Aliasing with Unequally Spaced Observations

Abstract

Data analysis with unequally spaced observations is approached by assuming that a finite number of observations are available at known locations in space or time. No assumptions are made about the distribution of the station locations. Two types of observational error are considered, stationary (or homogeneous) and independent. Variance transfer functions are calculated which, when multiplied by the signal spectrum or error spectrum and integrated, give the contribution to the variance of estimates. Operations such as smoothing, interpolation, estimating derivatives, gradients of two-dimensional fields, divergence of two-dimensional vector fields, and spectrum estimates are considered. Aliasing takes the form of irregular side lobes, and it is concluded that the variance transfer functions should be plotted in most practical situations involving unequally spaced observations. Simulation studies are presented where the station locations have a random distribution, but the analysis does not use this information and is applicable to any distribution of stations.