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Aliasing is a general problem in the analysis ofany measurements that make sampling at discrete points.Sampling in the spatial domain resultsin a periodic pattern of spectra in the wave vector domain.This effect is called spatial aliasing, and it isof particular importance for multi-spacecraft measurements in space.We first present the theoretical background of aliasing problemsin the frequency domain and generalize it tothe wave vector domain, and then presentmodel calculations of spatial aliasing.The model calculations are performed for various configurationsof the reciprocal vectors and energy spectra or distributionthat are placed at different positions in the wave vector domain,and exhibit two effects on aliasing.One is weak aliasing, in which the true spectrumis distorted because of non-uniform aliasing contributionsin the Brillouin zone. It is demonstrated that the energy distributionbecomes elongated in the shortest reciprocal lattice vectordirection in the wave vector domain. The other effectis strong aliasing, in which aliases have a significantcontribution in the Brillouin zone and the energy distributionshows a false peak.These results give a caveat in multi-spacecraft data analysisin that spectral anisotropy obtained by a measurement has in general two origins:(1) natural and physical origins like anisotropy imposedby a mean magnetic field or a flow direction; and (2) aliasingeffects that are imposed by the configuration of themeasurement array (or the set of reciprocal vectors).This manuscript also discusses a possible methodto estimate aliasing contributions in the Brillouin zonebased on the measured spectrum and to correct the spectra for aliasing

Spatial aliasing and distortion of energy distribution in the wave vector domain under multi-spacecraft measurements