Effective potential - Revision history

en>Monkbot: /* References */Task 3: Fix CS1 deprecated coauthor parameter errors

2014-05-07T20:38:18Z

References: Task 3: Fix CS1 deprecated coauthor parameter errors

← Older revision		Revision as of 22:38, 7 May 2014
Line 1:		Line 1:
	~~Myrtle Benny is how I'm called and I feel comfortable when individuals use the complete title. Puerto Rico is home std test exactly where he's been residing for many years and he home~~ [http://www.~~nytimes~~.com/~~ref/health/healthguide/esn~~-~~herpes~~-~~ess.html std test] kit will by no [http://www.associazioneitalianafotografi.it/community/gruppi/points~~-to-~~know~~-~~when~~-~~confronted~~-~~with-candidiasis~~/ over the counter std test] ~~means move~~. ~~For many years he's been operating as a receptionist~~. ~~One~~ of the ~~very best~~ issues ~~in the world for me~~ is ~~to do aerobics and I've been performing it for fairly~~ a ~~while.<br><br>My web page: std testing at [http://immbooks~~.~~com/blogs/post/44599 home std test kit], [http://www.escuelavirtual.registraduria.gov.co/user/view.php?id=140944&course=1 mouse click for source],~~		[http://www.hooddirectory.com/how-you-can-cure-an-unpleasant-yeast-infection/ over the counter std test] author is known as Irwin. My family members life in Minnesota and my family loves it. Body building is 1 of the issues I love most. He used to be unemployed but now he is a pc operator but his promotion by no means arrives.

24.84.50.111: Fixed syntax error

2014-02-10T06:55:22Z

Fixed syntax error

← Older revision		Revision as of 08:55, 10 February 2014
Line 1:		Line 1:
	~~{{notability\|date=February 2012}}~~		Myrtle Benny is how I'm called and I feel comfortable when individuals use the complete title. Puerto Rico is home std test exactly where he's been residing for many years and he home [http://www.nytimes.com/ref/health/healthguide/esn-herpes-ess.html std test] kit will by no [http://www.associazioneitalianafotografi.it/community/gruppi/points-to-know-when-confronted-with-candidiasis/ over the counter std test] means move. For many years he's been operating as a receptionist. One of the very best issues in the world for me is to do aerobics and I've been performing it for fairly a while.<br><br>My web page: std testing at [http://immbooks.com/blogs/post/44599 home std test kit], [http://www.escuelavirtual.registraduria.gov.co/user/view.php?id=140944&course=1 mouse click for source],

	~~The~~ ''~~'autocorrelation technique''' is a method~~ for ~~estimating the dominating frequency in a~~ [~~[Complex number\|complex]] signal, as well as its variance~~. ~~Specifically, it calculates the first two moments of the power spectrum, namely the mean and variance~~. ~~It is also known as the '''pulse~~-~~pair algorithm''' in [[radar]] theory~~.

	~~The algorithm is both computationally faster and significantly more accurate compared to the [[discrete Fourier transform\|Fourier transform~~]~~], since the resolution is not limited~~ by ~~the number of samples used.~~

	~~== Derivation ==~~
	~~The~~ [~~[autocorrelation]] of lag 1 can be expressed using the inverse Fourier transform of the power spectrum <math>S(\omega)<~~/~~math>:~~
	~~:<math> R(1) = \frac{1}{2\pi} \int_{-\pi}^{\pi} S(\omega) e^{i\,\omega\,1} d\omega~~. </~~math>~~
	~~If we model the power spectrum as a single frequency <math>S(\omega) \ \stackrel{\mathrm{def}}{=}\ \delta(\omega~~ - ~~\omega_0)</math>, this becomes:~~
	~~:<math> R(1) = \frac{1}{2\pi} \int_{~~-~~\pi}^{\pi} \delta(\omega~~ - ~~\omega_0) e^{i\,\omega} d\omega <~~/~~math>~~
	~~:<math> R(1) = \frac{1}{2\pi} e^{i\,\omega_0} </math>~~
	~~where it is apparent that~~ the ~~phase~~ of ~~<math>R(1)</math> equals~~ the ~~signal frequency.~~

	~~== Implementation ==~~
	~~The mean frequency~~ is ~~calculated based on the [[autocorrelation]] with lag one, evaluated over~~ a ~~signal consisting of N samples:~~
	:<~~math~~>~~\omega = \angle R_N(1) = \tan^{-1}\frac{im\{ R_N(1) \}}{re\{ R_N(1) \}}.~~ <~~/math~~>
	~~The spectral variance is calculated as follows~~:
	~~:<math>var\{ \omega \} = \frac{2}{N} \left( 1 - \frac{\|R_N(1)\|}{R_N(0)} \right). </math>~~

	~~== Applications ==~~
	* Estimation of blood velocity and turbulence in ''color flow imaging'' used in [[medical ultrasonography]].
	* Estimation of target velocity in [[pulse-doppler radar]]

	~~{{inline\|date=February 2012}}~~

	~~== External links ==~~
	* [http://~~ieeexplore~~.~~ieee.org~~/~~xpl~~/~~abs_free.jsp?arNumber=1054886 A covariance approach to spectral moment estimation~~], ~~Miller et al., IEEE Transactions on Information Theory. {{full\|date=November 2012}}~~
	* Doppler Radar Meteorological Observations [http://www.~~ofcm~~.gov/~~fmh11~~/~~fmh11partb/2005pdf/fmh-11B-2005~~.~~pdf Doppler Radar Theory].{{full\|date~~=~~November 2012}} Autocorrelation technique described on p.2-11~~
	* [http://server.oersted.dtu.dk/31655/documents/kasai_et_al_1985.pdf Real-Time Two-Dimensional Blood Flow Imaging Using an Autocorrelation Technique], ~~by Chihiro Kasai, Koroku Namekawa, Akira Koyano, and Ryozo Omoto, IEEE Transactions on sonics and ultrasonics, May 1985 {{full\|date=November 2012}}~~

	~~[[Category:Radar theory]]~~
	~~[[Category:Signal processing]]~~
	~~[[Category:Time series analysis]]~~

en>Anagogist: addling links, removing superfluous capitalisation, clarifying sentence structure

2013-04-24T11:52:05Z

addling links, removing superfluous capitalisation, clarifying sentence structure

← Older revision		Revision as of 13:52, 24 April 2013
Line 1:		Line 1:
	~~Nice to meet you~~, ~~I am Marvella Shryock~~. ~~North Dakota is exactly where me~~ and ~~my husband live~~. ~~My working day job~~ is ~~a meter reader. One of~~ the ~~very very best things~~ in ~~the world for me~~ is ~~to do aerobics~~ and ~~now I'm attempting~~ to ~~make cash with~~ it.<br><br>~~Have~~ a ~~look at my web~~-~~site~~ :: [http://~~riddlesandpoetry~~.~~com~~/?q=~~node~~/~~19209~~ http://~~riddlesandpoetry~~.~~com~~/]		{{notability\|date=February 2012}}

			The '''autocorrelation technique''' is a method for estimating the dominating frequency in a [[Complex number\|complex]] signal, as well as its variance. Specifically, it calculates the first two moments of the power spectrum, namely the mean and variance. It is also known as the '''pulse-pair algorithm''' in [[radar]] theory.

			The algorithm is both computationally faster and significantly more accurate compared to the [[discrete Fourier transform\|Fourier transform]], since the resolution is not limited by the number of samples used.

			== Derivation ==
			The [[autocorrelation]] of lag 1 can be expressed using the inverse Fourier transform of the power spectrum <math>S(\omega)</math>:
			:<math> R(1) = \frac{1}{2\pi} \int_{-\pi}^{\pi} S(\omega) e^{i\,\omega\,1} d\omega. </math>
			If we model the power spectrum as a single frequency <math>S(\omega) \ \stackrel{\mathrm{def}}{=}\ \delta(\omega - \omega_0)</math>, this becomes:
			:<math> R(1) = \frac{1}{2\pi} \int_{-\pi}^{\pi} \delta(\omega - \omega_0) e^{i\,\omega} d\omega </math>
			:<math> R(1) = \frac{1}{2\pi} e^{i\,\omega_0} </math>
			where it is apparent that the phase of <math>R(1)</math> equals the signal frequency.

			== Implementation ==
			The mean frequency is calculated based on the [[autocorrelation]] with lag one, evaluated over a signal consisting of N samples:
			:<math>\omega = \angle R_N(1) = \tan^{-1}\frac{im\{ R_N(1) \}}{re\{ R_N(1) \}}. </math>
			The spectral variance is calculated as follows:
			:<math>var\{ \omega \} = \frac{2}{N} \left( 1 - \frac{\|R_N(1)\|}{R_N(0)} \right). </math>

			== Applications ==
			* Estimation of blood velocity and turbulence in ''color flow imaging'' used in [[medical ultrasonography]].
			* Estimation of target velocity in [[pulse-doppler radar]]

			{{inline\|date=February 2012}}

			== External links ==
			* [http://ieeexplore.ieee.org/xpl/abs_free.jsp?arNumber=1054886 A covariance approach to spectral moment estimation], Miller et al., IEEE Transactions on Information Theory. {{full\|date=November 2012}}
			* Doppler Radar Meteorological Observations [http://www.ofcm.gov/fmh11/fmh11partb/2005pdf/fmh-11B-2005.pdf Doppler Radar Theory].{{full\|date=November 2012}} Autocorrelation technique described on p.2-11
			* [http://server.oersted.dtu.dk/31655/documents/kasai_et_al_1985.pdf Real-Time Two-Dimensional Blood Flow Imaging Using an Autocorrelation Technique], by Chihiro Kasai, Koroku Namekawa, Akira Koyano, and Ryozo Omoto, IEEE Transactions on sonics and ultrasonics, May 1985 {{full\|date=November 2012}}

			[[Category:Radar theory]]
			[[Category:Signal processing]]
			[[Category:Time series analysis]]

en>Citation bot 1: [Pu408]Add: issue. Tweak: title. Formatted dashes. You can use this bot yourself. Report bugs here.

2011-10-21T12:24:29Z

[Pu408]Add: issue. Tweak: title. Formatted dashes. You can use this bot yourself. Report bugs here.

New page

Nice to meet you, I am Marvella Shryock. North Dakota is exactly where me and my husband live. My working day job is a meter reader. One of the very very best things in the world for me is to do aerobics and now I'm attempting to make cash with it.<br><br>Have a look at my web-site :: [http://riddlesandpoetry.com/?q=node/19209 http://riddlesandpoetry.com/]