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I am analyzing the spectral components of a time series using the continuous wavelet transform following Torrence and Compo (1998). I would like to partition the signal variability or spectral power across different scales (e.g. 50% of the variability is in the scales X to Y).

As pointed out here the global wavelet spectrum is a biased estimator of the power spectrum, so is there a way to plot the power spectrum in a normalized way, where I can compare the power at different frequencies?

Would it be correct to just reconstruct each scale range I am interested in and calculate the variance over time?

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I've used the Liu-Liang-Weisberg paper before, and it worked pretty well. There's some example code on this page.

In short, they propose that squaring wavelet coefficients and dividing them by their respective scales normalizes the spectrum. The paper provides proof and motivation.

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  • $\begingroup$ Thanks, this allows normalizing the power spectrum. Any contributions on variance partitioning from the Wavelet transform will be welcome. $\endgroup$ – tams Jun 5 '14 at 9:02

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