Synopsis
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-Loéve 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.
From the Back Cover
Since the book, "Discrete Cosine Transform" by K. R. Rao and P. Yip, (Academic Press, Boston) was published in 1990, the DCT has increasingly attracted the attention of scientific, engineering and research communities. The DCT is used in many applications and in data compression in particular. This is due to the fact that the DCT has excellent energy-packing capability and also approaches the statistically optimal Karhunen-Loéve transform (KLT) in decorrrelating a signal. The development of various fast algorithms for the efficient implementation of the DCT involving real arithmetic only, further contributed to its popularity. In the last several years there have been significant advances and developments in both theory and applications relating to transform processing of signals. In particular, digital processing motivated the investigation of other forms of discrete cosine transforms (DCTs) for their integer approximations. International standards organizations (ISO/IEC and ITU-T) have adopted the use of various forms of the integer DCT. At the same time, the investigation of other forms of discrete sine transforms (DSTs) has made a similar impact. There is therefore a need to extend the coverage to include these techniques. This book is aimed at doing just that.
The book "Discrete Cosine and Sine Transforms: General properties, Fast algorithms and Integer Approximations" is aimed at both the novice and the expert. The fervent hopes and aspirations of the authors (V. Britanak, P.C. Yip and K.R. Rao) are that the latest developments in the general DCT/DST field further lead into additional applications and also provide the incentive and inspiration to further modify/customize these transforms with the overall motivation to improve their efficiencies while retaining the simplicity in implementations.|Since the book, "Discrete Cosine Transform" by K. R. Rao and P. Yip, (Academic Press, Boston) was published in 1990, the DCT has increasingly attracted the attention of scientific, engineering and research communities. The DCT is used in many applications and in data compression in particular. This is due to the fact that the DCT has excellent energy-packing capability and also approaches the statistically optimal Karhunen-Loéve transform (KLT) in decorrrelating a signal. The development of various fast algorithms for the efficient implementation of the DCT involving real arithmetic only, further contributed to its popularity. In the last several years there have been significant advances and developments in both theory and applications relating to transform processing of signals. In particular, digital processing motivated the investigation of other forms of discrete cosine transforms (DCTs) for their integer approximations. International standards organizations (ISO/IEC and ITU-T) have adopted the use of various forms of the integer DCT. At the same time, the investigation of other forms of discrete sine transforms (DSTs) has made a similar impact. There is therefore a need to extend the coverage to include these techniques. This book is aimed at doing just that.
The book "Discrete Cosine and Sine Transforms: General properties, Fast algorithms and Integer Approximations" is aimed at both the novice and the expert. The fervent hopes and aspirations of the authors (V. Britanak, P.C. Yip and K.R. Rao) are that the latest developments in the general DCT/DST field further lead into additional applications and also provide the incentive and inspiration to further modify/customize these transforms with the overall motivation to improve their efficiencies while retaining the simplicity in implementations.
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