Title :
A simple statistical analysis of wavelet-based multifractal spectrum estimation
Author :
Gonçalves, Paulo ; Riedi, Rudolf ; Baraniuk, Richard
Author_Institution :
Inst. Nat. de Recherche en Inf. et Autom., Rocquencourt, France
Abstract :
The multifractal spectrum characterizes the scaling and singularity structures of signals and proves useful in numerous applications, from network traffic analysis to turbulence. Of great concern is the estimation of the spectrum from a finite data record. We derive asymptotic expressions for the bias and variance of a wavelet-based estimator for a fractional Brownian motion (fBm) process. Numerous numerical simulations demonstrate the accuracy and utility of our results.
Keywords :
Brownian motion; fractals; parameter estimation; spectral analysis; statistical analysis; wavelet transforms; accuracy; asymptotic expressions; bias; discrete-time data sequence; finite data record; finite-length data sequence; fractional Brownian motion process; network traffic analysis; numerical simulations; scaling structure; singularity structure; statistical analysis; turbulence; variance; wavelet-based multifractal spectrum estimation; Application software; Brownian motion; Fractals; Motion estimation; Signal analysis; Spectral analysis; Statistical analysis; Wavelet analysis; Wavelet coefficients; Wavelet domain;
Conference_Titel :
Signals, Systems & Computers, 1998. Conference Record of the Thirty-Second Asilomar Conference on
Conference_Location :
Pacific Grove, CA, USA
Print_ISBN :
0-7803-5148-7
DOI :
10.1109/ACSSC.1998.750873
