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A Practical Guide to Wavelet Analysis (1998)
| Citations: | 866 - 3 self |
BibTeX
@MISC{Torrence98apractical,
author = {Christopher Torrence and Gilbert P. Compo},
title = {A Practical Guide to Wavelet Analysis},
year = {1998}
}
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Abstract
A practical step-by-step guide to wavelet analysis is given, with examples taken from time series of the El Nio-- Southern Oscillation (ENSO). The guide includes a comparison to the windowed Fourier transform, the choice of an appropriate wavelet basis function, edge effects due to finite-length time series, and the relationship between wavelet scale and Fourier frequency. New statistical significance tests for wavelet power spectra are developed by deriving theoretical wavelet spectra for white and red noise processes and using these to establish significance levels and confidence intervals. It is shown that smoothing in time or scale can be used to increase the confidence of the wavelet spectrum. Empirical formulas are given for the effect of smoothing on significance levels and confidence intervals. Extensions to wavelet analysis such as filtering, the power Hovmller, cross-wavelet spectra, and coherence are described. The statistical significance tests are used to give a qu...
Keyphrases
wavelet analysis practical guide significance level confidence interval empirical formula wavelet power spectrum cross-wavelet spectrum edge effect red noise process power hovmller statistical significance test el nio southern oscillation wavelet spectrum finite-length time series new statistical significance test practical step-by-step guide theoretical wavelet spectrum time series fourier frequency wavelet scale fourier transform appropriate wavelet basis function
