### convolution

(type of product function of two functions)

A **convolution** is a type of product function of two functions
defined as:

(f*g)(t) means ∫ f(x)g(t-x) dx
(for x from -∞ to ∞)

f*g - the convolution of functions f and g.

One way to explain it is that it is the amount of overlap when
one function is shifted over another. The **Voigt function** is
a convolution of two functions (for two processes)
affecting spectral line shape (the Voigt profile).
Convolution appears to be basic to some optical applications
and gives a mathematical model for effects of blurring,
e.g., from aberration, and also the effect of detectors
on images. It models the affect of a function representing
the intensity of incoming light with another function
representing the distortion, and the mathematics of convolutions
spells out the possibility and means of reversing the distortion.

In observed processes or observation techniques involving implicit
convolution, a step in analysis may carrying out the inverse
mathematical process, **deconvolution**. Other than
"take a shot at it" guesses,
there are mathematical methods to assist the process,
which is one use of the Fourier transform.
In addition to spectrography, deconvolution
is used in parsing of observation data in interferometry
and aperture synthesis.

(*mathematics*)
http://en.wikipedia.org/wiki/Convolution

http://en.wikipedia.org/wiki/Deconvolution

http://www.rodenburg.org/theory/convolution_integral_22.html

http://www.ifa.hawaii.edu/users/jpw/classes/alma/lectures/imaging.pdf

**Referenced by:**

line shape function

Voigt profile

index