A function f ∈ L2(R) is said to have bandwidth Ω > 0, if Ω is the maximal frequency contributing to f, which means that its Fourier transform vanishes outside the interval [−Ω, Ω].
When listening to a piece of music, the idea of variable bandwidth is very intuitive: the highest frequency in a musical composition is time-varying. With this motivation, it is reasonable to allow different local bandwidths to different intervals of a signal, when representing it mathematically.
Producing a rigorous definition of variable bandwidth is a challenging task since bandwidth is global by definition and the assignment of a local bandwidth finds an obstruction in the uncertainty principle.
In this talk, a new approach to the study of spaces of variable bandwidth is presented and some preliminary sampling theorems and density results for variable bandwidth spaces using Wilson bases are discussed.
This new model might be very attractive for the analysis of chirps and other time-varying signals with a hidden structure.