Wikipedia:Reference desk/Archives/Mathematics/2013 March 9
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March 9
editExamples of convolution
editI saw the wiki page, but I couldn't find any examples using actual numbers evaluating the formula. Could you give some examples of convolution, please? Mathijs Krijzer (talk) 22:41, 9 March 2013 (UTC)
Quoted content from our article on Convolution
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DefinitioneditThe convolution of f and g is written f∗g, using an asterisk or star. It is defined as the integral of the product of the two functions after one is reversed and shifted. As such, it is a particular kind of integral transform: Domain of definitioneditThe convolution of two complex-valued functions on Rd is well-defined only if f and g decay sufficiently rapidly at infinity in order for the integral to exist. Conditions for the existence of the convolution may be tricky, since a blow-up in g at infinity can be easily offset by sufficiently rapid decay in f. The question of existence thus may involve different conditions on f and g. Circular discrete convolutioneditWhen a function gN is periodic, with period N, then for functions, f, such that f∗gN exists, the convolution is also periodic and identical to: Circular convolutioneditWhen a function gT is periodic, with period T, then for functions, f, such that f∗gT exists, the convolution is also periodic and identical to: where to is an arbitrary choice. The summation is called a periodic summation of the function f. Discrete convolutioneditFor complex-valued functions f, g defined on the set Z of integers, the discrete convolution of f and g is given by: When multiplying two polynomials, the coefficients of the product are given by the convolution of the original coefficient sequences, extended with zeros where necessary to avoid undefined terms; this is known as the Cauchy product of the coefficients of the two polynomials. |
- A convolution maps 2 functions to a third function, it does not map numbers to anything or anything to numbers, so unless you are going to point wise define a function in terms of numbers, I can't show you anything "using actual numbers". — Preceding unsigned comment added by 123.136.64.14 (talk) 05:39, 12 March 2013 (UTC)