The Multiplicative Complexity and Algorithm of the Generalized Discrete Fourier Transform (GFT)

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.