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Volume 13, Issue 4
The Multiplicative Complexity and Algorithm of the Generalized Discrete Fourier Transform (GFT)

Y. H. Zeng

J. Comp. Math., 13 (1995), pp. 351-356.

Published online: 1995-08

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  • Abstract

In this paper, we have proved that the lower bound of the number of real multiplications for computing a length $2^{t}$ real GFT(a,b) $(a=\pm 1/2,b=0\ or\ b=\pm 1/2,a=0)$ is $2^{t+1}-2t-2$ and that for computing a length $2^{t}$ real GFT(a,b)$(a=\pm 1/2, b=\pm 1/2)$ is $2^{t+1}-2$. Practical algorithms which meet the lower bounds of multiplications are given.

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@Article{JCM-13-351, author = {Y. H. Zeng}, title = {The Multiplicative Complexity and Algorithm of the Generalized Discrete Fourier Transform (GFT)}, journal = {Journal of Computational Mathematics}, year = {1995}, volume = {13}, number = {4}, pages = {351--356}, abstract = {

In this paper, we have proved that the lower bound of the number of real multiplications for computing a length $2^{t}$ real GFT(a,b) $(a=\pm 1/2,b=0\ or\ b=\pm 1/2,a=0)$ is $2^{t+1}-2t-2$ and that for computing a length $2^{t}$ real GFT(a,b)$(a=\pm 1/2, b=\pm 1/2)$ is $2^{t+1}-2$. Practical algorithms which meet the lower bounds of multiplications are given.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9277.html} }
TY - JOUR T1 - The Multiplicative Complexity and Algorithm of the Generalized Discrete Fourier Transform (GFT) AU - Y. H. Zeng JO - Journal of Computational Mathematics VL - 4 SP - 351 EP - 356 PY - 1995 DA - 1995/08 SN - 13 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9277.html KW - AB -

In this paper, we have proved that the lower bound of the number of real multiplications for computing a length $2^{t}$ real GFT(a,b) $(a=\pm 1/2,b=0\ or\ b=\pm 1/2,a=0)$ is $2^{t+1}-2t-2$ and that for computing a length $2^{t}$ real GFT(a,b)$(a=\pm 1/2, b=\pm 1/2)$ is $2^{t+1}-2$. Practical algorithms which meet the lower bounds of multiplications are given.

Y. H. Zeng. (1995). The Multiplicative Complexity and Algorithm of the Generalized Discrete Fourier Transform (GFT). Journal of Computational Mathematics. 13 (4). 351-356. doi:
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