Based on the Fourier transform and spatial filtering theory of spectrum, the theoretical analysis of the light intensity and phase modulation of Gaussian beam after spatial filtering by 4F system is carried out. The MATLAB mathematics software is used to simulate the image formed by the high-pass and low-pass filtering of the "light" screen after 4F system. The differential screen was designed by ourselves, and the edge enhancement effect was realized by changing the phase of the diffracted light. The simulation results are in good agreement with the experimental data. Through theoretical simulation, the physical connotation of Gaussian beam Fourier transform and spatial filtering optical phenomena is vividly and deeply revealed, which lays a foundation for the design and effect demonstration of functional filters.