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Wigner distribution function of the sum of two Gaussian components consists of two auto terms and a cross term in between. Changing the relative phase between the components affects only the cross terms. The following are some examples that exhibit the cross-term feature of the Wigner distribution function.
The Wigner quasiprobability distribution (also called the Wigner function or the Wigner–Ville distribution, after Eugene Wigner and Jean-André Ville) is a quasiprobability distribution. It was introduced by Eugene Wigner in 1932 [1] to study quantum corrections to classical statistical mechanics.
A Modified Wigner distribution function is a variation of the Wigner distribution function (WD) with reduced or removed cross-terms. The Wigner distribution (WD) was first proposed for corrections to classical statistical mechanics in 1932 by Eugene Wigner. The Wigner distribution function, or Wigner–Ville distribution (WVD) for analytic ...
The kernel of the Wigner distribution function (WDF) is one. However, no particular significance should be attached to that, since it is possible to write the general form so that the kernel of any distribution is one, in which case the kernel of the Wigner distribution function (WDF) would be something else.
Wigner distribution or Wigner function may refer to: Wigner quasiprobability distribution (what is most commonly intended by term "Wigner function"): a quasiprobability distribution used in quantum physics, also known at the Wigner-Ville distribution; Wigner distribution function, used in signal processing, which is the time-frequency variant ...
The evolution equation for the Wigner function is then analogous to that of its classical limit, the Liouville equation of classical physics. In the limit of a vanishing Planck constant ℏ {\displaystyle \hbar } , W ( x , p , t ) {\displaystyle W(x,p,t)} reduces to the classical Liouville probability density function in phase space .
The Gabor transform, Gabor–Wigner distribution function, or Cohen's class distribution function may be better choices. The concept of signal decomposition relates to the need to separate one component from the others in a signal; this can be achieved through a filtering operation which require a filter design stage.
The resulting probability distribution is proportional to the absolute square of the amplitude, so then the above relativistic Breit–Wigner distribution for the probability density function. The form of this distribution is similar to the amplitude of the solution to the classical equation of motion for a driven harmonic oscillator damped and ...