related topics
{math, number, function}
{math, energy, light}
{system, computer, user}
{rate, high, increase}

In mathematics and, in particular, functional analysis, convolution is a mathematical operation on two functions f and g, producing a third function that is typically viewed as a modified version of one of the original functions. Convolution is similar to cross-correlation. It has applications that include statistics, computer vision, image and signal processing, electrical engineering, and differential equations.

The convolution can be defined for functions on groups other than Euclidean space. In particular, the circular convolution can be defined for periodic functions (that is, functions on the circle), and the discrete convolution can be defined for functions on the set of integers. These generalizations of the convolution have applications in the field of numerical analysis and numerical linear algebra, and in the design and implementation of finite impulse response filters in signal processing.

Computing the inverse of the convolution operation is known as deconvolution.


Full article ▸

related documents
Continuous function
Primitive recursive function
Euler's formula
Dual space
Hyperreal number
Fundamental theorem of algebra
Basis (linear algebra)
Fundamental group
BCH code
Computable number
Ackermann function
Multivariate normal distribution
Bessel function
Dynamic programming
Prime number theorem
Halting problem
Group action
Fermat number
Abelian group
Probability theory
Lp space
Monte Carlo method
Subset sum problem
Frame problem
Truth table
Uniform space
Taylor series