= Wigner distribution
{c}
{title2=$W[u,v](\mathbf z,\mathbf p)$}
= Wigner transform
{c}
{synonym}
The <Wigner distribution> of two fields is the <Fourier transform> of a field's two-point product in its separation variable:
$$
W[u,v](\mathbf z,\mathbf p)=(2\pi)^{-d}\int e^{-i\mathbf p\cdot\mathbf s}u(\mathbf z+\mathbf s/2)\overline{v(\mathbf z-\mathbf s/2)}\,d\mathbf s.
$$
Its inverse reconstructs $u(\mathbf z)\overline{v(\mathbf z')}$. For vector fields, specify whether the product is an outer product or a scalar contraction; the latter can encode an average over receiver channels.
Back to article page
