MULTIRATE POLYNOMIAL PREDICTION WITH UNEVENLY SPACED SAMPLES

A method for polynomial prediction with unevenly spaced samples is proposed for dynamic upsampling purposes, frequently needed in digital signal-processing applications. The procedure is based on Newton's divided-difference interpolation formula, which allows prediction along a polynomial of degree n if the samples are arbitrarily spaced. For this purpose, it is necessary to store n + 1 latest value pairs (x(i), y(i)) where x(i) is the time instant when the sample y(i) is available. Based on the (x(i), y(i)) pairs, the algorithm predicts y-samples for arbitrary values of x. Noise reduction techniques based on bandwidth limiting are discussed. As an application, a velocity measurement system is considered, based on pulse-width measuring, where the primary interest is in improving the accuracy at very low speeds.