NDLI: A wavelet-based measurement of signal fractal dimensions

Content Provider	IEEE Xplore Digital Library
Author	Langi, A.Z.R. Nugraha, H.B.
Copyright Year	2002
Description	Author affiliation: Dept. of Electr. Eng., Bandung Inst. of Technol., Indonesia (Langi, A.Z.R.; Nugraha, H.B.)
Abstract	This paper describes a study of measuring signal fractal dimensions (especially in a form of Lipschitz exponents /spl gamma/) using wavelets. The procedure is as follows. Given a one-dimensional signal f(t) and its corresponding wavelet transform (at a scale a and a position b) as W/sub f/(a, b), we find wavelet maxima lines l(a, b) and their corresponding wavelet maxima \|W/sub f/(a, b)\|. Suppose the signal f(t) has a Lipschitz exponent /spl gamma/ at t=b/sub 0/, and there is a maxima line l(a,b) reaching b/sub 0/ as a/spl rarr/0. The corresponding wavelet maxima in the line satisfy an inequality \|W/sub f/(a, b)\|/spl les/Ca/sup /spl gamma/+0.5/ for some constant C and a/spl rarr/0. A log-log plot on the inequality estimates the Lipschitz exponent /spl gamma/. We have performed an experiment of the procedure for f(t)=1-\|0.5-t\|/sup /spl gamma//, where the Lipschitz component /spl gamma/ varies from 0.1 to 0.9 at a 0.1 interval. The procedure provides relatively good estimates for 0.5/spl les//spl gamma//spl les/0.9, with relative errors less them 10%.
Sponsorship	Dept. Electr. & Comput. Eng. Faculty of Graduate Studies Faculty of Eng. TRLabs Internet Innovation Centre NRC Inst. Biodiagnostics APEGM IEEE Winnipeg Sec. IEEE Canada & IEEE Manitoba Hydro Vansco Electron. Bristol Aerosp. Nygard Int. Norsat
Starting Page	1001
Ending Page	1004
File Size	281289
Page Count	4
File Format	PDF
ISBN	0780375149
ISSN	08407789
DOI	10.1109/CCECE.2002.1013080
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2002-05-12
Publisher Place	Canada
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Fractals Wavelet transforms Signal processing Laboratories Signal processing algorithms Digital signal processing Microwave integrated circuits Signal design Microelectronics Electric variables measurement
Content Type	Text
Resource Type	Article
Subject	Electrical and Electronic Engineering Hardware and Architecture

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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