On Sampling Methods for Linear Scale-Invariant Systems

Pierre Borgnat (1)

1 Phys-ENS - Laboratoire de Physique de l'ENS Lyon

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.

Keywords: self-similarity; Euler-Cauchy process; sampling

Domains: Computer Science [cs]; Signal and Image Processing; Engineering Sciences [physics]; Signal and Image processing

Pierre Borgnat. On Sampling Methods for Linear Scale-Invariant Systems. IEEE International Conference in Acoustic, Speech, and Signal Processing (ICASSP) 2006, IEEE Signal Processing Society, May 2006, Toulouse, France. pp.III-345 III-348. ⟨ensl-00129551⟩