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en>BG19bot: WP:CHECKWIKI error fix for #61. Punctuation goes before References. Do general fixes if a problem exists. - using AWB (9916)

2014-02-06T18:50:30Z

WP:CHECKWIKI error fix for #61. Punctuation goes before References. Do general fixes if a problem exists. - using AWB (9916)

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	In [[mathematics]], the '''Bussgang theorem''' is a [[theorem]] of [[Stochastic process\|stochastic analysis]]. The theorem states that the crosscorrelation of a Gaussian signal before and after it has passed through a nonlinear operation are equal up to a constant. It was first published by Julian J. Bussgang in 1952 while he was at the [[Massachusetts Institute of Technology]].<ref>J.J. Bussgang,"Cross-correlation function of amplitude-distorted Gaussian signals", Res. Lab. Elec., Mas. Inst. Technol., Cambridge MA, Tech. Rep. 216, March 1952.</ref>

	~~==Statement of the theorem==~~

	~~Let <math> \left\{X(t)\right\} </math> be~~ a ~~zero-mean stationary [[Gaussian process\|Gaussian random process]]~~ and ~~<math> \left \{ Y(t) \right\} = g(X(t)) </math> where <math> g(\cdot) </math>~~ is a ~~nonlinear amplitude distortion~~.		It is a known fact that most creams and lotions contain harmful chemicals. We also use Sojourn Haircare which is toxin and gluten-free. Sylvia - Mucek CEO of THE VANITY BAG wants to have for you all the essential things you need when it comes in taking care for your beauty. The products are available at competitive prices in the market. Consume a lot of foods grown from the ground, vegetables, entire grains and lean proteins. <br><br>There are items developed for all different needs and all different hair types. Finally, your mood will soar when you get a glimpse of your gorgeous new look, sculpted by our visionary and experienced NAKe - D Hair Artistic Team. When you mix your own ingredients, it eliminates the guessing game about what exactly you are putting on your skin. Once you're finished using your spray for the day store it in the fridge so it won't spoil. Be it hair care, message, manicure and pedicure or any other beauty care products, the salon brands are available for all. <br><br>Basicare, at our marketplace, is all ready with its makeup items and self grooming kits to make you - a better you. There are several benefits to engage professional cleaning service to take care of your home hygiene. In general it is important to stay away from products that irritate or cause your skin to breakout. To be sure your precious get ready time goes smoothly, assign a separate hairstylist for your wedding party to ensure the bride gets undivided attention by her beauty professional. There are products for both men and women and are of various forms. <br><br>If you're not sure about a particular essential oil, check with a reliable resource. If all else fails, or nothing is available to you, use plain soap and water, but do not skip removing your makeup. If you liked this article and you would like to obtain additional data with regards to [https://tackk.com/3mpgb9 LD Hardas] kindly stop by the website. It was mentioned that these fragrances are generally being added to help the products to sell better, and there is some truth in this. The onesta hair products also act as finest hair product to improve the look of hair and come under the category of one of the most popular hair products. Cheap beauty products The online facility of buying and learning makeup has revolutionized the whole cosmetic industry. <br><br>Organic health and beauty products are definitely making a mark and increasing in popularity all over. This could be anything from soap to shower gel, deodorant, make-up and even moisturizers, cleanser and toner. They truly make a difference in everyday living and they are improving year by year. Do you feel that that your hair has taken the brunt of your everyday stress. Having a beautiful appearance can be significantly enhanced by using different types of beauty products.

	If <~~math~~> ~~R_X(\tau)~~ <~~/math~~> ~~is the [[autocorrelation function]]~~ of ~~<math> \left\{ X(t) \right\}</math>~~, ~~then~~ the ~~[[cross-correlation function]] of <math> \left\{ X(~~t~~) \right\}</math>~~ and <~~math~~> ~~\left\{ Y(t) \right\}~~<~~/math~~> is

	~~:<math> R_{XY}(\tau) = CR_X(\tau)~~, ~~</math>~~
	~~where <math>C</math>~~ is a ~~constant~~ that ~~depends only on <math> g(\cdot) </math>~~.

	~~It can~~ be ~~further shown that~~

	: <~~math~~> ~~C = \frac{1}{\sigma^3\sqrt{2\pi}}\int_{-\infty}^\infty ug(u)e^{-\frac{u^2}{2\sigma^2}} \, du.~~ <~~/math~~>

	~~==Application==~~
	~~This theorem implies that~~ a ~~simplified correlator can be designed~~.~~{{clarify\|reason=compared~~ to ~~what?\|date=December 2010}} Instead of having to multiply two signals~~, ~~the cross-correlation problem reduces~~ to ~~the gating{{clarify\|reason=undefined\|date=December 2010}} of one signal~~ with ~~another.{{citation needed\|date=December 2010}}~~

	~~==References==~~
	~~{{reflist}}~~

	~~==Further reading==~~
	* E.W. Bai; V. Cerone; D. Regruto (2007) [~~http~~://~~diegoregruto~~.com/~~P14~~.~~pdf "Separable inputs for~~ the ~~identification~~ of ~~block-oriented nonlinear systems"], ''Proceedings~~ of the ~~2007 American Control Conference'' (New York City~~, ~~July 11–13~~, ~~2007) 1548–1553~~

	~~{{DEFAULTSORT:Bussgang Theorem}}~~
	~~[[Category:Probability theorems]]~~
	~~[[Category:Stochastic processes]]~~

128.61.64.150 at 02:45, 10 April 2013

2013-04-10T02:45:59Z

← Older revision		Revision as of 04:45, 10 April 2013
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	~~Good day~~, ~~my name~~ is ~~Marielle but you can simply call me just about anything you like~~. ~~To design railways is~~ the ~~only hobby my spouse isn'~~t ~~going to~~ [~~http:~~//~~data~~.~~gov.uk~~/~~data~~/~~search?q=approve approve~~] of~~. Maryland~~ is ~~wherever our dwelling~~ is~~. Due to the fact I was eighteen I've been working as~~ a ~~inventory manage and get filler. I've been working~~ on ~~my website for some time now~~. ~~Check it out here~~: ~~http://khowallpaper.com/profile/inlindrum~~<br><br>~~Review my website~~ ... [http://~~khowallpaper~~.com/~~profile/inlindrum Oakley liv sunglasses~~]		In [[mathematics]], the '''Bussgang theorem''' is a [[theorem]] of [[Stochastic process\|stochastic analysis]]. The theorem states that the crosscorrelation of a Gaussian signal before and after it has passed through a nonlinear operation are equal up to a constant. It was first published by Julian J. Bussgang in 1952 while he was at the [[Massachusetts Institute of Technology]].<ref>J.J. Bussgang,"Cross-correlation function of amplitude-distorted Gaussian signals", Res. Lab. Elec., Mas. Inst. Technol., Cambridge MA, Tech. Rep. 216, March 1952.</ref>

			==Statement of the theorem==

			Let <math> \left\{X(t)\right\} </math> be a zero-mean stationary [[Gaussian process\|Gaussian random process]] and <math> \left \{ Y(t) \right\} = g(X(t)) </math> where <math> g(\cdot) </math> is a nonlinear amplitude distortion.

			If <math> R_X(\tau) </math> is the [[autocorrelation function]] of <math> \left\{ X(t) \right\}</math>, then the [[cross-correlation function]] of <math> \left\{ X(t) \right\}</math> and <math> \left\{ Y(t) \right\}</math> is

			:<math> R_{XY}(\tau) = CR_X(\tau), </math>
			where <math>C</math> is a constant that depends only on <math> g(\cdot) </math>.

			It can be further shown that

			: <math> C = \frac{1}{\sigma^3\sqrt{2\pi}}\int_{-\infty}^\infty ug(u)e^{-\frac{u^2}{2\sigma^2}} \, du. </math>

			==Application==
			This theorem implies that a simplified correlator can be designed.{{clarify\|reason=compared to what?\|date=December 2010}} Instead of having to multiply two signals, the cross-correlation problem reduces to the gating{{clarify\|reason=undefined\|date=December 2010}} of one signal with another.{{citation needed\|date=December 2010}}

			==References==
			{{reflist}}

			==Further reading==
			* E.W. Bai; V. Cerone; D. Regruto (2007) [http://diegoregruto.com/P14.pdf "Separable inputs for the identification of block-oriented nonlinear systems"], ''Proceedings of the 2007 American Control Conference'' (New York City, July 11–13, 2007) 1548–1553

			{{DEFAULTSORT:Bussgang Theorem}}
			[[Category:Probability theorems]]
			[[Category:Stochastic processes]]

128.227.181.142: /* Overview */

2012-08-22T19:23:45Z

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