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A Multifractal Wavelet Model for Positive Processes

By Matthew Crouse, Rudolf H. Riedi, Vinay Joseph Ribeiro and Richard G. BaraniukMatthew Crouse, Rudolf H. Riedi, Vinay Joseph Ribeiro and Richard G. Baraniuk


Conference PaperIn this paper, we develop a new multiscale modeling framework for characterizing positive-valued data with long-range-dependent correlations (1/f noise). Using the Haar wavelet transform and a special multiplicative structure on the wavelet and scaling coefficients to ensure positive results, the model provides a rapid O(N) cascade algorithm for synthesizing N-point data sets. We study both the second-order and multifractal properties of the model, the latter after a tutorial overview of multifractal analysis. We derive a scheme for matching the model to real data observations and, to demonstrate its effectiveness, apply the model to network traffic synthesis. The flexibility and accuracy of the model and fitting procedure result in a close fit to the real data statistics (variance-time plots and moment scaling) and queuing behavior. Although for illustrative purposes we focus on applications in network traffic modeling, the multifractal wavelet model could be useful in a number of other areas involving positive data, including image processing, finance, and geophysics

Topics: multifractal, wavelet model, Signal Processing for Networking, Multifractals, multifractal, wavelet model
Year: 2006
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