Efficient number theoretic transforms for convolutions using ROM arrays

Siu, Wan-Chi; Constantinides, A.G.

doi:10.1080/00207218908921087

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2014

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“…Transform domain methods are the most common way including fast Fourier transform (FFT) (Chang & Nguyen, 2008), Agarwal-Cooley (AC) short convolution algorithms, number theoretic transform (NTT) (Agarwal & Burrus, 1975;Bhattacharya & Agarwal, 1984;Siu & Constantinides, 1989;Toivonen & Heikkila, 2006), Winograd Fourier transform algorithm (WFTA) (Silverman, 1989) and discrete cosine transform (DCT) (Tatsaki, Burekas, & Goutis, 1994) along with their variants.…”

Section: Introductionmentioning

confidence: 99%

A low complexity realisation of Winograd number theoretic transform and its application

Hua

Zheng

et al. 2014

International Journal of Electronics

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This paper investigates a novel structure for the Winograd number theoretic transform algorithm (WNTA) to reduce the computation load. The proposed computing structure exploits the multiple constant multiplication to replace the standard multiplication, then, the multiplication of the WNTA can be realised in a shift-add way, which definitely decreases the complexity of WNTA and maintains the computing accuracy. Typical applications, such as the convolution and the filtering operation, are tested by computer simulations, while the result demonstrates that the proposed scheme is superior to conventional schemes in terms of the trade-off between the complexity.

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