How to optimize image convolution

First, the image convolution:

Two, DFT --- discrete Fourier transform (Discrete Fourier Transform)

      1, Fourier series (DFS): represents a family of orthogonal periodic signal may be a complete sine wave obtained by linear combination.

                                                Frequency relationship is established.

                                 

      2, a discrete Fourier transform (DFT)

           1) Why Dirac ( ) function: