Linear interpolation models for rapidly-sampled data

A numerically stable linear interpolation model for time series obtained by rapidly sampling continuous-time processes is developed. This model is based on the use of a second-order incremental difference operator in place of the forward shift operator conventionally used to model discrete-time dynamics. Unlike conventional shift-based models, this model has a meaningful limit as the sampling period goes to zero. Moreover, this model is more parsimonious than a difference-based predictor-type model developed previously for such situations. An O(n²) algorithm for estimating n^th-order model parameters is derived by exploiting a Hankel property of the linear interpolation model formulated by the difference operator defined in this paper. Numerical results show that this algorithm produces significantly lower relative error with finite wordlength computations than the conventional shift-based algorithm does, especially at high sampling rates.