Modified Discrete Cosine Transform - Revision history

168.1.3.36 at 13:07, 5 October 2016

2016-10-05T13:07:00Z

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	<center>[[Image:IMDCT.png\|IMDCT formula]]</center>		<center>[[Image:IMDCT.png\|IMDCT formula]]</center>

	The MDCT was developed by Henrique Malvar, ~~and~~ engineer now working for Microsoft ~~and that~~ had considerable participation in creating the [[WMA]] format.		The MDCT was developed by Henrique Malvar, an engineer now working for Microsoft who had considerable participation in creating the [[WMA]] format.

	== References ==		== References ==

Speckmade at 17:32, 13 June 2007

2007-06-13T17:32:37Z

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			The '''Modified Discrete Cosine Transform''' ('''MDCT''') is a [[DCT]]-IV transform. The MDCT tries to minimize blocking artifacts. It is common in lossy audio codecs including [[MP3]], [[Vorbis]], and [[AAC]].
	The ~~[[MDCT]] (~~Modified Discrete Cosine Transform) is a [[DCT]]-IV transform. The MDCT tries to minimize blocking artifacts. It is common in lossy audio codecs including [[MP3]], [[Vorbis]], and [[AAC]].


	As a lapped transform, the MDCT is a bit unusual compared to other Fourier-related transforms in that it has half as many outputs as inputs (instead of the same number). In particular, it is a linear function ''F'' : '''R'''<sup>2''n''</sup> <tt>-></tt> '''R'''<sup>''n''</sup> (where '''R''' denotes the set of real numbers). The 2''n'' real numbers ''x''<sub>0</sub>, ..., ''x''<sub>2''n''-1</sub> are transformed into the ''n'' real numbers ''f''<sub>0</sub>, ..., ''f''<sub>''n''-1</sub> according to the formula:		As a lapped transform, the MDCT is a bit unusual compared to other Fourier-related transforms in that it has half as many outputs as inputs (instead of the same number). In particular, it is a linear function ''F'' : '''R'''<sup>2''n''</sup> <tt>-></tt> '''R'''<sup>''n''</sup> (where '''R''' denotes the set of real numbers). The 2''n'' real numbers ''x''<sub>0</sub>, ..., ''x''<sub>2''n''-1</sub> are transformed into the ''n'' real numbers ''f''<sub>0</sub>, ..., ''f''<sub>''n''-1</sub> according to the formula:
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	<center>[[Image:MDCT.png\|MDCT formula]]</center>		<center>[[Image:MDCT.png\|MDCT formula]]</center>

			The inverse MDCT is known as the '''IMDCT'''. Because there are different numbers of inputs and outputs, at first glance it might seem that the MDCT should not be invertible. However, perfect invertibility is achieved by ''adding'' the overlapped IMDCTs of subsequent overlapping blocks, causing the errors to ''cancel'' and the original data to be retrieved; this technique is known as ''time-domain aliasing cancellation'' (TDAC).
	The inverse MDCT is known as the '''IMDCT'''. Because there are different numbers of inputs and outputs, at first glance it might seem that the MDCT should not be invertible. However, perfect invertibility is achieved by ''adding'' the overlapped IMDCTs of subsequent overlapping blocks, causing the errors to ''cancel'' and the original data to be retrieved; this technique is known as ''time-domain aliasing cancellation'' (TDAC).

	The IMDCT transforms ''n'' real numbers ''f''<sub>0</sub>, ..., ''f''<sub>''n''-1</sub> into 2''n'' real numbers ''y''<sub>0</sub>, ..., ''y''<sub>2''n''-1</sub> according to the formula:		The IMDCT transforms ''n'' real numbers ''f''<sub>0</sub>, ..., ''f''<sub>''n''-1</sub> into 2''n'' real numbers ''y''<sub>0</sub>, ..., ''y''<sub>2''n''-1</sub> according to the formula:

	<center>[[Image:IMDCT.png\|IMDCT formula]]</center>		<center>[[Image:IMDCT.png\|IMDCT formula]]</center>


	The MDCT was developed by Henrique Malvar, and engineer now working for Microsoft and that had considerable participation in creating the [[WMA]] format.		The MDCT was developed by Henrique Malvar, and engineer now working for Microsoft and that had considerable participation in creating the [[WMA]] format.

	==References==		== References ==

	* [http://www.dspguide.com/ch8.htm Discrete Fourier Transform] it's basic properties and applications.		* [http://www.dspguide.com/ch8.htm Discrete Fourier Transform] it's basic properties and applications.
	* [http://ccrma-www.stanford.edu/~bosse/proj/node27.html Planet CCRMA] description of the DCT-IV.		* [http://ccrma-www.stanford.edu/~bosse/proj/node27.html Planet CCRMA] description of the DCT-IV.

Speckmade: MDCT moved to Modified Discrete Cosine Transform

2007-06-13T17:30:29Z

MDCT moved to Modified Discrete Cosine Transform

← Older revision	Revision as of 17:30, 13 June 2007
(No difference)

Pepoluan at 20:34, 15 September 2006

2006-09-15T20:34:49Z

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	* [http://www.comp.nus.edu.sg/~wangye/publications/Conference%20papers/00027_aes22.pdf Modified Discrete Cosine Transform] a complete research paper on MDCT presented at the 22nd AES conference.		* [http://www.comp.nus.edu.sg/~wangye/publications/Conference%20papers/00027_aes22.pdf Modified Discrete Cosine Transform] a complete research paper on MDCT presented at the 22nd AES conference.

	[[Category:~~Digital~~ Signal Processing]]
			[[Category:Signal Processing]]

HotshotGG at 22:44, 7 September 2006

2006-09-07T22:44:12Z

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	* [http://www.comp.nus.edu.sg/~wangye/publications/Conference%20papers/00027_aes22.pdf Modified Discrete Cosine Transform] a complete research paper on MDCT presented at the 22nd AES conference.		* [http://www.comp.nus.edu.sg/~wangye/publications/Conference%20papers/00027_aes22.pdf Modified Discrete Cosine Transform] a complete research paper on MDCT presented at the 22nd AES conference.

	~~[[Category:Algorithms]]~~
	[[Category:Digital Signal Processing]]		[[Category:Digital Signal Processing]]

HotshotGG: /* References */

2006-09-07T22:41:21Z

References

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	[[Category:Algorithms]]		[[Category:Algorithms]]
			[[Category:Digital Signal Processing]]

HotshotGG at 22:39, 7 September 2006

2006-09-07T22:39:32Z

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	* [http://www.comp.nus.edu.sg/~wangye/publications/Conference%20papers/00027_aes22.pdf Modified Discrete Cosine Transform] a complete research paper on MDCT presented at the 22nd AES conference.		* [http://www.comp.nus.edu.sg/~wangye/publications/Conference%20papers/00027_aes22.pdf Modified Discrete Cosine Transform] a complete research paper on MDCT presented at the 22nd AES conference.

			[[Category:Algorithms]]
	[[Category:~~Technical]]~~
	~~[[Category:Digital Signal Processing~~]]

Beto at 21:06, 6 September 2006

2006-09-06T21:06:05Z

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	[[Category:Technical]]		[[Category:Technical]]
	[[Category:~~Algorithms~~]]		[[Category:Digital Signal Processing]]

Beto at 19:31, 5 September 2006

2006-09-05T19:31:02Z

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			{{stub}}


	The [[MDCT]] (Modified Discrete Cosine Transform) is a [[DCT]]-IV transform. The MDCT tries to minimize blocking artifacts. It is common in lossy audio codecs including [[MP3]], [[Vorbis]], and [[AAC]].		The [[MDCT]] (Modified Discrete Cosine Transform) is a [[DCT]]-IV transform. The MDCT tries to minimize blocking artifacts. It is common in lossy audio codecs including [[MP3]], [[Vorbis]], and [[AAC]].

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	[[Category:Technical]]		[[Category:Technical]]
			[[Category:Algorithms]]

Beto: category

2006-09-05T19:28:19Z

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	[[Category:~~Algorithms~~]]		[[Category:Technical]]