# Discrete Cosine and Sine Transforms: General Properties, Fast Algorithms and Integer Approximations

@inproceedings{Britanak2006DiscreteCA, title={Discrete Cosine and Sine Transforms: General Properties, Fast Algorithms and Integer Approximations}, author={Vladimir Britanak and Patrick C. Yip and K. R. Rao}, year={2006} }

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

## 290 Citations

Fast computing of discrete cosine and sine transforms of types VI and VII

- Computer ScienceOptical Engineering + Applications
- 2011

This work proposes fast algorithms for computing Discrete Sine and Discrete Cosine Transforms (DCT and DST) of types VI and VII, which are currently under consideration for inclusion in ISO/IEC/ITU-T High Efficiency Video Coding (HEVC) standard.

On the Discrete Cosine Transform of Weakly Stationary Signals

- Computer Science, Engineering
- 2012

The transformed autocorrelation matrix has half of its elements equal to zero, which means that it is possible to improve current DCT signal processing systems by means of more efficient implementation and algorithms.

Discrete Cosine-Sine Type VII Transform and Fast Integer Transforms for Intra Prediction of Images and Video Coding

- Computer ScienceCybernetics and Systems Analysis
- 2021

Algorithms for fast calculation of 2D separable directional integer cosine and cosine-sine type VII adaptive transforms for intra prediction with 8 × 8 chroma blocks are developed, which have a low multiplicative complexity that is 6.6 and 16.5 times lower than that in the well-known algorithms.

Discrete Transforms and Orthogonal Polynomials of (Anti)Symmetric Multivariate Cosine Functions

- MathematicsSIAM J. Numer. Anal.
- 2014

Four families of discretely and continuously orthogonal Chebyshev-like polynomials corresponding to the antisymmetric and symmetric generalizations of cosine functions are introduced.

Modified Integer Sine Transforms. Construction Method and Separable Directional Adaptive Transforms for Intra Prediction in Image/Video Coding

- Business
- 2020

Algorithms for fast implementation of 2D 8-point separable directional integer cosine and modified adaptive sine transforms for intra prediction with low computational complexity are developed, and their computational complexity is 4.62 and 8.24 times lower than that of the known algorithms.

A tutorial overview on the properties of the discrete cosine transform for encoded image and video processing

- Computer ScienceSignal Process.
- 2011

Discrete Fourier transform associated with generalized Schur polynomials

- Mathematics
- 2018

We prove the Plancherel formula for a four-parameter family of discrete Fourier transforms and their multivariate generalizations stemming from corresponding generalized Schur polynomials. For…

Discrete Transforms and Orthogonal Polynomials of (Anti)symmetric Multivariate Sine Functions

- MathematicsEntropy
- 2018

Sixteen types of the discrete multivariate transforms, induced by the multivariate antisymmetric and symmetric sine functions, are explicitly developed and inherent interpolation methods are formulated.

High-accuracy implementation of fast DCT algorithms based on algebraic integer encoding

- Computer Science2012 International Conference on Signals and Electronic Systems (ICSES)
- 2012

The paper presents a systematic approach to synthesizing and implementing fast algorithms for computing the DCT of a power-of-two size with regularity of their signal flow graphs and low arithmetic complexity.

Using the CS decomposition to compute the 8-point DCT

- Computer Science2015 IEEE International Symposium on Circuits and Systems (ISCAS)
- 2015

By iteratively decomposing matrices after reordering their columns or rows, novel factorizations of the DCT matrix have been obtained that describe interesting algorithms for computing the transform.

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