This paper considers general, pure linear prediction schemes, where the prediction of the input signal is based on IIR-filtered versions of the one-sample-delayed input signal. Properties of these schemes are discussed, in particular, the whitening property and the realization and stability of the synthesis filter. In contrast to warped linear prediction, the synthesis filter can be realized in a way similar to the analysis filter. Furthermore, we prove that, at least for a specific class of systems, input data windowing for the calculation of the optimal prediction coefficients guarantees the stability of the synthesis filters. By simulation we show that the proposed prediction scheme, using properly parameterized Laguerre or Kautz systems, shows a behavior similar to that of warped linear prediction.