"Fast" Linear Prediction and Its Application to NMR Spectroscopy

A general "fast" linear-prediction (FLP) algorithm is presented. It determines P linear-prediction coefficients from M equations in ∼ 9MP + 27/2P² operations by using only ∼ 5(M + P) locations of memory. The procedure does not rely on any assumption about the signal to be analyzed, and within numerical accuracy, it produces the same results as the QR method. It is demonstrated that, with the FLP routine, it is feasible to determine more than 10,000 linear-prediction coefficients.