Liquid membrane oscillators very frequently have an irregular oscillatory behavior. Fourier transformation cannot be used for these nonstationary oscillations to establish their power spectra. This important point seems to be overlooked in the field of chemical oscillators. A new approach is presented here based on Gábor transformation allowing one to obtain power spectra of any kind of oscillations that can be met experimentally. The proposed Gábor analysis is applied to a liquid membrane oscillator containing a cationic surfactant. It was found that the power spectra are strongly influenced by the presence of various added substances.