On Sampling Methods for Linear Scale-Invariant Systems

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 bandli...

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Bibliographic Details
Main Author: Borgnat, P.
Format: Conference Proceeding
Language:English
Subjects:
Brownian motion
Deformable models
Gaussian noise
Interpolation
Random processes
Sampling methods
Signal processing
Signal sampling
Signal synthesis
Spline
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Summary: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
ISSN:1520-6149
2379-190X
DOI:10.1109/ICASSP.2006.1660661