Digital algorithms for prediction,differentiation and integration

Abstract

The subject is dealt with in three parts, covered in three consecutive papers as follows.

Part 1 presents a method of calculating the coefficients required in digital algorithms for prediction (including interpolation and extrapolation), differentiation and integration, both on and off line. It provides the means of computing rapidly, by hand or with the aid of a small calculator, the coefficients required for algorithms of any order up to eight.

Parts 2 and 3, to be published in subsequent issues, will consider the errors inherent in using the algorithms derived in Part 1 and draw significant conclusions about the interaction of quantisation level, sampling frequency, order of the algorithm and the effects of these quantities on the accuracy of the results. Part 2 will deal with prediction and integration algorithms; Part 3 with differentiation.