Analysis of Competition between Patterns by Using Fast Fourier Transform

The Fast Fourier Transform is an important method in analysis patterns. In this paper, the FFT is used to the images of the patterns to analyze the competition of the modes and the evolution of the patterns. With the increase of applied voltage the competition between patterns are obtained in dielectric barrier discharge system with two liquid electrodes at the pressure p = 0.3 atm and p = 0.2 atm. The change of the modes and the Fourier spectral density reveal the process of the evolvement. It is found that the modes interact with each other and satisfy the three-wave resonance when the gas pressure is 0.3 atm, so, the hexagonal superlattice pattern is observed in the discharge area. However, only one mode dominates in the spatial power spectrum when the gas pressure becomes lower to 0.2 atm, so the square pattern dominates in the discharge area instead of the hexagonal superlattice pattern.