Fast algorithms for reduction a modulo polynomial and vandermonde transform using FFT

This paper shows on how the real algorithms for the reduction a modulo arbitrary polynomial and fast Vandermonde transform (FVT) are realized on computer using fast Fourier transform (FFT). This real-valued FVT algorithm on the developed fast reduction polynomial algorithm is based. The realization of FVT algorithm on computer with real multiplicative complexity O(2Nlog
2
²
N) and real additive complexity O(6Nlog
2
²
N) is obtained. New FVT algorithm is applied in digital signal, filtering and interpolation problems.