In mathematics, an integral transform is any transform T of the following form:
The input of this transform is a function f, and the output is another function Tf. An integral transform is a particular kind of mathematical operator.
There are numerous useful integral transforms. Each is specified by a choice of the function K of two variables, the kernel function or nucleus of the transform.
Some kernels have an associated inverse kernel K−1(u, t) which (roughly speaking) yields an inverse transform:
A symmetric kernel is one that is unchanged when the two variables are permuted.
Read more about Integral Transform: Motivation, History, Importance of Orthogonality, Usage Example, Table of Transforms, Different Domains, General Theory
Famous quotes containing the words integral and/or transform:
“Make the most of your regrets; never smother your sorrow, but tend and cherish it till it come to have a separate and integral interest. To regret deeply is to live afresh.”
—Henry David Thoreau (1817–1862)
“The lullaby is the spell whereby the mother attempts to transform herself back from an ogre to a saint.”
—James Fenton (b. 1949)