Discrete weighted transform
Encyclopedia
In mathematics
, the discrete weighted transform (DWT) is a variation on the discrete Fourier transform
over arbitrary fields
involving weighting
the input before transforming it.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, the discrete weighted transform (DWT) is a variation on the discrete Fourier transform
Discrete Fourier transform (general)
This article is about the discrete Fourier transform over any field , commonly called a number-theoretic transform in the case of finite fields...
over arbitrary fields
Field (mathematics)
In abstract algebra, a field is a commutative ring whose nonzero elements form a group under multiplication. As such it is an algebraic structure with notions of addition, subtraction, multiplication, and division, satisfying certain axioms...
involving weighting
Weight function
A weight function is a mathematical device used when performing a sum, integral, or average in order to give some elements more "weight" or influence on the result than other elements in the same set. They occur frequently in statistics and analysis, and are closely related to the concept of a...
the input before transforming it.