Algorithms for the nonuniform acquisition and subsequent reconstruction of data

Algorithms are presented for the purposes of nonuniform sampling and reconstruction of data. The sampling procedure is based on the Adams-Bashforth-Moulton multistep predictor-corrector method for the solution of ordinary differential equations, with Newton backward differencing interpolation formulae facilitating sample rate changes. It is necessary to store 2n + 1 equispaced past values of t and the corresponding values of y, where y = g(t), and n is the order of the Adams methods. The technique is demonstrated using third order methods and the results compared with those obtained using second and fourth order forms. The data reconstruction algorithm for unevenly spaced data is based on a Lagrange cubic polynomial.