Unaliasing of aliased line component frequencies

Abstract

This paper is concerned with undoing aliasing effects, which arise from discretely sampling a continuous‐time stochastic process. Such effects are manifested in the frequency‐domain relationships between the sampled and original processes. The authors describe a general technique to undo aliasing effects, given two processes, one being a time‐delayed version of the other. The technique is based on the observations that certain phase information between the two processes is unaffected by sampling, is completely determined by the (known) time delay, and contains sufficient information to undo aliasing effects. The authors illustrate their technique with a simulation example. The theoretical model is motivated by the helioseismological problem of determining modes of solar pressure waves. The authors apply their technique to solar radio data, and conclude that certain low‐frequency modes known in the helioseismology literature are likely the result of aliasing effects. The Canadian Journal of Statistics 38: 116–135; 2010 © 2010 Statistical Society of Canada