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Fast , Exact Synthesis of Gaussian and nonGaussianLong-Range-Dependent
| Content Provider | Semantic Scholar |
|---|---|
| Author | Crouse, Processes Matthew S. Baraniuk, Richard G. |
| Copyright Year | 1999 |
| Abstract | 1=f noise and statistically self-similar processes such as fractional Brownian motion (fBm) are vital for modeling numerous real-world phenomena, from network traac to DNA to the stock market. Although several algorithms exist for synthesizing discrete-time samples of a 1=f process, these algorithms are inexact, meaning that the covariance of the synthesized processes can deviate signiicantly from that of a true 1=f process. However, the Fast Fourier Transform (FFT) can be used to exactly and eeciently synthesize such processes in O(N log N) operations for a length-N signal. Strangely enough, the key is to apply the FFT to match the target process's covariance structure, not its frequency spectrum. In this paper, we prove that this FFT-based synthesis is exact not only for 1=f processes such as fBm, but also for a wide class of long-range dependent processes. Leveraging the exibility of the FFT approach, we develop new models for processes that exhibit one type of fBm scaling behavior over ne resolutions and a distinct scaling behavior over coarse resolutions. We also generalize the method in order to exactly synthesize various nonGaussian 1=f processes. Our nonGaussian 1=f synthesis is fast and simple. Used in simulations, our synthesis techniques could lead to new insights into areas such as computer networking, where the traac processes exhibit nonGaussianity and a richer covariance than that of a strict fBm process. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.dsp.rice.edu/publications/pub/fftMC.ps.Z |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
