  Optimal sampling of non band-limited functions is an issue of great
importance that has attracted considerable attention. We propose to tackle this
problem through the use of a frequency warping: First, by a nonlinear shrinking
of frequencies, the function is transformed into a band-limited one. One may
then perform a decomposition in Fourier series. This process gives rise to new
orthonormal bases of the Sobolev spaces H^alpha. When alpha is an integer,
these orthonormal bases can be expressed in terms of Laguerre functions. We
study the reconstruction and speed of convergence properties of the
warping-based sampling. Besides theoretical considerations, numerical
experiments are performed.
