Cone-shape distribution function
Overview
 
In mathematics, cone-shape distribution function is one of the members of Cohen's class distribution function
Cohen's class distribution function
Bilinear time–frequency distributions, or quadratic time–frequency distributions, arise in a sub-field field of signal analysis and signal processing called time–frequency signal processing, and, in the statistical analysis of time series data...

. It was first proposed by Yunxin Zhao, Lee. E. Atlas, and Robert J. Marks in 1990. The reason why this distribution is so named is because its kernel function in domain looks like two cones. The advantage of this special kernel function is that it can completely remove the cross-term between two components that have same center frequency, but on the other hand, the cross-term results form components with the same time center can not be removed by the cone-shape kernel.
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.
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