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Rectification of the bias in the wavelet power spectrum
Journal of Atmospheric and Oceanic Technology (2007)
  • Yonggang Liu, University of South Florida
  • X. San Liang
  • Robert H Weisberg

This paper addresses a bias problem in the estimate of wavelet power spectra for atmospheric and oceanic datasets. For a time series comprised of sine waves with the same amplitude at different frequencies the conventionally adopted wavelet method does not produce a spectrum with identical peaks, in contrast to a Fourier analysis. The wavelet power spectrum in this definition, that is, the transform coefficient squared (to within a constant factor), is equivalent to the integration of energy (in physical space) over the influence period (time scale) the series spans. Thus, a physically consistent definition of energy for the wavelet power spectrum should be the transform coefficient squared divided by the scale it associates. Such adjusted wavelet power spectrum results in a substantial improvement in the spectral estimate, allowing for a comparison of the spectral peaks across scales. The improvement is validated with an artificial time series and a real coastal sea level record. Also examined is the previous example of the wavelet analysis of the Niño-3 SST data.

  • wavelet,
  • power spectrum,
  • bias
Publication Date
Citation Information
Yonggang Liu, X. San Liang and Robert H Weisberg. "Rectification of the bias in the wavelet power spectrum" Journal of Atmospheric and Oceanic Technology Vol. 24 Iss. 12 (2007)
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