Edoardo Milotti - Research on noise processes

Many simulations of stochastic processes require colored noises, and I have recently proposed an exact numerical method to simulate power-law noises. The method can be extended to more general colored noises, and  is exact for all time steps, even when they are unevenly spaced (as may often happen for astronomical data). The algorithm has a well-behaved computational complexity, it produces a nearly perfect Gaussian noise, and its computational efficiency depends on the required degree of noise Gaussianity.




The figure shows a normalized noise process with power-law spectrum 1/f^{1.5} produced by my generator. This record contains 2^{18} = 262144 samples. Time does not start from 0 because the initial part of the noise record is used for initialization, and is in arbitrary units.

The process shown in this figure belongs to the class of 1/f noises.

Recent papers

1. E. Milotti: “New version of PLNoise: a package for exact numerical simulation of power-law noise”, (preprint arXiv:physics/0612104)

2. E. Milotti: "PLNoise: a package for exact numerical simulation of power-law noises", Comp. Phys. Comm., 175 (Amsterdam, 2006) 212 (abstract)
   
   
3. E. Milotti: "Model-based fit procedure for power-law-like spectra" J. Comp. Phys. 217 (Amsterdam, 2006) 834 (abstract)
   
   
4. E. Milotti: "Exact numerical simulation of power-law noises", Phys. Rev. E 72 (New York, 2005) 056701