Singular ARMA signals

Singular random signals are collections of singular random variables indexed over time. Singular random variables have continuous distribution with derivatives equal to zero almost everywhere. Such random variables do not seem interesting in signal processing. On the contrary, the paper shows that simple signals can be singular. This is especially the case of ARMA signals generated from discrete white noise with poles located inside a so-called singularity circle. The origin of singularity and its relations to a fractal structure are presented along with various simulations illustrating the theoretical results.