Type-II/III DCT/DST algorithms with reduced number of arithmetic operations

@article{Shao2008TypeIIIIIDA,
  title={Type-II/III DCT/DST algorithms with reduced number of arithmetic operations},
  author={Xuancheng Shao and Steven G. Johnson},
  journal={Signal Process.},
  year={2008},
  volume={88},
  pages={1553-1564}
}

Figures and Tables from this paper

Type-IV DCT, DST, and MDCT algorithms with reduced numbers of arithmetic operations
Odd type DCT/DST for video coding: Relationships and low-complexity implementations
TLDR
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.
Efficient Split-Radix and Radix-4 DCT Algorithms and Applications
TLDR
The proposed split-radix and radix-4 Discrete Cosine Transform algorithms attain the lowest theoretical multiplication complexity and arithmetic complexity for 8-point DCT II/III matrices and are more efficient than the Radix-2 DCT algorithms.
Realization of Systolic Architecture of Discrete Cosine Transform
  • Riya Jain, Priyanka Jain
  • Computer Science
    2021 International Conference on Computer Communication and Informatics (ICCCI)
  • 2021
TLDR
A DCT algorithm for N=16 where r=2 that computes 1D DCT is implemented that is based on systolic architecture and it utilizes Pre-Processing Units and Processing Elements to realize the same.
CORDIC-Based Unified Architectures for Computation of DCT/IDCT/DST/IDST
TLDR
The unfolding technique is used to overcome the problem of difficult to realize pipeline that occur in iterative CORDIC algorithms and has a superior performance in terms of hardware complexity, control complexity, throughput, scalability, modularity, and pipelinability.
Small-Size FDCT/IDCT Algorithms with Reduced Multiplicative Complexity
TLDR
This article proposes a set of parallel algorithms for the fast implementation of FDCT/IDCT and shows the effectiveness of the proposed solutions is justified by the possibility of the factorization of theFDCT/ IDCT matrices, which leads to a decrease in computational and implementation complexity.
Mixed-Radix Algorithm for the Computation of Forward and Inverse MDCTs
TLDR
A new mixed-radix algorithm for efficiently computing the MDCT/IMDCT is presented and it is shown that this algorithm is more suitable for parallel implementation and particularly suitable for the layer III of MPEG-1 and MPEG-2 audio encoding and decoding.
Canonic FFT flow graphs for real-valued even/odd symmetric inputs
TLDR
The FFT computation whose inputs are not only real but also even/odd symmetric, which indeed lead to the well-known discrete cosine and sine transforms (DCTs and DSTs) is considered.
Implementation and Optimization of Multi-dimensional Real FFT on ARMv8 Platform
TLDR
This paper implements 1D and 2D real DFT on ARMv8 platform which is the flagship architecture of ARM and proposes a cache-aware blocking approach to improve cache performance.
...
...

References

SHOWING 1-10 OF 76 REFERENCES
Type-IV DCT, DST, and MDCT algorithms with reduced numbers of arithmetic operations
Direct methods for computing discrete sinusoidal transforms
TLDR
By means of the Kronecker matrix product representation, the 1-D algorithms introduced in the paper can readily be generalised to compute transforms of higher dimensions and are more stable than and have fewer arithmetic operations than similar algorithms proposed by Yip and Rao.
Restructured recursive DCT and DST algorithms
TLDR
These new structured recursive algorithms are able to decompose the DCT and the DST into two balanced lower-order subproblems in comparison to previous research works, and require fewer hardware components than other recursive algorithms.
Cooley-Tukey FFT like algorithms for the DCT
TLDR
A theorem is presented that decomposes a polynomial transform into smallerPolynomial transforms, and it is shown that the FFT is obtained as a special case, which is used to derive a new class of recursive algorithms for the discrete cosine transforms of type II and type III.
A new algorithm to compute the DCT and its inverse
  • Weiping Li
  • Computer Science, Engineering
    IEEE Trans. Signal Process.
  • 1991
TLDR
A novel algorithm to convert the discrete cosine transform (DCT) to skew-circular convolutions is presented and it is shown that the inverse DCT (IDCT) can be computed using the same building blocks which are used for computing the DCT.
A fast cosine transform in one and two dimensions
TLDR
The discrete cosine transform (DCT) of an N-point real signal is derived by taking the discrete Fourier transform (DFT) of a 2N-point even extension of the signal and the method is extended to two dimensions, with a saving of 1/4 over the traditional method that uses the DFT.
Fast and numerically stable algorithms for discrete cosine transforms
A Modified Split-Radix FFT With Fewer Arithmetic Operations
TLDR
A simple recursive modification of the split-radix algorithm is presented that computes the DFT with asymptotically about 6% fewer operations than Yavne, matching the count achieved by Van Buskirk's program-generation framework.
Implementation of "Split-radix" FFT algorithms for complex, real, and real symmetric data
  • P. Duhamel, H. Hollmann
  • Computer Science
    ICASSP '85. IEEE International Conference on Acoustics, Speech, and Signal Processing
  • 1985
TLDR
This algorithm belongs to that class of recently proposed 2n-FFT's which present the same arithmetic complexity (the lowest among any previously published one) and can easily be applied to real and real symmetric data with reduced arithmetic complexity by removing all redundancy in the algorithm.
...
...