  Context: The technique of disentangling has been applied to numerous
high-precision studies of spectroscopic binaries and multiple stars. Although,
its possibilities have not yet been fully understood and exploited. Aims:
Theoretical background aspects of the method, its latest improvements and hints
for its use in practice are explained in this series of papers. Methods: In
this first paper of the series, we discuss spectral-resolution limitations due
to a discrete representation of the observed spectra and introduce a new method
how to achieve a precision higher than the step of input-data binning. Results:
Based on this principle, the latest version of the KOREL code for Fourier
disentangling achieves an increase in precision for an order of magnitude.
