A Class of Fast Methods for Processing Irregularly Sampled or Otherwise Inhomogeneous One-Dimensional Data

摘要

With the ansatz that a data set's correlation matrix has a certainparametrized form (one general enough, however, to allow the arbitraryspecification of a slowly-varying decorrelation distance and populationvariance) the general machinery of Wiener or optimal filtering can be reducedfrom $O(n^3)$ to $O(n)$ operations, where $n$ is the size of the data set. Theimplied vast increases in computational speed can allow many common sub-optimalor heuristic data analysis methods to be replaced by fast, relativelysophisticated, statistical algorithms. Three examples are given: datarectification, high- or low- pass filtering, and linear least squares fittingto a model with unaligned data points.