Band-limited function

Summary

A band-limited function is a function on $\R$ whose Fourier transform vanishes outside a bounded interval of frequencies $[-B, B]$. Such functions are very rigid: by the Paley–Wiener theorem they extend to entire functions, so they are determined by their values on any interval. They can be recovered from samples taken at a rate of $2B$ per unit time. This is the content of the sampling theorem. See the definition.