R. Baraniuk and M. Crouse, "Fast, Exact Synthesis of Gaussian and nonGaussian Long-Range-Dependent Processes," 2009.
Originally submitted to IEEE Transactions on Information Theory, August 1999.
1/f noise and statistically self-similar random processes such as fractional Brownian motion (fBm) and
fractional Gaussian noise (fGn) are fundamental models for a host of real-world phenomena, from network
traffic to DNA to the stock market. Synthesis algorithms play a key role by providing the feedstock
of data necessary for running complex simulations and accurately evaluating analysis techniques. Unfortunately,
current algorithms to correctly synthesize these long-range dependent (LRD) processes are
either abstruse or prohibitively costly, which has spurred the wide use of inexact approximations. To fill
the gap, we develop a simple, fast (O(N logN) operations for a length-N signal) framework for exactly
synthesizing a range of Gaussian and nonGaussian LRD processes. As a bonus, we introduce and study
a new bi-scaling fBm process featuring a "kinked" correlation function that exhibits distinct scaling laws
at coarse and fine scales.
National Science Foundation, grant no. MIP–9457438, the Office of Naval Research, grant
no. N00014–99–1–0813, by DARPA/AFOSR, grant no. F49620-97-1-0513, and by the Texas Instruments Leadership University
Rice ECE Department Technical Report TREE9913
||dc.subject||fractional Brownian motion
fractional Gaussian noise
Fast, Exact Synthesis of Gaussian and nonGaussian Long-Range-Dependent Processes