bandwidth arises naturally in signal processing and it is particularly intuitive when considering music, where the highest frequency varies with time.In this talk, we introduce a new space of variable bandwidth which is based on the truncation of Wilson expansions.We study the problem of finding sufficient conditions for sampling for this space of variable bandwidth and analyzing some MATLAB experiments, we motivate why these new spaces could be useful for the reconstruction of particular classes of functions.

The talk is based on joint work with Karlheinz Gröchenig.

K. Gröchenig, L. Liehr, J. L. Romero and I. Shafkulovska
SR11 (second floor)