In this paper, we propose a novel scheme that jointly employs sliding-window (SW) Prony and the discrete Fourier transform (DFT) for estimating power-quality indices based on the time-frequency analysis of non-stationary waveforms in power-system disturbances. These indices, recently proposed in the relevant literature, require the separation of the waveform in two parts, i.e., the fundamental component and the disturbance waveform. In the proposed scheme, Prony's method was applied to calculate only the fundamental component from low-pass, filtered data, while the disturbance waveform is obtained by using DFT. The application of Prony's method only to the fundamental component reduces the computational effort required by this method significantly and allows the size of the window of the DFT to be set as an integer multiple of the estimated fundamental period, which minimizes the spectral leakage of the DFT. The main advantages of the proposed, new approach include high resolution and accuracy in the estimation of indices and significant reduction of the computational cost. Experiments were conducted and comparisons were made using both synthetic and measured data. The results confirmed the effectiveness and efficiency of the proposed scheme. [ABSTRACT FROM AUTHOR]