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Why are you removing perfectly valid categories from articles? Merging to less specific categories is not acceptable. In at least one case, you have even removed the lead article from a category. If you are planning to empty these categories, take it to CfD first. If not, your actions would be consider vandalism. Vegaswikian (talk) 00:59, 19 January 2009 (UTC)
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A complement for your effort...
Examples of convolution
I 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) 22:13, 9 March 2013 (UTC)
The 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 definition
The 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 convolution
When 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:
When 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.
For 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.
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