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

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Title: Fast, Exact Synthesis of Gaussian and nonGaussian Long-Range-Dependent Processes
Author: Baraniuk, Richard; Crouse, Matthew
Type: Tech Report
Citation: R. Baraniuk and M. Crouse, "Fast, Exact Synthesis of Gaussian and nonGaussian Long-Range-Dependent Processes," 2009.
Abstract: 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.
Date Published: 2009-04-15

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  • DSP Publications [508 items]
    Publications by Rice Faculty and graduate students in digital signal processing.
  • ECE Publications [1043 items]
    Publications by Rice University Electrical and Computer Engineering faculty and graduate students