Characterization of self-similarity properties of discrete-time linear scale-invariant systems

Discrete-time linear systems that possess scale-invariance properties even in the presence of continuous dilation were proposed by Zhao and Rao (1998, 1999). The principal purpose of this article is to describe results of subsequent investigation which have led to characterization of self-similarity properties of discrete-time signals synthesized by these systems. It is shown that white noise inputs to these linear scale invariant systems, which are unique in the DSP literature, produce self-similar outputs regardless of the marginal distribution of the noise. In most instances the output is fractional Gaussian. For heavy-tailed input distributions, the output is also heavy-tailed and self-similar. It is also shown that it is possible to synthesize statistically self-similar signals whose self-similarity parameters are consistent with those observed in network traffic