Cascade algorithm - Revision history

Aavindraa: recover cascade applet

2024-06-10T19:15:21Z

recover cascade applet

← Previous revision		Revision as of 19:15, 10 June 2024
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	* [[C. Sidney Burrus\|C.S. Burrus]], R.A. Gopinath, H. Guo, ''Introduction to Wavelets and Wavelet Transforms: A Primer'', Prentice-Hall, 1988, {{ISBN\|0-13-489600-9}}.		* [[C. Sidney Burrus\|C.S. Burrus]], R.A. Gopinath, H. Guo, ''Introduction to Wavelets and Wavelet Transforms: A Primer'', Prentice-Hall, 1988, {{ISBN\|0-13-489600-9}}.
	* http://cnx.org/content/m10486/latest/		* http://cnx.org/content/m10486/latest/
	* https://web.archive.org/web/20070615055323/http://cm.bell-labs.com/cm/ms/who/wim/cascade/index.html		* http://plan9.bell-labs.co/who/wim/cascade/ {{Webarchive\|url=https://web.archive.org/web/20070615055323/http://cm.bell-labs.com/cm/ms/who/wim/cascade/index.html\|date=2007-06-15}}

	[[Category:Wavelets]]		[[Category:Wavelets]]

InternetArchiveBot: Rescuing 1 sources and tagging 0 as dead. #IABot (v1.5beta)

2017-07-31T17:23:18Z

Rescuing 1 sources and tagging 0 as dead. #IABot (v1.5beta)

← Previous revision		Revision as of 17:23, 31 July 2017
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	* [[C. Sidney Burrus\|C.S. Burrus]], R.A. Gopinath, H. Guo, ''Introduction to Wavelets and Wavelet Transforms: A Primer'', Prentice-Hall, 1988, {{ISBN\|0-13-489600-9}}.		* [[C. Sidney Burrus\|C.S. Burrus]], R.A. Gopinath, H. Guo, ''Introduction to Wavelets and Wavelet Transforms: A Primer'', Prentice-Hall, 1988, {{ISBN\|0-13-489600-9}}.
	* http://cnx.org/content/m10486/latest/		* http://cnx.org/content/m10486/latest/
	* https://web.archive.org/web/20070615055323/http://cm.bell-labs.com~~:80~~/cm/ms/who/wim/cascade/index.html		* https://web.archive.org/web/20070615055323/http://cm.bell-labs.com/cm/ms/who/wim/cascade/index.html

	[[Category:Wavelets]]		[[Category:Wavelets]]

Magic links bot: Replace magic links with templates per local RfC and MediaWiki RfC

2017-05-31T17:11:25Z

Replace magic links with templates per local RfC and MediaWiki RfC

← Previous revision		Revision as of 17:11, 31 May 2017
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	Successive approximation can also be derived in the frequency domain.		Successive approximation can also be derived in the frequency domain.
	== References ==		== References ==
	* [[C. Sidney Burrus\|C.S. Burrus]], R.A. Gopinath, H. Guo, ''Introduction to Wavelets and Wavelet Transforms: A Primer'', Prentice-Hall, 1988, ISBN 0-13-489600-9.		* [[C. Sidney Burrus\|C.S. Burrus]], R.A. Gopinath, H. Guo, ''Introduction to Wavelets and Wavelet Transforms: A Primer'', Prentice-Hall, 1988, {{ISBN\|0-13-489600-9}}.
	* http://cnx.org/content/m10486/latest/		* http://cnx.org/content/m10486/latest/
	* https://web.archive.org/web/20070615055323/http://cm.bell-labs.com:80/cm/ms/who/wim/cascade/index.html		* https://web.archive.org/web/20070615055323/http://cm.bell-labs.com:80/cm/ms/who/wim/cascade/index.html

InternetArchiveBot: Rescuing 1 sources and tagging 0 as dead. #IABot (v1.2.7.1)

2016-11-16T13:02:50Z

Rescuing 1 sources and tagging 0 as dead. #IABot (v1.2.7.1)

← Previous revision		Revision as of 13:02, 16 November 2016
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	* [[C. Sidney Burrus\|C.S. Burrus]], R.A. Gopinath, H. Guo, ''Introduction to Wavelets and Wavelet Transforms: A Primer'', Prentice-Hall, 1988, ISBN 0-13-489600-9.		* [[C. Sidney Burrus\|C.S. Burrus]], R.A. Gopinath, H. Guo, ''Introduction to Wavelets and Wavelet Transforms: A Primer'', Prentice-Hall, 1988, ISBN 0-13-489600-9.
	* http://cnx.org/content/m10486/latest/		* http://cnx.org/content/m10486/latest/
	* http://cm.bell-labs.com/cm/ms/who/wim/cascade/index.html		* https://web.archive.org/web/20070615055323/http://cm.bell-labs.com:80/cm/ms/who/wim/cascade/index.html

	[[Category:Wavelets]]		[[Category:Wavelets]]

137.205.112.13 at 11:45, 13 November 2015

2015-11-13T11:45:11Z

← Previous revision		Revision as of 11:45, 13 November 2015
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	: <math>\psi(t)= \sum_{n=- \infty}^{\infty} g[n]{\sqrt 2} \varphi^{(k)} (2t-n).</math>		: <math>\psi(t)= \sum_{n=- \infty}^{\infty} g[n]{\sqrt 2} \varphi^{(k)} (2t-n).</math>

	Plots of the function at each iteration is shown in Figure 1.

	Successive approximation can also be derived in the frequency domain.		Successive approximation can also be derived in the frequency domain.

	<!-- Missing image removed: [[File:Figure cascade.png\|'''Figure 1. Iterations of the successive approximations of Daubechies wavelet and scale function by the cascade algorithm.''']] -->

	== References ==		== References ==
	* [[C. Sidney Burrus\|C.S. Burrus]], R.A. Gopinath, H. Guo, ''Introduction to Wavelets and Wavelet Transforms: A Primer'', Prentice-Hall, 1988, ISBN 0-13-489600-9.		* [[C. Sidney Burrus\|C.S. Burrus]], R.A. Gopinath, H. Guo, ''Introduction to Wavelets and Wavelet Transforms: A Primer'', Prentice-Hall, 1988, ISBN 0-13-489600-9.

129.110.242.17: /* Successive approximation */

2014-12-17T18:45:12Z

Successive approximation

← Previous revision		Revision as of 18:45, 17 December 2014
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	== Successive approximation ==		== Successive approximation ==

	The iterative algorithm ~~generate~~ successive approximations to ψ(''t'') or φ(''t'') from {''h''} and {''g''} filter coefficients. If the algorithm converges to a fixed point, then that fixed point is the basic scaling function or wavelet.		The iterative algorithm generates successive approximations to ψ(''t'') or φ(''t'') from {''h''} and {''g''} filter coefficients. If the algorithm converges to a fixed point, then that fixed point is the basic scaling function or wavelet.

	The iterations are defined by		The iterations are defined by

Yobot: changes per WP:ORDINAL, replaced: ^th → th using AWB (10080)

2014-04-23T09:27:46Z

changes per WP:ORDINAL, replaced: <sup>th</sup> → th using AWB (10080)

← Previous revision		Revision as of 09:27, 23 April 2014
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	In the [[mathematics\|mathematical]] topic of [[wavelet]] theory, the '''cascade algorithm''' is a [[numerical method]] for calculating function values of the basic [[Wavelet#~~Scaling_function~~\|scaling]] and [[wavelet]] functions of a [[discrete wavelet transform]] using an iterative algorithm. It starts from values on a coarse sequence of sampling points and produces values for successively more densely spaced sequences of sampling points. Because it applies the same operation over and over to the output of the previous application, it is known as the ''cascade algorithm''.		In the [[mathematics\|mathematical]] topic of [[wavelet]] theory, the '''cascade algorithm''' is a [[numerical method]] for calculating function values of the basic [[Wavelet#Scaling function\|scaling]] and [[wavelet]] functions of a [[discrete wavelet transform]] using an iterative algorithm. It starts from values on a coarse sequence of sampling points and produces values for successively more densely spaced sequences of sampling points. Because it applies the same operation over and over to the output of the previous application, it is known as the ''cascade algorithm''.

	== Successive approximation ==		== Successive approximation ==
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	: <math>\varphi^{(k+1)}(t)=\sum_{n=0}^{N-1} h[n] \sqrt 2 \varphi^{(k)} (2t-n)</math>		: <math>\varphi^{(k+1)}(t)=\sum_{n=0}^{N-1} h[n] \sqrt 2 \varphi^{(k)} (2t-n)</math>

	For the ''k''~~<sup>~~th~~</sup>~~ iteration, where an initial φ<sup>(0)</sup>(''t'') must be given.		For the ''k''th iteration, where an initial φ<sup>(0)</sup>(''t'') must be given.

	The frequency domain estimates of the basic scaling function is given by		The frequency domain estimates of the basic scaling function is given by

Dekart: −Category:Numerical analysis; −Category:Signal processing; −Category:Image processing - the article already belongs to category Category:Wavelets which is a subcategory of these 3 categories

2013-06-02T16:56:46Z

−Category:Numerical analysis; −Category:Signal processing; −Category:Image processing - the article already belongs to category Category:Wavelets which is a subcategory of these 3 categories

← Previous revision		Revision as of 16:56, 2 June 2013
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	* http://cm.bell-labs.com/cm/ms/who/wim/cascade/index.html		* http://cm.bell-labs.com/cm/ms/who/wim/cascade/index.html

	[[Category:Numerical analysis]]
	[[Category:Signal processing]]
	[[Category:Image processing]]
	[[Category:Wavelets]]		[[Category:Wavelets]]

Glenn: +links

2012-08-31T17:24:56Z

+links

← Previous revision		Revision as of 17:24, 31 August 2012
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	In the [[mathematics\|mathematical]] topic of [[wavelet]] theory, the '''cascade algorithm''' is a [[numerical method]] for calculating function values of the basic scaling and wavelet functions of a [[discrete wavelet transform]] using an iterative algorithm. It starts from values on a coarse sequence of sampling points and produces values for successively more densely spaced sequences of sampling points. Because it applies the same operation over and over to the output of the previous application, it is known as the ''cascade algorithm''.		In the [[mathematics\|mathematical]] topic of [[wavelet]] theory, the '''cascade algorithm''' is a [[numerical method]] for calculating function values of the basic [[Wavelet#Scaling_function\|scaling]] and [[wavelet]] functions of a [[discrete wavelet transform]] using an iterative algorithm. It starts from values on a coarse sequence of sampling points and produces values for successively more densely spaced sequences of sampling points. Because it applies the same operation over and over to the output of the previous application, it is known as the ''cascade algorithm''.

	== Successive approximation ==		== Successive approximation ==

ShelfSkewed: fix isbn, rm notice

2012-05-28T21:08:22Z

fix isbn, rm notice

← Previous revision		Revision as of 21:08, 28 May 2012
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	== References ==		== References ==
	* [[C. Sidney Burrus\|C.S. Burrus]], R.A. Gopinath, H. Guo, ''Introduction to Wavelets and Wavelet Transforms: A Primer'', Prentice-Hall, 1988, ISBN 0-12-489600-9 ~~{{Please check ISBN\|reason=Check digit (9) does not correspond to calculated figure.}}~~.		* [[C. Sidney Burrus\|C.S. Burrus]], R.A. Gopinath, H. Guo, ''Introduction to Wavelets and Wavelet Transforms: A Primer'', Prentice-Hall, 1988, ISBN 0-13-489600-9.
	* http://cnx.org/content/m10486/latest/		* http://cnx.org/content/m10486/latest/
	* http://cm.bell-labs.com/cm/ms/who/wim/cascade/index.html		* http://cm.bell-labs.com/cm/ms/who/wim/cascade/index.html