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

@article{Vashkevich2012HighaccuracyIO,
  title={High-accuracy implementation of fast DCT algorithms based on algebraic integer encoding},
  author={Maxim Vashkevich and Marek Parfieniuk and Alexander A. Petrovsky},
  journal={2012 International Conference on Signals and Electronic Systems (ICSES)},
  year={2012},
  pages={1-6}
}
The paper presents a systematic approach to synthesizing and implementing fast algorithms for computing the DCT of a power-of-two size. The main features of the obtainable algorithms are regularity of their signal flow graphs and low arithmetic complexity. Multiplierless implementation of the algorithms is based on the algebraic integer (AI) technique. A general AI encoding scheme for fast DCT algorithms is presented. The approach is demonstrated by using it to derive an AI-based low-error fast… 
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References

SHOWING 1-10 OF 17 REFERENCES
MULTIPLIERLESS DCT ALGORITHM FOR IMAGE COMPRESSION APPLICATIONS
TLDR
A novel error-free (infinite-precision) architecture for the fast implementation of 8x8 2-D Discrete Cosine Transform is presented, which eliminates the requirements to approximate the transformation matrix elements by obtaining their exact representations and hence mapping the transcendental functions without any errors.
Practical fast 1-D DCT algorithms with 11 multiplications
TLDR
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.
Shortening the critical path in CORDIC-based approximations of the eight-point DCT
  • M. Parfieniuk
  • Computer Science
    2008 International Conference on Signals and Electronic Systems
  • 2008
TLDR
A novel family of CORDIC-based multiplierless algorithms for computing good approximations of the eight-point DCT with inherent orthogonality of computations, i.e. energy preservation between the signal and transform domains, regardless of the accuracy of DCT approximation.
FPGA implementation of short critical path CORDIC-based approximation of the eight-point DCT
TLDR
An efficient approach for multiplierless implementation for eight-point DCT approximation, which based on coordinate rotation digital computer (CORDIC) algorithm, to make critical path of corresponding circuits shorter and reduce the combinational delay of proposed scheme.
Structurally Orthogonal Finite Precision Implementation of the Eight Point DCT
  • M. Parfieniuk, A. Petrovsky
  • Computer Science
    2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings
  • 2006
TLDR
A novel approach to the finite precision implementation of the eight point discrete cosine transform (DCT) using the denormalized lattice and the three-value coordinate rotation digital computer (CORDIC) algorithm with double mu-rotations.
Algebraic Signal Processing Theory: Cooley–Tukey Type Algorithms for DCTs and DSTs
TLDR
This paper presents a systematic methodology to derive and classify fast algorithms for linear transforms by a stepwise decomposition of the associated signal models, or polynomial algebras.
Fast multiplierless approximations of the DCT with the lifting scheme
TLDR
The binDCT can be tuned to cover the gap between the Walsh-Hadamard transform and the DCT, and allows a 16-bit implementation, enables lossless compression, and maintains satisfactory compatibility with the floating-point DCT.
A Fast Computational Algorithm for the Discrete Cosine Transform
A Fast Discrete Cosine Transform algorithm has been developed which provides a factor of six improvement in computational complexity when compared to conventional Discrete Cosine Transform algorithms…
Algebraic Signal Processing Theory: Cooley–Tukey Type Algorithms for Real DFTs
In this paper, we systematically derive a large class of fast general-radix algorithms for various types of real discrete Fourier transforms (real DFTs) including the discrete Hartley transform (DHT)…
Efficient large size transforms for high-performance video coding
TLDR
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.
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