Fractional Fourier transform in spherical polar coordinates

Abstract

The fractional Fourier transform (FRFT) is a generalized form of the Fourier transform (FT), and it is another important class of time-frequency analysis tool in signal processing. In this paper, we generalize the three-dimensional (3-D) FRFT to the spherical polar coordinates setting. Then, some properties are obtained associate with the 3-D FRFT such as the inverse transform, spatial shift and multiplication. Moreover, the new convolution theorem and correlation theorem for the 3-D FRFT is studied by these properties, and then Parseval theorem of the 3-D FRFT is also obtained.