Discrete Cosine and Sine Transforms

General Properties, Fast Algorithms and Integer Approximations


  • Vladimir Britanak, Slovak Academy of Sciences, Institute of Informatics, Bratislava, Slovak Republic
  • Patrick Yip, McMaster University, Department of Mathematics and Statistics, Hamilton, Canada
  • K. R Rao, University of Texas at Arlington, Department of Electrical Engineering, Texas, U.S.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-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.
View full description


This book is suitable for scientists, researchers and engineers (research institutes, universities and companies). It is also suitable for graduate students in Electrical Engineering and Computer Science.


Book information

  • Published: September 2006
  • ISBN: 978-0-12-373624-6

Table of Contents

List of Acronyms
1. Discrete Cosine and Sine Transforms
2. Definitions and General Properties
3. The Karhunen-Loéve Transform and Optimal Decorrelation
4. Fast DCT/DST Algorithms
5. Integer Discrete Cosine/Sine Transforms