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In this contribution, a time-varying linear prediction method is applied to speech processing. In contrast to the commonly used linear prediction approach, the proposed time-varying method considers the continuous time evolution of the vocal tract and, additionally, avoids block-wise processing. On the assumption that the linear predictor coefficients evolve linearly in sections and continuously over the whole signal, the optimum time-varying coefficients can be determined quasi-analytically by a least mean square approach. The investigations show that the method fits very well the realization of a time-varying pre-emphasis. Furthermore, the results show that the method is suitable for time-varying inverse filtering.