The signal to noise ratio in hyperfine spectra split by nuclear quadru
pole interactions can be improved significantly by cross correlating e
xperimental with theoretical spectra, especially for higher spins. In
part I of the paper we present all technical details of this new appro
ach and give examples for half integer and integer spins. In part II w
e elucidate the difficulties which arise in the attempt to reconstruct
distribution functions of the largest component of the electric held
gradient tensor V-ZZ and the asymmetry parameter eta from experimental
line positions and profiles.