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Encyclopedia > Convolution (computer science)
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In computer science, specifically formal languages, a convolution is defined as follows: Wikibooks Wikiversity has more about this subject: School of Computer Science Open Directory Project: Computer Science Downloadable Science and Computer Science books Collection of Computer Science Bibliographies Belief that title science in computer science is inappropriate Categories: Computer science ... In mathematics, logic and computer science, a formal language is a set of finite-length words (i. ...


Let ∑ be an alphabet, # a symbol not in ∑.


Let x1x2... x|x|, y1y2... y|y|, z1z2... z|z|, ... be n words over ∑*. Let ell denote the maximum length.


The convolution of these words is

(x_1,y_1,ldots)(x_2,y_2,ldots)ldots(x_ell,y_ell,ldots)

where for any index i > |w|, the wi is #. This is a new word in

((Sigmacup{# })^n)^*.

The convolution of x, y, z, ... is sometimes denoted conv( x, y, z, ...), or x ⋆ y ⋆ z ⋆ ...


Example

The convolution of and, fish, be is

(a,f,b)(n,i,e)(d,s,#)(#,h,#)
 * Nevermind if you could not understand the notations because nobody undertands those compact math "definitions" at all

This article incorporates material from convolution on PlanetMath, which is licensed under the GFDL. PlanetMath is a free, collaborative, online mathematics encyclopedia. ...


  Results from FactBites:
 
Convolution - Wikipedia, the free encyclopedia (723 words)
In mathematics and in particular, functional analysis, convolution is a mathematical operator which takes two functions f and g and produces a third function that in a sense represents the amount of overlap between f and a reversed and translated version of g.
An out-of-focus photograph is the convolution of the sharp image with the blur circle formed by the iris diaphragm.
In acoustics, an echo is the convolution of the original sound with a function representing the various objects that are reflecting it.
Computer Science (5453 words)
Courses: Computer Science 25; Mathematics 16, 20, 22; and one of Mathematics 38 or 88 or Computer Science 85 with approval of the Undergraduate Advisor.
This course provides an overview of computing and computer science, including such topics as the history of computers, computer applications, introductory concepts in digital electronics and computer architecture, computer languages, theory of computation, artificial intelligence, and the impact that computers have had on society and are likely to have in the future.
Prerequisite: Computer Science 18 and Computer Science 19.
  More results at FactBites »


 

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