Integer 2-D Discrete Fourier Transform Pairs and Eigenvectors using Ramanujan’s Sum
A novel method to generate integer 2-D discrete Fourier transform (DFT) pairs and eigenvectors was proposed. Using projection slice theorem and Ramanujan's sum, the 2-D spatial signal is decomposed into 2-D gcd-delta functions which contain only zeroes and ones. The 2-D DFT of 2-D gcd-delta functions are also integers. The integer 2-D DFT pairs can be applied to obtain integer 2-D DFT eigenvectors and 2-D period detection. The connection between 2-D gcd-delta function and multidimensional Ramanujan's Sum is also illustrated with two numerical examples.