Using a micro-gap dielectric barrier discharge (DBD) decive in a parallel plate geometry, the frequency of the saw-tooth voltage has been varied to investigate the discharge image, the light emission signal and the optical emission spectrum of the DBD by using argon as the working gas. It is found that with increasing frequency of the saw-tooth wave, DBD could be in a diffuse mode less than 10 kHz, then it transits to many micro-discharge filaments occupying the whole electrode area (higher than 35 kHz) after the coexistence of micro-discharge filaments and diffuse discharge. Waveform of the applied voltage and the light emission indicates that, at a lower saw-tooth wave frequency, the diffuse discharge emits a stepped light emission signal with a high duty ratio. When increasing the saw-tooth wave frequency, the light emission transits into a multi-pulsed mode after the emergence of micro-discharge filaments. Moreover, the number of the light pulses per half voltage cycle decreases with increasing the driving frequency. The light pulse number presents one per half voltage cycle (single pulsed discharge) when the saw-tooth wave frequency is higher than 35 kHz. Scanning the optiacl spectra of the discharge, it can find the second positive system of nitrogen molecule（C3Πu→B3Πu）, OH(A2Σ+→X2Π) and ArI. The spectral intensity of OH (3088 nm) and ArI (7504 nm) is investigated as a function of the saw-tooth wave frequency, and the results show that they both increase when increasing the saw-tooth wave frequency.