NDLI: Wavelet spectrum and its characterization property for random processes

Content Provider	IEEE Xplore Digital Library
Author	Ta-Hsin Li Hee-Seok Oh
Copyright Year	1963
Abstract	The wavelet spectrum of a random process comprises the variances of the wavelet coefficients of the process computed within each scale. This paper investigates the possibility of using the wavelet spectrum, obtained from a continuous wavelet transform (CWT), to uniquely represent the second-order statistical properties of random processes-particularly, stationary processes and long-memory nonstationary processes. As is well known, the Fourier spectrum of a stationary process is mathematically equivalent to the autocovariance function (ACF) and thus uniquely determines the second-order statistics of the process. This characterization property is shown to be possessed also by the wavelet spectrum under very mild regularity conditions that are easily satisfied by many widely used wavelets. It is also shown that under suitable regularity conditions, the characterization property remains valid for processes with stationary increments including 1/f noise.
Sponsorship	IEEE Information Theory Society
Starting Page	2922
Ending Page	2937
Page Count	16
File Size	629741
File Format	PDF
ISSN	00189448
Volume Number	48
Issue Number	11
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2002-11-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Stochastic processes Spectral analysis Signal processing Wavelet transforms Statistics Random noise Digital filters Filtering
Content Type	Text
Resource Type	Article
Subject	Library and Information Sciences Information Systems Computer Science Applications

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