So the Gaussian function is an eigenfunction of the Fourier transform because it transforms into itself, right?
But this isn't true for the sampled Gaussian in the DFT because the tails of the function are truncated, right?
the discrete counterpart of the continuous Gaussian in that it is the solution to the discrete diffusion equation (discrete space, continuous time), just as the continuous Gaussian is the solution to the continuous diffusion equation
Does that mean it also DFT transforms exactly into itself? If not, is there a similar Gaussian-like function that does?