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sergiventosa / ts-PWS

Time-scale phase-weighted stack software for seismic signal denoising
GNU Lesser General Public License v3.0
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A question about ts-PSW #3

Closed xichaoqiang closed 3 months ago

xichaoqiang commented 3 months ago

Dear Sergi,

I found your ts-PWS work to be very intriguing. I have a question regarding the use of the

exp(2𝑗𝜋𝑓𝑡) term in the continuous wavelet transform (CWT). Is this term still necessary for ts-PWS?

I noticed that this term is used in the S-transform for tf-PWS.

Attached below is the figure generated by my code:

image

Best regards,

sergiventosa commented 3 months ago

Dear Xichaoqiang,

The exp(2𝑗𝜋𝑓𝑡) term you introduce in your (matlab) code would be necessary only if you want to implement the tf-PWS using the wavelet transform, by applying the relationship between the (Morlet) CWT and the ST. However, as I show in (Ventosa et al., 2017) and you can see in the C code, we can compute the phase coherence from the (pseudo-)analytic wavelet transform of the data sequence directly because this term is constant, i.e., independent of the data.

I hope this solves your doubt.

Best, Sergi

xichaoqiang commented 3 months ago

Dear Sergi,

Thank you for your detailed explanation. I now understand why the exp(2𝑗𝜋𝑓𝑡) term is unnecessary for computing the phase coherence using the (pseudo-)analytic wavelet transform. I have reviewed the referenced C code and Ventosa et al. (2017) as well, which have clarified the implementation further.

Your guidance has been very helpful in resolving my doubt.

Best regards, Xichaoqiang