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I am analyzing some time series of sea surface water temperature and am using wavelet analysis to do so. I am computing the continuous wavelet transform and then removing some specific frequencies and then converting the series back from the frequency to the time domain. I am following the methods of torrence and compo 1998 (Practical guide to wavelet analysis) to perform this operation but am a bit confused as to why my results are not as expected. As an example, I will fist decompose the time series into the frequency domain and then reconstruct the signal without altering any of the coefficients:

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In the attached figure we have the original series in red and the reconstructed series in blue, straight away we can see that the the reconstructed signal is much lower than the original series. The main reason I think this occurs is that the wavelet transform normalizes the series to have unit energy (in order to compare the coefficients across scales). Therefore, I was wondering if it was possible to convert the reconstructed signal back to have the same magnitude (?) as the original series i.e. reverse the normalizing to have unit energy stage?

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up vote 4 down vote accepted

Take the mean of the original signal and add it to the reconstructed signal. IIRC wavelets have no DC response, and so the reconstructed signal will have 0 mean.

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