User talk:Mojodaddy

Category changes
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)

Hi dats grt —Preceding unsigned comment added by 203.115.12.114 (talk) 11:24, 1 September 2010 (UTC)

Your recent edits
Hi there. In case you didn't know, when you add content to talk pages and Wikipedia pages that have open discussion, you should sign your posts by typing four tildes ( &#126;&#126;&#126;&#126; ) at the end of your comment. If you can't type the tilde character, you should click on the signature button located above the edit window. This will automatically insert a signature with your name and the time you posted the comment. This information is useful because other editors will be able to tell who said what, and when. Thank you! --SineBot (talk) 06:48, 19 January 2009 (UTC)

Hello! there still are some issues that may need to be clarified. Please review the comment(s) underneath and respond there as soon as possible.

A complement for your effort...
...on creating template:channel access methods! Mange01 (talk) 23:33, 12 February 2009 (UTC)

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)

Definition
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:




 * $$(f * g )(t)\ \ \,$$
 * $$\stackrel{\mathrm{def}}{=}\ \int_{-\infty}^\infty f(\tau)\, g(t - \tau)\, d\tau$$
 * $$= \int_{-\infty}^\infty f(t-\tau)\, g(\tau)\, d\tau.$$      (commutativity)
 * }
 * $$= \int_{-\infty}^\infty f(t-\tau)\, g(\tau)\, d\tau.$$      (commutativity)
 * }

Domain of definition
The convolution of two complex-valued functions on Rd
 * $$(f*g)(x) = \int_{\mathbf{R}^d}f(y)g(x-y)\,dy$$

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:


 * $$(f * g_N)[n] \equiv \sum_{m=0}^{N-1} \left(\sum_{k=-\infty}^\infty {f}[m+kN] \right) g_N[n-m].\,$$

Circular convolution
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:


 * $$(f * g_T)(t) \equiv \int_{t_0}^{t_0+T} \left[\sum_{k=-\infty}^\infty f(\tau + kT)\right] g_T(t - \tau)\, d\tau,$$

where to is an arbitrary choice. The summation is called a periodic summation of the function f.

Discrete convolution
For complex-valued functions f, g defined on the set Z of integers, the discrete convolution of f and g is given by:


 * $$(f * g)[n]\ \stackrel{\mathrm{def}}{=}\ \sum_{m=-\infty}^\infty f[m]\, g[n - m]$$
 * $$= \sum_{m=-\infty}^\infty f[n-m]\, g[m].$$      (commutativity)

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.

ArbCom elections are now open!
MediaWiki message delivery (talk) 16:22, 23 November 2015 (UTC)