User talk:Mojodaddy

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Welcome[edit]

Hello, Mojodaddy! Welcome to Wikipedia! Thank you for your contributions to this free encyclopedia. If you decide that you need help, check out Getting Help below, ask me on my talk page, or place {{helpme}} on your talk page and ask your question there. Please remember to sign your name on talk pages by clicking Button sig.png or using four tildes (~~~~); this will automatically produce your name and the date. Finally, please do your best to always fill in the edit summary field. Below are some useful links to facilitate your involvement. Happy editing! Cheers, :) Dlohcierekim 13:07, 27 August 2007 (UTC)
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DYK for Bootstrapping node[edit]

Updated DYK query On 30 December, 2008, Did you know? was updated with a fact from the article Bootstrapping node, which you created or substantially expanded. If you know of another interesting fact from a recently created article, then please suggest it on the Did you know? talk page.

Dravecky (talk) 03:22, 30 December 2008 (UTC)

Category changes[edit]

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[edit]

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 ( ~~~~ ) at the end of your comment. If you can't type the tilde character, you should click on the signature button Button sig.png 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)

DYK nomination of Insert Subscriber Data[edit]

Symbol question.svg Hello! Your submission of Insert Subscriber Data at the Did You Know nominations page has been reviewed, and there still are some issues that may need to be clarified. Please review the comment(s) underneath your nomination's entry and respond there as soon as possible. Thank you for contributing to Did You Know! Shubinator (talk) 04:50, 20 January 2009 (UTC)

A complement for your effort...[edit]

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

Examples of convolution[edit]

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[edit]

The convolution of f and g is written fg, 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)

Domain of definition[edit]

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[edit]

When a function gN is periodic, with period N, then for functions, f, such that fgN 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[edit]

Main article: Circular convolution

When a function gT is periodic, with period T, then for functions, f, such that fgT 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[edit]

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.