Difference between Shannon entropy and shannon entropy from wavelet packet?

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.

[Jyotish Kumar]

Hi,

I didn't find any help documents with the formula you have mentioned. Can you provide the link of the MATLAB help which you have mentioned?

[Beatriz Ruiz]

This is the link:

https://es.mathworks.com/help/wavelet/ref/wentropy.html

[Bala Amala Kannan]

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.

Answer 1

[John Navarro]

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)