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

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dc.contributor.author Baraniuk, Richard
Crouse, Matthew
dc.date.accessioned 2009-04-15T16:59:06Z
dc.date.available 2009-04-15T16:59:06Z
dc.date.issued 2009-04-15
dc.identifier.uri http://hdl.handle.net/1911/21941
dc.description Originally submitted to IEEE Transactions on Information Theory, August 1999.
dc.description.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.
dc.description.sponsorship 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 Program
dc.language.iso en_US
dc.relation.ispartofseries Rice ECE Department Technical Report;TREE9913
dc.subject fractional Brownian motion
FFT
random process
fractional Gaussian noise
synthesis
dc.title Fast, Exact Synthesis of Gaussian and nonGaussian Long-Range-Dependent Processes
dc.type Tech Report
dc.identifier.citation R. Baraniuk and M. Crouse, "Fast, Exact Synthesis of Gaussian and nonGaussian Long-Range-Dependent Processes," 2009.
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    Publications by Rice Faculty and graduate students in digital signal processing.
  • ECE Publications [1028 items]
    Publications by Rice University Electrical and Computer Engineering faculty and graduate students