Skip to Main content Skip to Navigation
Journal articles

SINGULAR RANDOM SIGNAL

Abstract : Singular random signals are characterized by the fact that their values at each time are singular random variables, which means that their distribution functions are continuous but with a derivative almost everywhere equal to zero. Such random variables are usually considered as without interest in engineering or signal processing problems. The purpose of this paper is to show that very simple signals can be singular. This is especially the case for autoregressive moving average (ARMA) signals defined by white noise taking only discrete values and filters with poles located in a circle of singularity introduced in this paper. After giving the origin of singularity and analyzing its relationships with fractal properties, various simulations highlighting this structure will be presented. Index Terms ARMA models, fractals, stochastic signals.
Complete list of metadatas

Cited literature [9 references]  Display  Hide  Download

https://hal-centralesupelec.archives-ouvertes.fr/hal-01707533
Contributor : Bernard Picinbono <>
Submitted on : Monday, February 12, 2018 - 7:34:55 PM
Last modification on : Wednesday, September 16, 2020 - 4:47:32 PM
Long-term archiving on: : Tuesday, May 8, 2018 - 12:35:31 AM

File

Singular Signals.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01707533, version 1

Citation

Bernard Picinbono, Jean-Yves Tourneret. SINGULAR RANDOM SIGNAL. IEEE Transactions on Signal Processing, Institute of Electrical and Electronics Engineers, 2005, 53, pp.499 - 504. ⟨hal-01707533⟩

Share

Metrics

Record views

349

Files downloads

121