In conventional one-step forward linear prediction, an estimate for the current sample value is formed as a linear combination of previous sample values. In this paper, a generalized form of this scheme is studied. Here, the prediction is not based simply on the previous sample values but on the signal history as seen through an arbitrary filterbank. It is shown in the paper how the coefficients of a modified model can be obtained and how the inverse and synthesis filters can be implemented. Various properties of such systems are derived in this article. As an example, a novel linear predictive system using inherently logarithmic frequency representation is introduced.