The relation of the Allan- and Delta-variance to the continuous wavelet transform

This paper is understood as a supplement to the paper by Stutzki et al. 199 8, where we have shown the usefulness of the Allan-variance and its higher dimensional generalization, the Delta-variance, for the characterization of molecular cloud structures. In this study we present the connection betwee n the Allan- and Delta-variance and a more popular structure analysis tool: the wavelet transform. We show that the Allan- and Delta-variances are the variances of wavelet transform coefficients.