pink_noise_2010_fsu "Colored Noise Functions for Stochastic Analysis", presents a procedure for generating colored noise functions. This paper was written with Max Gunzburger and Miro Stoyanov at Florida State University in 2010.
This paper considers alternatives to the common use of white noise for the analysis of the behavior of a system known to be subject to random perturbations. White noise is a natural choice to model noise, but it is not the only choice, and its use implies certain statistical properties of the noise that may not correspond with experimental or theoretical considerations.
We can develop a parameterized family of noise functions, with white noise corresponding to ALPHA = 0, and Brownian motion with ALPHA = 2. For intermediate choices of ALPHA, there are corresponding noise functions with behavior that varies "smoothly" between these two well-understood cases. These intermediate functions are known as colored noise functions; the case ALPHA = 1 is of particular interest.