In this paper, light emission signal are analyzed from the pattern composed of hexagonal distributed micro-discharge filament by using a dielectric barrier discharge device in the mixed working gas of argon and air at atmospheric pressure. The experimental results show that the patterned discharge undergoes a scenario: stochastic filaments, hexagonal pattern, square pattern, honeycombed pattern, and stripe pattern with the applied voltage increasing. Through analyzing the temporal sequence of the different filaments in a hexagon, it has been found that the waveform of total light signals gives two pulses at each half cycle of the applied voltage. The spatial-temporal correlations between discharge filaments in hexagonal pattern are studied by analyzing the light emission signals from different discharge filaments in the hexagon pattern. The results show that the hexagonal pattern is an interleaving of two sub-patterns. These research results are of great importance for the further study of pattern formation dynamics and signal process in gas discharge systems.