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en>Monkbot: /* References */Task 5: Fix CS1 deprecated coauthor parameter errors

2014-07-23T22:25:09Z

References: Task 5: Fix CS1 deprecated coauthor parameter errors

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	In [~~[signal processing~~]~~], a ''~~'~~digital biquad filter''' is a second-order [[recursive filter\|recursive]] [[linear filter]], containing two [[Pole-zero_diagram\|poles]] and two [[Pole-zero_diagram\|zeros]]~~. ~~"Biquad" is an abbreviation of "''biquadratic''", which refers to the fact that in the~~ [~~[Z-transform\|Z domain]], its [[transfer function]] is the ratio of two [[quadratic function]]s~~:		[http://www.aaautowarranty.com/ Yoshiko] is her title but she doesn't like when people use her full name. Playing [http://boatshomefurnishings.com/Default.aspx?tabid=97&userId=18651 extended auto warranty] [http://Www.ct.gov/dmv/cwp/view.asp?a=799&q=245376 croquet] is some thing I will never give up. Managing individuals is how she makes cash and she will not change it whenever soon. [https://www.hyundaiusa.com/assurance/america-best-warranty.aspx Alabama] [http://wafclan.com/index.php?mod=users&action=view&id=8557 extended car warranty] has usually extended car warranty been his extended car warranty home.<br><br>Take a look at my web blog ... [http://Xn--h1aecfj6f.xn--p1ai/content/auto-repair-tips-youll-wish-youd-read-sooner http://Xn--h1aecfj6f.рф/content/auto-repair-tips-youll-wish-youd-read-sooner]

	~~:<math>\ H(z)=\frac{b_0+b_1z^{-1}+b_2z^{-2}} {1+a_1z^{-1}+a_2z^{-2} }<~~/~~math>~~

	~~High-order recursive filters can be highly sensitive to [[Quantization (signal processing)\|quantization]] of their coefficients, and can easily become [[BIBO stability\|unstable]]~~. This is much less of a problem with first and second-order filters; therefore, higher-order filters are typically implemented as serially-cascaded biquad sections (and a first-order filter if necessary). The two poles of the biquad filter must be inside the unit circle for it to be stable. In general, this is true for all filters i.e. all poles must be inside the unit circle for the filter to be stable.

	==~~Implementation==~~

	~~===Direct Form 1===~~
	~~The most straightforward implementation is the Direct Form 1, which has the following~~ [~~[difference equation]]~~:

	~~:<math>\ y[n] = b_0x[n] + b_1x[n-1] + b_2x[n-2] - a_1y[n-1] - a_2y[n-2] <~~/~~math>~~

	~~Here the <math>b_0<~~/~~math>, <math>b_1<~~/~~math> and <math>b_2</math> coefficients determine zeros, and <math>a_1<~~/~~math>, <math>a_2<~~/~~math> determine the position of the poles~~.

	~~Flow graph of biquad filter in Direct Form 1:~~

	~~[[File:Biquad filter DF-I.svg\|400px\|]]~~

	==~~=Direct Form 2===~~
	~~The Direct Form 1 implementation requires four delay registers. An equivalent circuit~~ is ~~the Direct Form 2 implementation, which requires only two delay registers:~~

	~~[[File:Biquad filter DF-II~~.~~svg\|400px\|]]~~

	~~The Direct Form 2 implementation~~ is ~~called the canonical form, because~~ it ~~uses the minimal amount of delays, adders and multipliers, yielding in the same transfer function as the Direct Form 1 implementation. The [[difference equation]]s for DF2 are:~~

	~~:<math>\ y[n]=b_0 w[n]+b_1 w[n-1]+b_2 w[n-2],</math>~~

	~~where~~

	~~:<math>\ w[n]=x[n]-a_1 w[n-1]-a_2 w[n-2]~~.~~</math>~~

	~~===Transposed direct forms===~~

	[~~[File:Biquad direct form 2 transposed .svg\|right\|thumb\|Transposed direct form biquadratic section]]~~

	~~See:~~ https://~~ccrma~~.~~stanford~~.~~edu~~/~~~jos~~/~~fp/Transposed_Direct_Forms~~.~~html~~

	~~==References==~~
	*[http://~~www.wiley~~.com/~~WileyCDA/WileyTitle/productCd-047003551X~~.~~html Sen M. Kuo, Bob H. Lee, Wenshun Tian: ''Real-Time Digital Signal Processing: Implementations and Applications, 2nd Edition'', Wiley~~ & ~~Sons Ltd, 2006 (E-book)~~]
	*[http://www.~~musicdsp~~.~~org/files/Audio-EQ-Cookbook~~.~~txt Cookbook formulae for audio EQ biquad filter coefficients]~~
	*[http://~~peabody~~.~~sapp.org~~/~~class~~/~~350.838/lab/biquad/ Biquad filter]~~
	*[http://~~ccrma~~.~~stanford.edu~~/~~~jos~~/~~filters/BiQuad_Section.html JOS BiQuad section]~~

	~~==See also==~~
	*[[Electronic_filter_topology#Biquad_filter\|Biquad filter]]
	*[[Digital filter]]

	~~[[Category:Linear filters]]~~
	~~[[Category:Audio engineering]]~~
	~~[[Category:Filter theory]~~]

en>Yobot: /* Properties */Reference before punctuation detected and fixed using AWB (9585)

2013-11-07T22:10:31Z

Properties: Reference before punctuation detected and fixed using AWB (9585)

← Older revision		Revision as of 00:10, 8 November 2013
Line 1:		Line 1:
	I'~~m Yoshiko~~ [~~http~~:/~~/www~~.~~vegan~~-~~victory~~.de/~~index~~/~~users~~/~~view~~/id/~~5378 extended car warranty~~] ~~extended auto warranty Oquendo~~. The ~~job I've auto warranty been occupying for many years~~ is ~~a extended~~ [~~http~~:~~//glskating.com/groups/great~~-~~ideas~~-~~about~~-~~auto~~-~~repair~~-~~that~~-~~you-can-use~~/ ~~car warranty~~] ~~[http~~://~~Www~~.~~5starwarranty~~.~~com~~/ ~~warranty bookkeeper] but I've currently~~ [http://www.~~nbcnews~~.com/id/~~23147777~~/~~ns/business~~-~~consumer_news/t/auto~~-~~warranty-firms-launch-sleazy~~-~~scam/ utilized~~] ~~for another 1. Her spouse and her selected to reside in Delaware but she requirements to~~ [http://www.~~Mass~~.~~gov~~/~~ocabr~~/~~consumer~~-~~rights~~-~~and-resources~~/~~autos~~/~~lemon-laws~~/~~used-vehicle-warranty-law~~.~~html transfer simply~~] ~~because of her family members. The favorite hobby for my kids and me is dancing and now I'm trying to earn money with it.<br><br>Feel free to surf to my web blog:~~ [http://~~Www~~.~~ebc-Clan~~.ch/~~index~~.~~php?mod~~=~~users&action~~=~~view&id~~=~~12304 Www.ebc-Clan.ch~~]		In [[signal processing]], a '''digital biquad filter''' is a second-order [[recursive filter\|recursive]] [[linear filter]], containing two [[Pole-zero_diagram\|poles]] and two [[Pole-zero_diagram\|zeros]]. "Biquad" is an abbreviation of "''biquadratic''", which refers to the fact that in the [[Z-transform\|Z domain]], its [[transfer function]] is the ratio of two [[quadratic function]]s:

			:<math>\ H(z)=\frac{b_0+b_1z^{-1}+b_2z^{-2}} {1+a_1z^{-1}+a_2z^{-2} }</math>

			High-order recursive filters can be highly sensitive to [[Quantization (signal processing)\|quantization]] of their coefficients, and can easily become [[BIBO stability\|unstable]]. This is much less of a problem with first and second-order filters; therefore, higher-order filters are typically implemented as serially-cascaded biquad sections (and a first-order filter if necessary). The two poles of the biquad filter must be inside the unit circle for it to be stable. In general, this is true for all filters i.e. all poles must be inside the unit circle for the filter to be stable.

			==Implementation==

			===Direct Form 1===
			The most straightforward implementation is the Direct Form 1, which has the following [[difference equation]]:

			:<math>\ y[n] = b_0x[n] + b_1x[n-1] + b_2x[n-2] - a_1y[n-1] - a_2y[n-2] </math>

			Here the <math>b_0</math>, <math>b_1</math> and <math>b_2</math> coefficients determine zeros, and <math>a_1</math>, <math>a_2</math> determine the position of the poles.

			Flow graph of biquad filter in Direct Form 1:

			[[File:Biquad filter DF-I.svg\|400px\|]]

			===Direct Form 2===
			The Direct Form 1 implementation requires four delay registers. An equivalent circuit is the Direct Form 2 implementation, which requires only two delay registers:

			[[File:Biquad filter DF-II.svg\|400px\|]]

			The Direct Form 2 implementation is called the canonical form, because it uses the minimal amount of delays, adders and multipliers, yielding in the same transfer function as the Direct Form 1 implementation. The [[difference equation]]s for DF2 are:

			:<math>\ y[n]=b_0 w[n]+b_1 w[n-1]+b_2 w[n-2],</math>

			where

			:<math>\ w[n]=x[n]-a_1 w[n-1]-a_2 w[n-2].</math>

			===Transposed direct forms===

			[[File:Biquad direct form 2 transposed .svg\|right\|thumb\|Transposed direct form biquadratic section]]

			See: https://ccrma.stanford.edu/~jos/fp/Transposed_Direct_Forms.html

			==References==
			*[http://www.wiley.com/WileyCDA/WileyTitle/productCd-047003551X.html Sen M. Kuo, Bob H. Lee, Wenshun Tian: ''Real-Time Digital Signal Processing: Implementations and Applications, 2nd Edition'', Wiley & Sons Ltd, 2006 (E-book)]
			*[http://www.musicdsp.org/files/Audio-EQ-Cookbook.txt Cookbook formulae for audio EQ biquad filter coefficients]
			*[http://peabody.sapp.org/class/350.838/lab/biquad/ Biquad filter]
			*[http://ccrma.stanford.edu/~jos/filters/BiQuad_Section.html JOS BiQuad section]

			==See also==
			*[[Electronic_filter_topology#Biquad_filter\|Biquad filter]]
			*[[Digital filter]]

			[[Category:Linear filters]]
			[[Category:Audio engineering]]
			[[Category:Filter theory]]

en>Helpful Pixie Bot: ISBNs (Build KE)

2012-05-11T17:53:43Z

ISBNs (Build KE)

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