Cross Term Property
The Wigner distribution function is not a linear transform. A cross term ("time beats") occurs when there is more than one component in the input signal, analogous in time to frequency beats. In the ancestral physics Wigner quasi-probability distribution, this term has important and useful physics consequences, required for faithful expectation values. By contrast, the short-time Fourier transform does not have this feature. The following are some examples that exhibit the cross-term feature of the Wigner distribution function.
In order to reduce the cross term problem, many other transforms have been proposed, including the modified Wigner distribution function, the Gabor–Wigner transform, and Cohen’s class distribution.
Read more about this topic: Wigner Distribution Function
Famous quotes containing the words cross, term and/or property:
“Life is a bridge. Cross over it, but build no house on it.”
—Indian proverb, quoted in Bruce Chatwin, The Songlines, ch. 30, “From the Notebooks” (1987)
“No—is a term very frequently employed by the fair, when they mean everything else but a negative. Their yes is always yes; but their no is not always no.”
—Anonymous, U.S. women’s magazine contributor. M, Weekly Visitor or Ladies Miscellany, p. 203 (April 1803)
“The property of rain is to wet and fire to burn.”
—William Shakespeare (1564–1616)