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I'm really a begginer at Wavelet transform and I'm starting to use the pywt module. I have some difficulties understanding the link between the following integral and the coefficients of the DWT:

$$ W(a) = \int_{- \infty}^{+ \infty}|T(a,b)|^2db $$ (where a is the scale, b the translation and T(a,b) is the wavelet transform of a certain signal)

Do I apply directly the integral on my coefficients ? If I do so (on approximated coefficients for exemple) the values at given levels of decomposition is huge compared to author's ones (<0.01 for each a)... And I'm supposed to find a spike for a certain scale but my curves are all monotones !

If someone would like to enlighten me.

Thanks in advance.

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It's because it was CWT not DWT ! The paper was old and didn't mention a single time continuous wavelet so I assumed (a bit fast I admit) that it was discrete...

The integration yields a spike as intended at a certain scale that is responsible for most of the energy of the signal. It is possible to find a caracteristic time/length from it by multiplying this scale by a wavelet dependent constant (that can be calculated analytically).

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