Discrete Fourier transform computation via the Walsh transform

Abstract

This paper presents a new computational algorithm for the discrete Fourier transform (DFT). In an algorithm proposed here, DFT coefficients are computed via the Walsh transform (WT). The number of multiplications required by the new algorithm is approximately NL/6, where N is the number of data points and L is the number of Fourier coefficients desired. As such, it is superior to the fast Fourier transform (FFT) approach in applications where L is relatively small compared with N. It is also useful in cases where the Walsh and Fourier coefficients are both desired.