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Astron. Astrophys. 347, 630-633 (1999)

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The relation of the Allan- and [FORMULA]-variance to the continuous wavelet transform

M. Zielinsky and J. Stutzki

I. Physikalisches Institut, Universität zu Köln, Zülpicherstrasse 77, D-50937 Köln, Germany (zielinsky, stutzki@ph1.uni-koeln.de)

Received 23 December 1998 / Accepted 14 April 1999


This paper is understood as a supplement to the paper by Stutzki et al. 1998, where we have shown the usefulness of the Allan-variance and its higher dimensional generalization, the [FORMULA]-variance, for the characterization of molecular cloud structures. In this study we present the connection between the Allan- and [FORMULA]-variance and a more popular structure analysis tool: the wavelet transform. We show that the Allan- and [FORMULA]-variances are the variances of wavelet transform coefficients.

Key words: ISM: clouds – ISM: structure

Send offprint requests to: zielinsky@ph1.uni-koeln.de

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© European Southern Observatory (ESO) 1999

Online publication: June 30, 1999