In this paper, we extend the concept of Eigen functions of the Fourier transform discussed by P. P. Vaidyanathan [9]. But for a scaling factor, if there is no change in the function after the application of the Fourier transform, we term them as Eigen functions of the Fourier transform. Gaussian is the well known Eigen function. But, there are various other functions that can be developed systematically. The theory developed by P. P. Vaidyanathan for 1-D signals is extended for 2-D case in this paper. We also presented extensions for the complex signal case. © 2012 IEEE.