The local structure and regime transition in a gas-liquid bubble column are studied via multi-resolution analysis of the local gas holdup signal. We show that the flow in a bubble column is characterized by the energy content of the measured gas holdup signal in the time-frequency plane, and intermittence of the gas holdup signal, as characterized by its multifractal nature. The measured signal is decomposed into its contributions in various regions of time and frequency using wavelet-based techniques. We show that the energy distribution in time and frequency provides greater insight into the physical processes underlying the gas-liquid flow, and may be used for on-line regime identification. The intermittence of the measured signal allows characterization of the transition of the flow from the homogeneous to the heterogeneous flow regime. Both, the time-frequency distribution of energy, and the intermittence of the local gas holdup signal, are extracted via techniques. derived from wavelet theory. Thus, wavelet analysis provides a rigorous framework for unifying statistical, spectral and fractal analysis methods.