Spatial aliasing ($|k|<\pi /\Delta x$)

Ambiguity between spatial oscillations sampled on a grid. At positions $x_j=j\Delta x$, the factors $e^{ik{x}_j}$ and $e^{i(k+2\pi m/\Delta x)x_j}$ agree for every integer $m$. Spatial wavenumbers outside $|k|<\pi /\Delta x$ therefore cannot be distinguished without additional assumptions. For a traveling event of temporal frequency $f$ and apparent speed $v_{\mathrm{app}}$, the associated criterion is $\Delta x<v_{\mathrm{app}}/(2f)$, with a margin for filtering. Temporal oversampling does not remove this spatial ambiguity.