Mathematical Definition
The definition of the cone-shape distribution function is shown as follows:
where
and the kernel function is
The kernel function in domain is defined as:
Following are the magnitude distribution of the kernel function in domain.
Following are the magnitude distribution of the kernel function in domain with different values.
As we can see from the figure above, a properly chosen kernel of cone-shape distribution function can filter out the interference on the axis in the domain, or the ambiguity domain. Therefore, unlike the Choi-Williams distribution function, the cone-shape distribution function can effectively reduce the cross-term results form two component with same center frequency. However, the cross-terms on the axis are still preserved.
Read more about this topic: Cone-shape Distribution Function
Famous quotes containing the words mathematical and/or definition:
“The circumstances of human society are too complicated to be submitted to the rigour of mathematical calculation.”
—Marquis De Custine (1790–1857)
“I’m beginning to think that the proper definition of “Man” is “an animal that writes letters.””
—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)