Removing Large-scale Variations in Regularly and Irregularly Spaced Data

In many astrophysical systems, smooth large-scale variations coexist with small-scale fluctuations. For example, a large-scale velocity or density gradient can exist in molecular clouds that have small-scale fluctuations by turbulence. In redshifted 21cm observations, we also have two types of signals - the Galactic foreground emissions that change smoothly and the redshifted 21cm signals that fluctuate fast in frequency space. In many cases, the large-scale variations make it difficult to extract information on small-scale fluctuations. We propose a simple technique to remove smooth large-scale variations. Our technique relies on multi-point structure functions and can obtain the magnitudes of small-scale fluctuations. It can also be used to design filters that can remove large-scale variations and retrieve small-scale data. We discuss how to apply our technique to irregularly spaced data, such as rotation measure observations toward extragalactic radio point sources.