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Cross-correlation techniques have been used since 1974 and, since 1979, theanalysis based on the Fourier Method has been applied. However, we arecurrently obtaining data with spectral resolution higher than those for whichthis technique was developed, hence some revision seems timely. The principalaim of this work is to adapt Tonry and Davis' method and implementing it forthe treatment of very high spectral resolution data. We have applied thistechnique to two different sets of spectroscopic data of moderate and highresolutions obtained with the MUSE and MEGARA spectrographs respectively. Usingstellar spectra obtained with these two instruments (i) we have optimised theinput parameters; (ii) we have analysed the method assumptions; and (iii) wehave compared the results for the two sets of data. The optimal methodparameters applied to MUSE data are $k_{min}$ $\sim$ 3, $k_{max}$ $\sim$ 60 and512 bins, which correspond to a uniform velocity shift value of $\Delta $v =27.1 km/s. For MEGARA data, we propose the values $k_{min}$ $\sim$ 3, $k_{max}$$\sim$ 350 and 4096 bins finding that the cross-correlation function lost itsGaussian behavior at higher resolutions. Thus, we have developed an equivalentmathematical method that can be used for this kind of data. Additionally, thevelocity dispersion error analysis suggests that the greatest error introducedin this method is due to the subtraction or masking of the nebular lines. Forthe application cross-correlation techniques to high spectral resolution data,we propose to calculate the galaxy-galaxy and star-galaxy correlations, withwidths $\mu_{gg}$ and $\mu_{gt}$ respectively. Then, the width of thebroadening function can be calculated as $\sigma = \sqrt{\mu_{gg}^2 -\mu_{gt}^2}$.

Revising the cross correlation technique at high spectral resolution