On Sampling Methods for Linear Scale-Invariant Systems

Abstract : We study a class of self-similar processes that are not stationary, nor have stationary increments. They are called Euler-Cauchy (EC) processes and are built as output of linear scale-invariant parametric systems. This article study several discretization methods of EC processes which are not bandlimited processes: direct sampling, bilinear transformation and approximation on fractional B-splines. For the three different methods, we obtain theoretical formulae and compute numerical realizations and properties.