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Wigner distribution function
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<p>The Wigner distribution function (WDF) is used in <a href="/facts/Signal_processing/Npaja6zb">signal processing</a> as a transform in <a href="/facts/Time-frequency_analysis/oeysrIKN">time-frequency analysis</a>. </p><p>The WDF was first proposed in physics to account for quantum corrections to classical statistical mechanics in 1932 by <a href="/facts/Eugene_Wigner/HvWgw4KX">Eugene Wigner</a>, and it is of importance in <a href="/facts/Phase_space_formulation/ogvtdMNs">quantum mechanics in phase space</a> (see, by way of comparison: <i><a href="/facts/Wigner_quasi-probability_distribution/5tyVfdFF">Wigner quasi-probability distribution</a></i>, also called the <i>Wigner function</i> or the <i>Wigner–Ville distribution</i>). </p><p>Given the shared algebraic structure between position-momentum and time-frequency <a href="/facts/Conjugate_variables/NQca4AKf">conjugate pairs</a>, it also usefully serves in signal processing, as a transform in time-frequency analysis, the subject of this article. Compared to a <a href="/facts/Short-time_Fourier_transform/XHo1t2m6">short-time Fourier transform</a>, such as the <a href="/facts/Gabor_transform/dbbHrA1l">Gabor transform</a>, the Wigner distribution function provides the highest possible temporal vs frequency resolution which is mathematically possible within the limitations of the uncertainty principle. The downside is the introduction of large cross terms between every pair of signal components and between positive and negative frequencies, which makes the original formulation of the function a poor fit for most analysis applications. Subsequent modifications have been proposed which preserve the sharpness of the Wigner distribution function but largely suppress cross terms. </p>