  The pulsations of X-ray pulsars carry information about the accretion and
magnetic field geometry. Here we present a study and classification of energy
resolved pulse profiles of a sample of X-ray pulsars, focusing on high-mass
X-ray binaries. Our goal is to perform a classification of X-ray pulsars based
on their observed pulse profiles and look for correlations between this
classification and their principle physical observables. The analysis pipeline
is available online. We analysed the pulse profiles of a sample of X-ray
pulsars using data obtained with the XMM-Newton and NuSTAR. We fit the energy
resolved pulse profiles with a Fourier series of up to five harmonics. We
investigate relationships between the pulse profile properties and other
observables of the systems (e.g., orbital period, magnetic field strength, and
luminosity) to study the extreme physics of these systems. The sources were
divided into three groups by a classification based on the shape, the dominance
of the fitted Fourier harmonics and their respective evolution with energy. We
do not find a conclusive correlation between the pulse profile shapes or groups
and other parameters of the systems. However, a weak trend was found when
comparing our classification to the sources' location in the spin
period-orbital period diagram. Further studies are required to confirm this
trend. Despite the large variety of pulse profiles of the X-ray pulsars, we
found that with our approach clear categories emerge which we use to classify
their behavior as function of energy. As we do not find a clear relationship
between our classification scheme and other parameters we conclude that X-ray
pulse profiles are influenced by other hidden variables.
