Construction of discrete-time linear scale-invariant systems using kernels

A linear scale invariant (LSI) system model in discrete-time was suggested by Zhao and Rao using a specialized dilation or scaling operation. This scaling operation relies on a frequency warping transformation between discrete-time and continuous-time frequencies. The DLSI systems have been shown to provide synthesis of self-similar random signals such as those seen in network traffic. In this paper, we provide a more general method for DLSI system modeling based on linear kernels. The alternative expression of DLSI system provided by linear kernels has several desirable properties lacking in the earlier formulation. In particular, the new formulation (a) allows commutativity between input and system characteristic sequence and (b) permits definition of a scale domain transform operator analogous to the Fourier transform for time-invariant systems.