Cross-correlation techniques have been used since 1974 and, since 1979, the analysis based on the Fourier Method has been applied. However, we are currently obtaining data with spectral resolution higher than those for which this technique was developed, hence some revision seems timely. The principal aim of this work is to adapt Tonry and Davis' method and implementing it for the treatment of very high spectral resolution data. We have applied this technique to two different sets of spectroscopic data of moderate and high resolutions obtained with the MUSE and MEGARA spectrographs respectively. Using stellar spectra obtained with these two instruments (i) we have optimised the input parameters; (ii) we have analysed the method assumptions; and (iii) we have compared the results for the two sets of data. The optimal method parameters applied to MUSE data are 3, 60 and 512 bins, which correspond to a uniform velocity shift value of v = 27.1 km/s. For MEGARA data, we propose the values 3, 350 and 4096 bins finding that the cross-correlation function lost its Gaussian behavior at higher resolutions. Thus, we have developed an equivalent mathematical method that can be used for this kind of data. Additionally, the velocity dispersion error analysis suggests that the greatest error introduced in this method is due to the subtraction or masking of the nebular lines. For the application cross-correlation techniques to high spectral resolution data, we propose to calculate the galaxy-galaxy and star-galaxy correlations, with widths and respectively. Then, the width of the broadening function can be calculated as .