Discrete time processing of linear scale-invariant signals and systems

In this paper, we formulate a framework for discrete-time processing of Linear Scale Invariant (LSI) systems which are invariant to scale changes in time. Continuous-time LSI systems can be processed by Mellin and Modified Scale Transforms analogous to the use of the Laplace and Fourier Transforms in the continuous- time processing of LTI systems. In this work, we present the geometric sampling theorem to prevent aliasing in the scale domain. We also derive the perfect reconstruction filter in time domain, the discrete-time convolution sum, the Discrete Time Modified Scale Transform (DTMST) and the Discrete Modified Scale Transform (DMST) for geometrically sampled signals.