NEWTON-TYPE PREDICTORS - A SIGNAL-PROCESSING ORIENTED VIEWPOINT

Newton-type extrapolation and interpolation have been used for a long time by numerical analysts, who are mainly interested in temporal characteristics of the algorithms. In this paper, we study the spectral and implementation aspects of forward and backward predictors based on Newton-type extrapolation. Compact formulae for calculating the predictor coefficients are derived. Also suggestions for an appropriate primary signal bandwidth and practical predictor lengths are provided. The family of Newton-type predictors works accurately with different types of signals, particularly with low-order polynomials, when the SNR level is high. It is found out that those predictors have a partially symmetrical structure that leads to computationally efficient FIR implementations, especially with some DSP-ASIC technology when a one-cycle parallel multiplier is not available. A numerical example is presented that shows the potential of applying Newton-type predictors in reducing the required memory size of large look-up tables, used commonly to store consecutive values of transcendental functions in applications without math coprocessor support.