= Spatial aliasing
{title2=$|k|<\pi/\Delta x$}
Ambiguity between spatial oscillations sampled on a grid. At positions $x_j=j\Delta x$, the factors $e^{ikx_j}$ 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.
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