Period mapping - Revision history

128.197.60.207: /* Local polarized period mappings */ Spelling fix

2014-03-03T18:56:14Z

Local polarized period mappings: Spelling fix

← Older revision		Revision as of 20:56, 3 March 2014
Line 1:		Line 1:
	~~[[File:Alpha Max Beta Min approximation.png\|800px\|centre]]~~		Irwin Butts is what my wife enjoys to contact me although I don't truly like becoming called like that. For a whilst I've been in South Dakota and my mothers and fathers live close by. For years he's been operating as a receptionist. To gather cash is a thing that I'm totally addicted to.<br><br>My web-site :: home std test kit ([http://www.animecontent.com/blog/436250 click here to read])

	~~The '''alpha max plus beta min algorithm''' is a high-speed approximation of the [[square root]] of the sum of two squares. That~~ is to ~~say, it gives the approximate absolute magnitude of a [[vector (geometric)\|vector]] given the [[Real number\|real]] and [[Imaginary number\|imaginary]] parts.~~

	~~:<math> \|V\| = \sqrt{~~ I~~^2 + Q^2 } </math>~~

	~~The algorithm avoids the necessity of performing the square and square-root operations and instead uses simple operations such as comparison, multiplication and addition~~. ~~Some choices of the α and β parameters of the algorithm allow the multiplication operation to be reduced to~~ a ~~simple shift of binary digits that is particularly well suited to implementation~~ in ~~high-speed digital circuitry.~~

	~~The approximation is expressed as:~~

	~~:<math> \|V\| = \alpha\,\! \mathbf{Max} + \beta\,\! \mathbf{Min} </math>~~

	~~Where <math>\mathbf{Max}</math> is the maximum absolute value of I~~ and Q and ~~<math>\mathbf{Min}</math> is the minimum absolute value of I and Q~~.

	For ~~the closest approximation, the optimum values for <math>\alpha\,\!</math> and <math>\beta\,\!</math> are <math>\alpha_0 = \frac{2 \cos \frac{\pi}{8}}{1 + \cos \frac{\pi}{8}} = 0~~.~~96043387...</math> and <math>\beta_0 = \frac{2 \sin \frac{\pi}{8}}{1 + \cos \frac{\pi}{8}} = 0.39782473...</math>, giving~~ a ~~maximum error of 3.96%~~.

	~~{\| class="wikitable"~~
	\|-
	! <~~math~~>~~\alpha\,\!</math> \|\| <math>\beta\,\!</math> \|\| Largest error (%) \|\| Mean error (%)~~<br />
	\|-
	~~\| align="right" \| 1/1 \|\| align="right" \| 1/2 \|\| align="right" \| 11.80 \|\| align="right" \| 8.68~~
	\|-
	~~\| align="right" \| 1/1 \|\| align="right" \| 1/4 \|\| align="right" \| 11.61 \|\| align="right" \| 0.65~~
	\|-
	~~\| align="right" \| 1/1 \|\| align="right" \| 3/8 \|\| align="right" \| 6.80 \|\| align="right" \| 4.01~~
	\|-
	~~\| align="right" \| 7/8 \|\| align="right" \| 7/16 \|\| align="right" \| 12.5 \|\| align="right" \| 4.91~~
	\|-
	~~\| align="right" \| 15/16 \|\| align="right" \| 15/32 \|\| align="right" \| 6.25 \|\| align="right" \| 1.88~~
	\|-
	~~\| align="right" \| <math>\alpha_0</math> \|\| align="right" \| <math>\beta_0</math> \|\| align="right" \| 3.96 \|\| align="right" \| 1.30~~
	\|-
	\|}

	~~==References==~~

	*[[Richard Lyons\|Lyons, Richard G]]. ''Understanding Digital Signal Processing, section 13.2.'' Prentice Hall, 2004 ISBN 0-13-108989-7.
	* Griffin, Grant. [http://www.~~dspguru~~.com/~~dsp~~/~~tricks/magnitude-estimator DSP Trick: Magnitude Estimator].~~

	~~[[Category:Approximation algorithms]]~~
	~~[[Category:Root-finding algorithms]~~]

en>Enyokoyama: /* Local polarized period mappings */ add a link bilinear form

2013-11-15T10:12:31Z

Local polarized period mappings: add a link bilinear form

← Older revision		Revision as of 12:12, 15 November 2013
Line 1:		Line 1:
	~~Greetings!~~ I ~~am Marvella~~ and ~~I really feel comfortable when people use~~ the ~~complete title~~. The ~~factor she adores most~~ is ~~physique building~~ and ~~now she~~ is ~~trying to earn money with it~~. ~~California is our beginning place~~. ~~In her expert lifestyle she is~~ a ~~payroll clerk but she's always wanted her personal business~~.<br><br>~~My webpage; std testing at home~~ [[http://~~Xn--299Ay03byycca57h~~.kr/~~zbxe~~/~~?document_srl=319947 click the up coming web site~~]]		[[File:Alpha Max Beta Min approximation.png\|800px\|centre]]

			The '''alpha max plus beta min algorithm''' is a high-speed approximation of the [[square root]] of the sum of two squares. That is to say, it gives the approximate absolute magnitude of a [[vector (geometric)\|vector]] given the [[Real number\|real]] and [[Imaginary number\|imaginary]] parts.

			:<math> \|V\| = \sqrt{ I^2 + Q^2 } </math>

			The algorithm avoids the necessity of performing the square and square-root operations and instead uses simple operations such as comparison, multiplication and addition. Some choices of the α and β parameters of the algorithm allow the multiplication operation to be reduced to a simple shift of binary digits that is particularly well suited to implementation in high-speed digital circuitry.

			The approximation is expressed as:

			:<math> \|V\| = \alpha\,\! \mathbf{Max} + \beta\,\! \mathbf{Min} </math>

			Where <math>\mathbf{Max}</math> is the maximum absolute value of I and Q and <math>\mathbf{Min}</math> is the minimum absolute value of I and Q.

			For the closest approximation, the optimum values for <math>\alpha\,\!</math> and <math>\beta\,\!</math> are <math>\alpha_0 = \frac{2 \cos \frac{\pi}{8}}{1 + \cos \frac{\pi}{8}} = 0.96043387...</math> and <math>\beta_0 = \frac{2 \sin \frac{\pi}{8}}{1 + \cos \frac{\pi}{8}} = 0.39782473...</math>, giving a maximum error of 3.96%.

			{\| class="wikitable"
			\|-
			! <math>\alpha\,\!</math> \|\| <math>\beta\,\!</math> \|\| Largest error (%) \|\| Mean error (%)<br />
			\|-
			\| align="right" \| 1/1 \|\| align="right" \| 1/2 \|\| align="right" \| 11.80 \|\| align="right" \| 8.68
			\|-
			\| align="right" \| 1/1 \|\| align="right" \| 1/4 \|\| align="right" \| 11.61 \|\| align="right" \| 0.65
			\|-
			\| align="right" \| 1/1 \|\| align="right" \| 3/8 \|\| align="right" \| 6.80 \|\| align="right" \| 4.01
			\|-
			\| align="right" \| 7/8 \|\| align="right" \| 7/16 \|\| align="right" \| 12.5 \|\| align="right" \| 4.91
			\|-
			\| align="right" \| 15/16 \|\| align="right" \| 15/32 \|\| align="right" \| 6.25 \|\| align="right" \| 1.88
			\|-
			\| align="right" \| <math>\alpha_0</math> \|\| align="right" \| <math>\beta_0</math> \|\| align="right" \| 3.96 \|\| align="right" \| 1.30
			\|-
			\|}

			==References==

			*[[Richard Lyons\|Lyons, Richard G]]. ''Understanding Digital Signal Processing, section 13.2.'' Prentice Hall, 2004 ISBN 0-13-108989-7.
			* Griffin, Grant. [http://www.dspguru.com/dsp/tricks/magnitude-estimator DSP Trick: Magnitude Estimator].

			[[Category:Approximation algorithms]]
			[[Category:Root-finding algorithms]]

198.102.153.1: simplify nowrap

2012-08-20T21:25:16Z

simplify nowrap

New page

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