3-D fast algorithm for the 3-D New Mersenne Number Transform

The New Mersenne Number Transform (NMNT) has been introduced in order to solve the problem of short transform lengths associated with other Mersenne number transforms (MNTs). In this paper, the three-dimensional NMNT and the 3-D radix-2×2×2 fast algorithm are introduced and discussed. The mathematical derivation of the new algorithm is presented and the number of arithmetic operations is calculated and compared to the row-column approach. Using single and multiple butterflies implementations, the radix-2×2×2 is found to reduce the number of arithmetic operations significantly.