Difference between Shannon entropy and shannon entropy from wavelet packet?

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Beatriz Ruiz on 19 May 2019
Answered: John Navarro on 29 Nov 2021
I wanted to calculate the shannon entropy of a signal and I used the command
entropia_sha(1,i)=wentropy(ventana(i,:), 'shannon');
I thought this function used the following formula: but in the Matlab help the formula applied is: I don't understand where does this formula come from and what's the connection with the first one.
Thanks.
Bala Amala Kannan on 10 Jan 2020
You can find this formula in this literature:
https://www.spiedigitallibrary.org/journals/journal-of-biomedical-optics/volume-21/issue-9/096007/Retinal-image-quality-assessment-based-on-image-clarity-and-content/10.1117/1.JBO.21.9.096007.full?SSO=1.
In section 4.1: sharpness, this is the equation for Entropy_subband.
I don't know about the connection between these two equations.

John Navarro on 29 Nov 2021
I would guess it is because the first equation is evaluating the Shannon entropy of the signal as a series, while the second is evaluating the entropy of the energy of the signal (energy is the square value)