Implementación computacional de la transformada fraccional de Fourier discreta

Abstract

This paper provides an introduction of the fractional Fourier transform (FRFT) and describes the process of implementing the discrete fractional Fourier transform (DFRFT) based on the spectral decomposition of the discrete Fourier transform (DFT) matrix operator. In the last decade, the FRFT has been considered as a useful tool for signal processing applications. In the theoretical evolution of FRFT, many definitions of the DFTFT have been proposed in the literature. However, few definitions of the DFRFT present similar results to those provided by the FRFT without losing its most important properties. Therefore, some theoretical clarifications are made with respect to previous works. Moreover, the relationship between the FRFT and the DFRFT is also shown. Finally, in order to promote the use of this transform in the signal processing community, some algorithms of the DFRFT with low computational costs are described.