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

  title={Fast computing of discrete cosine and sine transforms of types VI and VII},
  author={Ravi K. Chivukula and Yuriy A. Reznik},
  booktitle={Optical Engineering + Applications},
We propose fast algorithms for computing Discrete Sine and Discrete Cosine Transforms (DCT and DST) of types VI and VII. Particular attention is paid to derivation of fast algorithms for computing DST-VII of lengths 4 and 8, which are currently under consideration for inclusion in ISO/IEC/ITU-T High Efficiency Video Coding (HEVC) standard. 
Relationship between DCT-II, DCT-VI, and DST-VII transforms
  • Y. Reznik
  • Engineering
    2013 IEEE International Conference on Acoustics, Speech and Signal Processing
  • 2013
It is shown that there exists a direct connection between DST-VII and DCT-II transforms, allowing their joint computation for certain transform sizes, and this connection also yields fast algorithms for constructing D CT-VI and Dct-VII.
Discrete Cosine-Sine Type VII Transform and Fast Integer Transforms for Intra Prediction of Images and Video Coding
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    Cybernetics 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.
Odd type DCT/DST for video coding: Relationships and low-complexity implementations
A class of relationships which link Discrete Cosine Transforming and Discrete Sine Transforms of types V, VI, VII and VIII, which have been recently considered for inclusion in the future video coding technology, are shown.
Algorithms for Fast Implementation of 4-Point Integer Sine Type Vii Transformswithout Multiplication and Separable Directional Adaptive Transforms for Intra Prediction in Image/Video Coding
Algorithms for fast implementation of 2D 4-point separable directional integer cosine and sine transforms with 4×4 blocks are developed, which require 7 times fewer multiplication operations and provide higher compression ratio than the well-known algorithms.
Fast Transforms for Intra-prediction-based Image and Video Coding
An overview of the DCT/DST transform scheme for intra coding in the HEVC standard is provided and factorizations for fast joint computation of DCT-II and DST-VII transforms of several sizes are derived.
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Fast Computation of Integer DCT-V, DCT-VIII, and DST-VII for Video Coding
This paper presents fast computation methods of N-point D CT-V and DCT-VIII, which reduce the number of addition and multiplication operations by 38% and 80.3%, respectively, in average, compared to the original JEM.
Hardware-friendly DST-VII/DCT-VIII approximations for the Versatile Video Coding Standard
The proposed solution enables to preserve the coding gain achieved by the MTS and considerably reduces the complexity in terms of required number of multiplications by coefficient.
Forward-Inverse 2D Hardware Implementation of Approximate Transform Core for the VVC Standard
An approximation approach is proposed to reduce the computational cost of the DST-VII and DCT-VIII and is able to sustain a video in 2K and 4K resolutions at 386 and 96 frames per second, respectively, while using only 12% of Alms, 22% of registers and 30% of DSP blocks of the Arria10 SoC platform.
Implementation of rectangular windowed odd discrete cosine transform update algorithm using distributed arithmetic approach
VHDL implementation of Odd Discrete Cosine Transform (ODCT-II) coefficient computation using independent update algorithm is discussed and shows that DA based approach is more efficient in terms of device utilization.


Discrete Cosine and Sine Transforms: General Properties, Fast Algorithms and Integer Approximations
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
Efficient fixed-point approximations of the 8×8 inverse discrete cosine transform
This paper describes fixed-point design methodologies and several resulting implementations of the Inverse Discrete Cosine Transform (IDCT) contributed by the authors to MPEG's work on defining the
On the multiplicative complexity of discrete cosine transforms
The multiplicative complexity of discrete cosine transforms (DCTs) of arbitrary dimensions on input sizes, which are powers of two, are obtained. New upper bounds on the multiplicative complexity of
Fast algorithm for computing discrete cosine transform
  • C. Kok
  • Computer Science, Engineering
    IEEE Trans. Signal Process.
  • 1997
An efficient method for computing the discrete cosine transform (DCT) is proposed, which is a generalization of the radix 2 DCT algorithm, and the recursive properties of the DCT for an even length input sequence are derived.
Design of fast transforms for high-resolution image and video coding
In the construction and analysis, an array of known techniques are utilized, including Heideman's mapping between DCT and DFT, Winograd short length DFT modules, prime-factor and common-factor algorithms, and also a new factorization scheme for even-sized scaled transforms are offered.
Practical fast 1-D DCT algorithms with 11 multiplications
A class of practical fast algorithms is introduced for the discrete cosine transform (DCT) and the structure of many of the published algorithms can be found in members of this class.
The discreteW transform
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The proposed transforms are orthogonal integer transforms, based on a simple recursive factorization structure, and allow very compact and efficient implementations in VCEG's H.265/JMKTA framework.
Computation of an odd-length DCT from a real-valued DFT of the same length
  • M. Heideman
  • Engineering, Computer Science
    IEEE Trans. Signal Process.
  • 1992
It is shown that a DCT of odd length can be computed by an identical-length DFT algorithm, by simply permuting the input and output sequences.