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Title:
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Fast, Exact Synthesis of Gaussian and nonGaussian Long-Range-Dependent Processes |
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Author:
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Baraniuk, Richard; Crouse, Matthew
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Type:
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Tech Report |
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Citation:
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R. Baraniuk and M. Crouse, "Fast, Exact Synthesis of Gaussian and nonGaussian Long-Range-Dependent Processes," 2009. http://hdl.handle.net/1911/21941. |
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Abstract:
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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. |
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Date Published:
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2009-04-15 |
