An efficient algorithm for cyclic convolution based on fast-polynomial and fast-W transforms

This paper first presents a fastW-transform (FWT) algorithm for computing one-dimensional cyclic and skew-cyclic convolutions. By using this FWT in conjunction with the fast polynomial transform (FPT), an efficient algorithm is then proposed for calculating the two-dimensional cyclic convolution (2D CC). Compared to the conventional row-column 2D discrete Fourier transform algorithm or the FPT Fast Fourier transform algorithm for 2D CC, the proposed algorithm achieves 65% or 40% savings in the number of multiplications, respectively. The number of additions required is also reduced considerably.[PUBLICATION ABSTRACT]