Discrete cosine and sine transforms: general properties, fast algorithms and integer approximations
The Discrete Cosine Transform (DCT) is used in many applications by the scientific, engineering and research communities and in data compression in particular. Fast algorithms and applications of the DCT Type II (DCT-II) have become the heart of many established international image/video coding stan...
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| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam Boston London
Academic
2007
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| Ausgabe: | [New ed.] |
| Schlagworte: | |
| Online-Zugang: | FLA01 URL des Erstveröffentlichers |
| Zusammenfassung: | The Discrete Cosine Transform (DCT) is used in many applications by the scientific, engineering and research communities and in data compression in particular. Fast algorithms and applications of the DCT Type II (DCT-II) have become the heart of many established international image/video coding standards. Since then other forms of the DCT and Discrete Sine Transform (DST) have been investigated in detail. This new edition presents the complete set of DCT and DST discrete trigonometric transforms, including their definitions, general mathematical properties, and relations to the optimal Karhunen-Lǒve transform (KLT), with the emphasis on fast algorithms (one-dimensional and two-dimensional) and integer approximations of DCTs and DSTs for their efficient implementations in the integer domain. DCTs and DSTs are real-valued transforms that map integer-valued signals to floating-point coefficients. To eliminate the floating-point operations, various methods of integer approximations have been proposed to construct and flexibly generate a family of integer DCT and DST transforms with arbitrary accuracy and performance. The integer DCTs/DSTs with low-cost and low-powered implementation can replace the corresponding real-valued transforms in wireless and satellite communication systems as well as portable computing applications. The book is essentially a detailed excursion on orthogonal/orthonormal DCT and DST matrices, their matrix factorizations and integer aproximations. It is hoped that the book will serve as a valuable reference for industry, academia and research institutes in developing integer DCTs and DSTs as well as an inspiration source for further advanced research. Key Features - Presentation of the complete set of DCTs and DSTs in context of entire class of discrete unitary sinusoidal transforms: the origin, definitions, general mathematical properties, mutual relationships and relations to the optimal Karhunen-Lǒve transform (KLT). - Unified treatment with the fast implementations of DCTs and DSTs: the fast rotation-based algorithms derived in the form of recursive sparse matrix factorizations of a transform matrix including one- and two-dimensional cases. - Detailed presentation of various methods and design approaches to integer approximation of DCTs and DSTs utilizing the basic concepts of linear algebra, matrix theory and matrix computations leading to their efficient multiplierless real-time implementations, or in general reversible integer-to-integer implementations. |
| Beschreibung: | Previous edition: published as Discrete cosine transform by K.R. Rao, P. Yip. 1990 Includes bibliographical references and index |
| Beschreibung: | 1 online resource (xiv, 349 pages) illustrations |
| ISBN: | 9780123736246 0123736242 0080464645 9780080464640 |
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| 100 | 1 | |a Britanak, Vladimir |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Discrete cosine and sine transforms |b general properties, fast algorithms and integer approximations |c Vladimir Britanak, Patrick C. Yip, K.R. Rao |
| 250 | |a [New ed.] | ||
| 264 | 1 | |a Amsterdam |a Boston |a London |b Academic |c 2007 | |
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| 500 | |a Previous edition: published as Discrete cosine transform by K.R. Rao, P. Yip. 1990 | ||
| 500 | |a Includes bibliographical references and index | ||
| 520 | |a The Discrete Cosine Transform (DCT) is used in many applications by the scientific, engineering and research communities and in data compression in particular. Fast algorithms and applications of the DCT Type II (DCT-II) have become the heart of many established international image/video coding standards. Since then other forms of the DCT and Discrete Sine Transform (DST) have been investigated in detail. This new edition presents the complete set of DCT and DST discrete trigonometric transforms, including their definitions, general mathematical properties, and relations to the optimal Karhunen-Lǒve transform (KLT), with the emphasis on fast algorithms (one-dimensional and two-dimensional) and integer approximations of DCTs and DSTs for their efficient implementations in the integer domain. DCTs and DSTs are real-valued transforms that map integer-valued signals to floating-point coefficients. | ||
| 520 | |a To eliminate the floating-point operations, various methods of integer approximations have been proposed to construct and flexibly generate a family of integer DCT and DST transforms with arbitrary accuracy and performance. The integer DCTs/DSTs with low-cost and low-powered implementation can replace the corresponding real-valued transforms in wireless and satellite communication systems as well as portable computing applications. The book is essentially a detailed excursion on orthogonal/orthonormal DCT and DST matrices, their matrix factorizations and integer aproximations. It is hoped that the book will serve as a valuable reference for industry, academia and research institutes in developing integer DCTs and DSTs as well as an inspiration source for further advanced research. | ||
| 520 | |a Key Features - Presentation of the complete set of DCTs and DSTs in context of entire class of discrete unitary sinusoidal transforms: the origin, definitions, general mathematical properties, mutual relationships and relations to the optimal Karhunen-Lǒve transform (KLT). - Unified treatment with the fast implementations of DCTs and DSTs: the fast rotation-based algorithms derived in the form of recursive sparse matrix factorizations of a transform matrix including one- and two-dimensional cases. - Detailed presentation of various methods and design approaches to integer approximation of DCTs and DSTs utilizing the basic concepts of linear algebra, matrix theory and matrix computations leading to their efficient multiplierless real-time implementations, or in general reversible integer-to-integer implementations. | ||
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| 700 | 1 | |a Yip, P. |d 1956- |e Sonstige |4 oth | |
| 700 | 1 | |a Rao, K. Ramamohan |e Sonstige |4 oth | |
| 700 | 1 | |a Rao, K. Ramamohan |e Sonstige |4 oth | |
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| dewey-full | 621.38220151 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 621 - Applied physics |
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| dewey-tens | 620 - Engineering and allied operations |
| discipline | Elektrotechnik / Elektronik / Nachrichtentechnik |
| edition | [New ed.] |
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| spelling | Britanak, Vladimir Verfasser aut Discrete cosine and sine transforms general properties, fast algorithms and integer approximations Vladimir Britanak, Patrick C. Yip, K.R. Rao [New ed.] Amsterdam Boston London Academic 2007 1 online resource (xiv, 349 pages) illustrations txt rdacontent c rdamedia cr rdacarrier Previous edition: published as Discrete cosine transform by K.R. Rao, P. Yip. 1990 Includes bibliographical references and index The Discrete Cosine Transform (DCT) is used in many applications by the scientific, engineering and research communities and in data compression in particular. Fast algorithms and applications of the DCT Type II (DCT-II) have become the heart of many established international image/video coding standards. Since then other forms of the DCT and Discrete Sine Transform (DST) have been investigated in detail. This new edition presents the complete set of DCT and DST discrete trigonometric transforms, including their definitions, general mathematical properties, and relations to the optimal Karhunen-Lǒve transform (KLT), with the emphasis on fast algorithms (one-dimensional and two-dimensional) and integer approximations of DCTs and DSTs for their efficient implementations in the integer domain. DCTs and DSTs are real-valued transforms that map integer-valued signals to floating-point coefficients. To eliminate the floating-point operations, various methods of integer approximations have been proposed to construct and flexibly generate a family of integer DCT and DST transforms with arbitrary accuracy and performance. The integer DCTs/DSTs with low-cost and low-powered implementation can replace the corresponding real-valued transforms in wireless and satellite communication systems as well as portable computing applications. The book is essentially a detailed excursion on orthogonal/orthonormal DCT and DST matrices, their matrix factorizations and integer aproximations. It is hoped that the book will serve as a valuable reference for industry, academia and research institutes in developing integer DCTs and DSTs as well as an inspiration source for further advanced research. Key Features - Presentation of the complete set of DCTs and DSTs in context of entire class of discrete unitary sinusoidal transforms: the origin, definitions, general mathematical properties, mutual relationships and relations to the optimal Karhunen-Lǒve transform (KLT). - Unified treatment with the fast implementations of DCTs and DSTs: the fast rotation-based algorithms derived in the form of recursive sparse matrix factorizations of a transform matrix including one- and two-dimensional cases. - Detailed presentation of various methods and design approaches to integer approximation of DCTs and DSTs utilizing the basic concepts of linear algebra, matrix theory and matrix computations leading to their efficient multiplierless real-time implementations, or in general reversible integer-to-integer implementations. Signal processing / Mathematics fast Transformations (Mathematics) fast Signal processing Mathematics Transformations (Mathematics) Yip, P. 1956- Sonstige oth Rao, K. Ramamohan Sonstige oth http://www.sciencedirect.com/science/book/9780123736246 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Britanak, Vladimir Discrete cosine and sine transforms general properties, fast algorithms and integer approximations Signal processing / Mathematics fast Transformations (Mathematics) fast Signal processing Mathematics Transformations (Mathematics) |
| title | Discrete cosine and sine transforms general properties, fast algorithms and integer approximations |
| title_auth | Discrete cosine and sine transforms general properties, fast algorithms and integer approximations |
| title_exact_search | Discrete cosine and sine transforms general properties, fast algorithms and integer approximations |
| title_full | Discrete cosine and sine transforms general properties, fast algorithms and integer approximations Vladimir Britanak, Patrick C. Yip, K.R. Rao |
| title_fullStr | Discrete cosine and sine transforms general properties, fast algorithms and integer approximations Vladimir Britanak, Patrick C. Yip, K.R. Rao |
| title_full_unstemmed | Discrete cosine and sine transforms general properties, fast algorithms and integer approximations Vladimir Britanak, Patrick C. Yip, K.R. Rao |
| title_short | Discrete cosine and sine transforms |
| title_sort | discrete cosine and sine transforms general properties fast algorithms and integer approximations |
| title_sub | general properties, fast algorithms and integer approximations |
| topic | Signal processing / Mathematics fast Transformations (Mathematics) fast Signal processing Mathematics Transformations (Mathematics) |
| topic_facet | Signal processing / Mathematics Transformations (Mathematics) Signal processing Mathematics |
| url | http://www.sciencedirect.com/science/book/9780123736246 |
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