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Linear prediction has been successfully applied in many speech and audio processing systems. This paper presents the similarities and differences between two classes of linear prediction schemes, namely, Warped Linear Prediction (WLP) and Laguerre Linear Prediction (LLP). It is shown that both systems are closely related. In particular, we show that the LLP is in fact a WLP system where the optimization procedure is adapted such that the whitening property is automatically incorporated. The adaptation consists of a new linear constraint on the parameters. Furthermore, we show that an optimized WLP scheme where whitening is achieved by prefiltering before estimating the optimal coefficients results in a filter having all except the last reflection coefficient equal to those of the optimal LLP filter.