More precisely take a set of points, do a DFT, then make it infinite by making the rest of the terms 0. You now have the Fourier series of a periodic function that takes hits all of those points. Furthermore it is the "smallest" possible such periodic function in the L2 norm on periodic functions.
More precisely take a set of points, do a DFT, then make it infinite by making the rest of the terms 0. You now have the Fourier series of a periodic function that takes hits all of those points. Furthermore it is the "smallest" possible such periodic function in the L2 norm on periodic functions.