Smoothing kernel ↩

Metadata 
aliases: [Smoothing function, Smoothing kernel function]
shorthands: {}
created: 2022-04-24 23:02:34
modified: 2022-04-24 23:18:32

The smoothing kernel or smoothing function is used in the kernel approximation of functions and it defines the characteristics of the approximation. It is usually chosen to be an even function.

It has to satisfy three conditions:

  1. The normalization condition (or unity condition):

  1. The Delta function property:

    Where is the Dirac delta function.

  2. The compact condition (pretty much that has to have compact support):

Where is a constant related to the smoothing function in question and defines the effective area of the smoothing function (support domain) the integration domain can be the same as the support domain