We know that when the space function is continuous and aperiodic that it’s Fourier transform is also continuous and aperiodic. When the space function becomes periodic, we then have the Fourier series, which is discrete in the frequency domain. Likewise, we have just learned that when the function is discrete in space, its Fourier transform is continuous and periodic in the frequency variable. There is one block left - the block where both the space variable and the frequency variable are discrete. Based on symmetry, we would also expect the functions to be periodic in both space and in frequency. Is this the case too? We will see now that this last block is occupied by the discrete Fourier transform (or DFT).