Real time reconstruction errors in digital telemetry

It is known that excellent polynomial approximations can be constructed for any given continuous function, f. If f is not known the author examines what can be said of a low order polynomial approximation based on samples of f. This question is of practical significance in digital telemetry applications where bandwidth constraints require minimizing signal sampling rates. The author answers the question under the assumption, consistent with normal engineering practice for telemetry signals, that f is bandwidth limited. Worst case error bounds as a function of sampling rate are developed for three classes of digital-to-analog converters. Results are compared with some spline errors given by C. de Boor (1978). For a fixed design goal on worst case errors, it is clear that significant reductions in sample rate are possible by using higher order interpolation. The required circuitry for a real-time reconstruction is of straightforward design