  Resampling is an operation costly in calculation time and accuracy. It
regularizes irregular sampling, replacing N data by N periodic estimations.
This stage can be suppressed, using formulas built with incoming data and
completed by sequences of elements which influence decreases when the number of
data increases. Obviously, some spectral properties (for processes) and some
asymptotic properties (for the sampling sequence) have to be fulfilled. In this
paper, we explain that it is possible to elaborate a logical theory, starting
from the ordinary periodic sampling, and generalized by the PNS (Periodic
Nonuniform Sampling), to treat more general irregular samplings. The "baseband
spectrum" hypothesis linked to the "Nyquist bound" (or Shannon bound) is
generalized to spectra in a finite number of intervals, suited to the "Landau
condition".
