Computationally efficient linear prediction from past samples of a band-limited signal and its derivative

Formulas for linear prediction of a band-limited signal are developed, where the signal may be either deterministic or wide-sense stationary. The prediction formulas are based on finite differences modified by two or more parameters, and finite differences allow the formulas to be easily adapted to changes in order of the prediction. It is shown that a formula to predict the next signal value from a set of past, equally spaced values is a formula that can be extended to provide prediction at points even beyond that. In addition, the formula is extended to a difference scheme involving an arbitrary number of parameters as well as to a formula that includes samples of the derivative of the signal. This approach differs from that of solving the normal (or Yule-Walker) equations, but it has the advantage that the (suboptimal) prediction coefficients are independent of the particular signal spectrum or autocorrelation function.<
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