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} }
59 Citations
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References
SHOWING 1-10 OF 76 REFERENCES
Type-IV DCT, DST, and MDCT algorithms with reduced numbers of arithmetic operations
- Computer ScienceSignal Process.
- 2008
Direct methods for computing discrete sinusoidal transforms
- Computer Science
- 1990
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.
Simple FFT and DCT algorithms with reduced number of operations
- Computer Science
- 1984
Restructured recursive DCT and DST algorithms
- Computer Science, EngineeringIEEE Trans. Signal Process.
- 1994
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
- Computer Science, MathematicsICASSP
- 2003
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
- Computer Science, EngineeringIEEE Trans. Signal Process.
- 1991
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
- Computer Science
- 1980
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.
A Modified Split-Radix FFT With Fewer Arithmetic Operations
- Computer ScienceIEEE Transactions on Signal Processing
- 2007
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
- Computer ScienceICASSP '85. IEEE International Conference on Acoustics, Speech, and Signal Processing
- 1985
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.