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Due to the switching action and the presence of parasitics, waveforms arising from power electronics circuits often contain high-frequency ringings embedded in slowly varying segments. Such a feature is consistent with the localization property of wavelets which has previously been exploited for fast approximations of steady-state waveforms. This paper proposes an improved and more robust approach for calculating the wavelet coefficients, exploiting the orthogonal property of the Chebyshev polynomials. Simulation results demonstrate the effectiveness of the new algorithm.