Fast, Exact Synthesis of Gaussian and nonGaussian Long-Range-Dependent Processes
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.